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November Issue
The Nucleus 2015
American School of Milan
BIOLOGY AND ENVIRONMENTAL SCIENCE
Climate Change Could Benefit Northern Lizards
By Andrea Russo
ABSTRACT— Since climate change has been one of the most recurring subjects in the past twenty years, and a
phenomenon causing numerous problems both to nature and ourselves, such a happening had to be taken into
consideration. This writing will examine the causes, the consequences, and some unexpected advantages of climate
change. Reading this article should be, and hopefully will be, an interesting as well as an instructive experience.
It’s happening fast!
activities. Activities causing release of Carbon dioxide
(CO2). This release has gotten so extreme in the recent
All of us know what it is, most of us don’t notice it,
years because of the interest we humans have in producing
but the point is that it’s real. Climate change is a
energy for our own benefit. And the most efficient method
phenomenon that has been worrying many scientists and
that produces energy is the burning of fossil fuels such as,
countries for many years. This is understandable due to the
coal, oil and natural gas. Method that, nevertheless,
fact that it causes life on earth to transform. Examples of
produces carbon dioxide as well. Therefore, the conclusion
these transformations are: season shifts, rise in
that many accept, and that is after all pretty accurate, is
temperatures, rise in sea levels, and so on. However,
that industrialization is what begun climate change.
although climate change might appear as a completely
negative occurrence, it has some benefits as well. But
before we get into the main argument of this article, we
must first understand what causes this contingency.
What are these benefits?
Although right now it may seem that climate
change only creates negative happenings, some aspects of
it actually help or create some sort of support to life on our
planet. To be more precise, some species in particular are
able to benefit from the phenomenon, specifically the
Northern sand lizards. These lizards are unlike most lizards
Why is it happening?
we know of. They are a bit larger, they develop very
Climate change occurs for both natural causes,
interesting patterns, and most importantly they are
therefore the earth’s cycles, and human causes. But in the ectothermic.
recent years what really intensified the event are human
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The Nucleus 2015
This means that they are unable to generate their own
body heat, and to compensate they normally bask in the
sun to heat up their body. Therefore it is pretty easy to
notice one advantage already from the information about
the reptile. As carbon dioxide causes climate change, and
therefore global warming, these lizards benefit from it by
taking advantage of the higher temperatures and heat their
bodies. According to UCAR (university corporation for
atmosphere research) the average temperature on our
planet has risen by almost 1 degree Celsius in the past 100
years. Although this doesn’t seem much it is an average
based on, ocean temperature, and temperatures all over
the planet. Thus, after all it’s a pretty strong change in
temperature, especially when taking into account that 12%
of the artic sea has melted.
American School of Milan
and physical behavior. In fact, the warming temperatures
would bring the body temperature of the specie to its
optimal hence enhance fitness. Additionally, has individuals
don’t need basking as a ‘daily’ activity for their health, the
time spent is usually used to ensure other priorities such
as food and shelter are fulfilled.
Last, but not least, one other great benefit this
phenomenon could bring regards egg laying, and the topic
of reproductive success. As a matter of fact, data shows
that female Northern lizards lay their eggs earlier during
the warmer years, which indicates the rapid adaptations
these reptiles are able to achieve. Also, as this occurred,
the overall population of the lizards could reach a positive
trend, and therefore increase in the years to come. This
would have a large (positive) effect on population survival.
Moving forward, other advantages due to climate
To conclude…
change vary based on the nature of the Northern lizard. For
example it has an enormous effect on their psychological
Occasionally, there are some, like the Northern
sand lizards, who are able to take advantage of the
situations they face, and benefit from them in numerous
ways. However the overall effect of global warming is
entirely negative, causing the destruction of huge parts of
our planet such as ecosystems and natural resources.
Therefore, since as mentioned earlier, this phenomenon
has began because of us, it’s in the best interest of life on
this planet that we solve it.
A Nap to Recap: How Rewards, Daytime Sleep Boost Learning
By Lucas Peralta
ABSTRACT—A new study suggests that receiving rewards as you learn can help cement new facts and skills in your
memory, particularly when combined with a daytime nap.
If you’ve ever stayed up late getting ready for a final, you’ve probably experienced feeling “foggy-brained”, that
strange sense of mental fatigue that puts some facts or information just out of reach.
A team of researchers from the University of Geneva may have come up with additional information to help
explain this phenomenon. Their experiment involved thirty-one adults who were randomly separated into two groups: a
“sleep” group and an “awake” group. While their brains were being scanned, the subjects were shown a series images
and were told that some image associations had a higher reward than others. This was done to help researchers
segregate memories by level of importance.
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November Issue
The Nucleus 2015
American School of Milan
Ms. Kinga Igloi, lead researcher from the University of Geneva explains “ that rewards may act as a kind of tag,
sealing information in the brain during learning. During sleep, that information is favorably consolidated over information
associated with a low reward and is transferred to areas of the brain associated with long-term memory."
After the learning session, the participants from the “sleep” group took a 90-minute nap while the members of the
“awake” group just took a quiet rest without sleeping.
Following this break, the subjects were tested on their ability to recall the pair of images and on their confidence level
regarding the accuracy of their recollections. Three months later, the participants were asked to take a surprise test
similar to the one they have taken after the rest period.
After analyzing the tests results, researchers were able to determine that, not surprisingly, both groups were
able to better recall highly rewarded pictures (important information), with the “sleep” group performing slightly better.
The important findings, however, were derived from the results of the surprise test taken three months later. In this
second instance, the participants who had slept performed unequivocally better and showed a significantly higher level of
confidence than the other group. The researchers also observed that the “sleep” group showed a higher level of activity
of the hippocampus, an area of the brain associated with the formation of memories.
While researchers already knew that sleep helps strengthen memories, this experiment has shown that during
sleep, the brain is able to identify important information and transfer it to an area associated with long-term memory.
“Our findings are relevant for understanding the devastating effects that lack of sleep can have on achievement,” says
Ms. Igloi.
So, next time you are preparing for an exam, try to sleep on it instead of pulling an all-nighter!
Earth Climate— The Yellow River in China
By Gabriele Calabria
ABSTRACT — By analyzing sediment deposits in the Yellow River, a swedish-chinese research group deduced Earth’s
surface appearance over millions of year ago and determined that the River’s drainage was caused by a change in the
monsoon more than 3 million years ago.
A common way to recreate and simulate how Earth’s surface’s
appearance, geological structure, and climate changed and developed
over millions of year, is to collect deposits of sediments from the
ocean’s floor. These deposits of eroded land are actually transported by
rivers, and when analyzed using special tools, yield lots of information
on the Earth’s surface. Even though this process works, there are still
many gaps and inconsistent data in the knowledge gathered by
researchers. Because of this, researchers have been gathering
samples in the world’s most sediment-rich river: The Yellow River in
China. The yellow river is in act known for its small water discharge, but
incredible sediment load. It amounts to about 11*10^8, contributing 17%
of the world’s fluvial sediment discharge to the ocean.
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November Issue
The Nucleus 2015
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Researchers from Uppsala and Lanzhou University analyzed the samples of the Yellow River and determined the
age of zircon present in the sediments. Zircon is a mineral which is very resistant to weathering. Zircon is very important,
as it yields big amounts of information about the sediment residues themselves and their sources. In fact, the
researchers came to the conclusion that the Yellow River’s sediment is wind-blown mineral dust that comes from the
Chinese Loess Plateau, which is the largest and most important past climate archives on land. The Chinese Loess
Plateau can also tell us about past atmospheric dust activity, which is a major factor in climate change.
However, these wind-blown minerals aren’t the main source of the sediments. In fact, the found that the Loess
Plateau acts as a sink for Yellow River material eroded from the uplifting Tibetan plateau. This explains the contradictory
findings in the area, as it demonstrates large scale sediment storage on land. Researchers have been able to conclude
that the Yellow River’s drainage was caused by a major change in the monsoon 3.6 million years ago.
The weathering of zircon also is part of a much bigger mechanism that may give us an answer regarding the
reduced levels of atmospheric carbon dioxide at the beginning of the Ice Age. The researchers’ next step will be to
compare terrestrial and marine records of erosion to gauge how far sediment storage on land has impacted the marine
record.
Dr. Jan-Pieter buylaert from the Danish Technical university stated that
these results are “radically new”. “[They have] solved a big research question,
by resolving one of the largest debates about where the sediment that makes
up these vast landscapes actually comes from,” says Buylaert. Institute for
Geosciences in the Aarhus University of Denmark professor Andrew Murray
also states that “probably the most important record of climate change that we
have for the Quaternary period--the last 2 million years or so--on dry land.”
Understanding how the plateau formed can give us information of the short
term climate changes that happen within the span of 100 years or the longer
term changes that happen over thousands or millions of years. Buylaert agrees,
stating that “Anything we can do to improve our understanding of how this
landscape formed is important and will help us understand global climate.”
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November Issue
The Nucleus 2015
American School of Milan
BIO AND ES: Crossword Puzzle
By: Giovanna Pinciroli
Acclimation
Aerobic
Atmosphere
Biodiversity
Carnivore
Concentration
Desertification
Ecosystem
Eukaryotic
Fungi
Globalization
Habitat
Hydropower
Macroevolution
Metabolism
Organic
Permeability
Pollution
Recycling
Reforestation
Salinity
Smog
Symbiosis
Toxicity
Wilderness
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November Issue
The Nucleus 2015
American School of Milan
CHEMISTRY
Element 118
By Leo Segre
ABSTRACT—The periodic table has been evolving due to the creation of new man-made elements. The latest addition
was Ununoctium in 2006. It was found by a team in Russia, composed by Russian and American scientists.
The periodic table today is made out of 118
elements. From the atomic number 95 to 118 the
elements are all synthetic, man-made. They are extremely
unstable and they decay rapidly into other elements. The
atoms of synthetic elements can only be made through
experiments that involve nuclear reactors or particle
accelerators. The first element to be considered synthetic
was curium, in 1944. To create it scientists bombarded
Plutonium with alpha particles. However, no element that
has an atomic number greater than 99, is only used in
scientific research. This is due to their extremely short
half-life.
The last man-made element created was element
118, Ununoctium. That is not its official name yet, it is
temporary and simply means one-one-eighth in Latin. On
the periodic table its symbol is Uuo. It is the element,
naturally occurring or man-made, that weighs the most
thanks to its 118 protons. On the periodic table it is found
right under radon in the 18th group.
Ununoctium’s production was made great
progress in 2006. A combination of Russian scientists,
from the Joint Institute of Nuclear Research, and American
researchers from the Lawrence Livermore Laboratory,
attempted to create the element in Dubna. However,
chemists had been discussing the creation of element 118
since the late 1990’s. A Polish scientists, Robert
Smolanczuk, published a research essay in 1998 stating
that element 118 could be created by fusing lead with
krypton. Later, in 1999, scientist from Lawrence Berkley
Laboratory, used this information and claimed to have
created ununoctium. Unfortunately, they retracted their
discovery since no other laboratory managed to replicate
their experiment.
This brings us back to Ubna, in 2006. The group
of scientists shot a beam of Calcium-48 particles into
Californium-249. This last element, is also another
synthetic element found on the periodic table with 98
protons. To finally create
element-118 it took the group of
researchers two whole months
during which 10 billion
bombardments of Calcium had
been conducted. Mark Stoyer, a
nuclear chemist who was part of
the research team, explained why it took so long. He said,
“Most of them just go right through the target and don't do
anything.” The only time an atom of Ununoctium was going
to generate was when a head-on collision with the right
energy occurred. In fact the team of researchers in Dubna,
say that in six months they managed to produce three
atoms of element 118. Furthermore, the team discovered
that Ununoctium had a half-life of 0.89 milliseconds and
was extremely radioactive. However, Dr. Stoyer, revealed
that the team had calculated that there was less than 1
chance in 100,000 that their discovery was wrong. By
finding element 118 scientist now feel closer to finding the
“island of stability”, of even heavier atoms and with longer
half-life’s.
As synthetic elements do, Ununoctium decayed
rapidly. It decayed into Livermorium (element 116), then into
Flerovium (element 114) and finally into Copernicium
(element 112). This last one divided in two parts.
As its position on the periodic table is in the 18th
group, it is expected to be a gas. It has also been
hypothesized that at room temperature it could be a solid.
However, not enough Ununoctium has been synthesized to
prove this.
In 2011, the International Union of Pure and Applied
Chemistry stated that they would not accept Ununoctium
as an established element. This was due to the lack of
evidence. The IUPAC stated that, “The three events
reported for the Z=118 isotope have very good internal
redundancy but with no anchor to known nuclei do not
satisfy the criteria for discovery.”
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November Issue
The Nucleus 2015
American School of Milan
How Does a Microwave Oven Work?
By Francesco Grechi
ABSTRACT— In this article the basic functionality of a microwave oven is explained, analyzing the chemistry underlying
its ability to heat up food.
With many seniors applying to college, it is only
appropriate that we address a key tool in their future
survival away from home, the Microwave Oven. Sure,
understanding the scientific explanation underlying this
fascinating technological development is not essential to
heating a ramen noodle cup to the perfect temperature.
However, it is still very interesting. So how does the
Microwave Oven work?
As the name might suggest, the Microwave Oven
works by generating microwaves. This is done by a
the oxygen will have a greater pull on the electrons in the
O-H bonds than the hydrogen will. Since the H2O molecule
is asymmetrical across the x-axis drawn in the figure, it will
have a slight negative charge on the oxygen end, and a
slight positive charge on the hydrogen end. This is known
as a dipole.
The oscillating electric field will cause the water
molecules present in food to move, orienting their positive
and negative ends (shown in the figure as and
respectively) to “match up” with those of the electric field.
component known as a “vacuum tube”, found in the back of
If you find this hard to visualize, consider the
the oven. Microwaves are part of the electromagnetic
following situation. Imagine putting a bar magnet between
spectrum, and have a frequency of oscillation of
two fixed magnets, with orientation shown in section 1 of the
approximately 2.4GHz. Translated into English, this means figure below. In this configuration, the bar magnet will feel a
that the orientation of the electric and magnetic fields
force pushing its poles to match up with the poles of the
generated by the vacuum tube changes 2.4 billion times
fixed magnets. It will therefore move to the configuration
per second. This creates a rapidly alternating electric field, shown in section 2 of the figure. Now imagine the poles of
which causes the water molecules in food to move.
the two fixed magnets are swapped. What would happen?
Well, the bar magnet would flip its orientation to line up
with the new poles. This is in essence what happens to the
water molecules when put in an alternating electric field.
To understand this, consider a water molecule
(H2O). In a water molecule, one central oxygen atom forms
two bonds with hydrogen atoms. The remaining four
electrons (left over because only four of the available eight
electrons are used in bond formation) are located on the
central oxygen atom. The electric repulsion between these
two lone pairs of electrons pushes the two hydrogen atoms
closer to each other, giving the molecule what is known as
a “bent” geometric shape. This is shown in the figure below.
The oxygen atom has a greater electronegativity
than the two hydrogen atoms combined. This means that
Due to molecular frictions, the induced motion by
the electric field causes the water molecules to dissipate
heat energy. This ends up increasing the temperature of
the food. Therefore, by creating a microwaves the
Microwave Oven is able to heat up food.
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November Issue
The Nucleus 2015
American School of Milan
Radioisotopes—Decay
By Ella Fadool
ABSTRACT— The article provides a brief explanation of the uses of radioisotopes in today’s world.
Over 100 years ago, in 1913, the radio chemist,
Frederick Soddy, suggested the existence of the “isotope”.
Through his studies, involving demonstrations and
experimentation of the element helium, Soddy was able to
formulate the concept of isotopes, stating “certain
elements exist in two or more forms which have different
atomic weights but which are indistinguishably chemically.”
Therefore the nucleus of the isotope’s atom, loses a
neutron to regain its stable conformation. Throughout the
process of the isotope creation through neutron donation,
radiation energy is given off. These unstable combinations
of neutrons and protons of specific elements that can occur
naturally or artificially are called radioisotopes. These
elements have excess nuclear energy that can either create
or emit specific radiation particles. During this process of
energy transmission, the radioisotope is said to undergo
radioactive decay. The energy that they emit in the form of
radiation can be categorized in three types of radioactivity:
alpha decay, beta decay, and gamma decay.
In alpha decay, the nucleus of a radioisotope emits
an alpha particle, a particle containing two protons and two
neutrons. For examples, the radioactive isotope, Americium
(Am), is used in the operation of smoke detectors. The
detectors contain an ionization chamber, holding a small
amount of the radioisotope, Americium-241. When the
alpha particles collide with air (oxygen and nitrogen),
through an open channel in the ionization chamber, the
molecules ionize, resulting in both positively and negatively
charged atoms. In contrast, if smoke were to enter through
the channels, the collision of alpha particles and smoke will
not result in ionization. The electric current will recognize
this, thus triggering the smoke alarm. A benefit of using
Americium-241 in smoke detectors is its half-life of 432
years. Half life refers to the amount of time needed for an
isotope to lose half its radioactivity. The half life of
Americium-241 ensures a long lasting source of reliable,
continuous alpha particles.
Another
example of decay is
beta decay, a decay
that is used in
quality control to
test the thickness of
a certain material,
such as paper. Beta
decay is caused
when too many
neutrons are present in the nucleus, therefore the element
will emit radiation in the form of negatively charged
particles. When used in thickness detectors, beta radiation
passes through a certain material. The thicker the
material, the more radiation is absorbed, and the less
radiation is able to pass through the material. Finally, it
signals to the equipment to adjust the thickness of the
material being produced.
The final type of decay is gamma decay. Gamma
decay is known as a type of radioactivity in which, through
emission of electromagnetic radiation (or photons), a
nucleus transfers from a higher energy state to a lower
energy state. An example of the use of gamma decay is in
the sterilization of food. Waves of radiation pass through
the food type, interacting with harmful substances. For
example, in the sterilization of food, radiation will react to
and kill dangerous bacteria and other organisms present.
However, these radiation waves will not cause the food to
become radioactive, as they are not interacting with the
nuclei of the atoms of the food directly, although, it is
possible that the radiation change the color, flavor or
texture of the food. As a result of this process, food is able
to maintain a longer shelf life.
In conclusion, the discovery of the isotope by
Frederick Soddy in 1913, has sparked/introduced a
wave/range of beneficial uses and applications, advancing
medicine, technology, and industries.
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November Issue
The Nucleus 2015
American School of Milan
CHEMISTRY: Crossword Puzzle
By: Giovanna Pinciroli
HORIZONTAL
VERTICAL
2) It is a sugar and a product of Photosynthesis.
5) When this acid is a product of a reaction, it automatically
decomposes into water and carbon dioxide.
7) This element has been discussed in this newspaper edition.
9) The quantum number used to describe the main energy level
in which an electron is found.
11) The color of the flame produced when burning sodium.
12) Without him chemistry would be an enigma.
13) Discovered by Thomson, this subatomic particle has a
negative charge and an extremely small mass.
14) This series represents the visible section of the Hydrogen
Spectrum.
1) During chemical reactions, this type of molecule
tends to accept an electron pair.
3) Sr.
4) He coined the term orbital.
6) These metals are found in the first group of the
Periodic Table.
8) He first arranged the elements in order of mass.
9) This scale is used to determine whether a
solution is acidic, basic, or neutral.
10) Multiple trials and measurements will reduce
this type of error.
10
Carbonic
5.
Schrodinger
4.
Strontium
3.
Glucose
2.
Acid
1.
10.
9.
8.
7.
6.
Random
PH
Mendeleev
Ununoctium
Alkali
14.
13.
12.
11.
Balmer
Electron
Mr Capello
Yellow
November Issue
The Nucleus 2015
American School of Milan
MATHEMATICS
Trigonometry—History and Applications
By Ted Yoon
ABSTRACT— Trigonometry is the branch of mathematics that deals with the relations between the sides and angles of
plane or spherical triangles, and the calculations based on them. This article provides partial awareness of the use of
trigonometry and what it is. Everywhere you go and see, this article might remind you of trigonometry.
Sine, Cosine, and Tangent are the values that comes
into mind when someone mentions the word “trigonometry”.
No matter what position you’re standing at and what you’re
seeing, in fact, an average mathematician would think about
the trigonometry of every single thing they see! But to be
spot on, what is trigonometry?
According to Dictionary.com, trigonometry is the
branch of mathematics that deals with the relations between
the sides and angles of plane or spherical triangles, and the
calculations based on them. To make it more simple and
comprehensive, the prefix of the word “tri-” means “three”
while the suffix “-onometry” means the study of measuring
by numbers. To be even more simplistic for the ones who
still can’t memorize the word “trigonometry”, most
mathematicians call it “trig” for short.
So who made Trigonometry? It was created by a
Greek astronomer and mathematician, Hipparchus and his
work was later expanded by Ptolemy and many more ancient
mathematicians. As time elapsed, the names and
significances of those mathematicians has been forgotten
and lost, according to research. Hipparchus developed a
table set of trigonometry, which was useful for his research
on astronomy. When Ptolemy came along, he sought that
Hipparchus’s work was incomplete and he further expanded
it, which made more sense.
Trigonometry is sometimes difficult to understand,
so people on the internet posted jokes or “memes” to
provide students to apprehend trigonometry faster in a
hilarious way, such as this one:
Also, an unknown mathematician provided students
a “secret message” to know the trigonometry very well which
is “SOHCAHTOA”. The initials are Sine. Opposite.
Hypotenuse. Cosine. Adjacent. Hypotenuse. Tangent.
Opposite. Adjacent. Which is further defined as: Sine =
Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse,
Tangent = Opposite/Adjacent. See the pattern? To make
mathematicians and students remember trigonometry, they
specially created a funny initial message.
But what do we use it for? Originally it was used for
astronomy, and later on it is used to measure the height of
an object such as the Eiffel Tower. Many of you would think,
“Why not use a ruler or search it on the web?” Yes it would
be quick and sufficient to surf on the web to find it, but what
if you were at a time when the Eiffel Tower was finished
constructing? Architects need to define the height of the
Eiffel Tower and it would be a waste of time if they used a
meter tape to find out what the height is. Instead, they use
calculations such as using trigonometry to find the height. If
you stand at a position and measure the distance away from
the tower and measure the angle of looking towards the tip
of the Eiffel Tower, and a calculator in hand, you are ready to
go. The undefined height is the “opposite” and the ground
level distance from the tower to the position you’re standing
is defined as “adjacent” and you have an measured angle. In
this situation, you can use Tangent = Opposite/Adjacent.
Since we need to find Opposite, multiply adjacent both sides
and you get: tangent * adjacent = opposite. Click on tangent
and then the measured angle, then multiply by the distance
from where you’re standing to the Eiffel Tower. Then you’ll
get the height of the Eiffel Tower! It seems a bit complicated
but it’s less time consuming than using a measure tape to
measure the height of the Eiffel Tower.
If you dream of being an architect, oceanologist,
sailor, or a genius, trigonometry would be the best
mathematical branch for you to be aware of distance, height,
angle, and most of all coordination.
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November Issue
The Nucleus 2015
American School of Milan
The Wonders of Pascal’s Triangle
By Lisa Saebin Kwon
ABSTRACT—Pascal’s triangle exhibits numerous complex patterns and applications that are core to mathematics.
Beauty, Symmetry, and Pascal’s triangle. The infinite triangular arrangement of numbers is one of the most
fundamental number patters in mathematics. The Pascal’s triangle is named after the French mathematician, physicist,
and philosopher Blaise Pascal. Although his name is accredited, Pascal was not the first to discover the properties of
this array of numbers.
To begin with, an Indian mathematician from 450 BC, Pingala referred to the triangular arrangement as Meru –
prastaara, the “staircase of Mount Meru”. The references also started in China in the 10th century when Jia Xian first
devised a triangular representation for coefficients. Another Chinese Mathematician, Yang Hui from the 13th century,
studied his ideas more in depth. Therefore, Pascal’s triangle is also caused Yang Hui’s triangle in China. Futrthemore, an
Italian mathematician living just a century before Pascal, Niccolo Fontana Tartaglia also devised a method to obtain
binomial coefficients, which is known as Tartaglia’s triangle.
One interesting feature of the triangle is that it is symmetrical. Therefore, the numbers on the left hand side and
those on the right hand side are identical to each other.
Pascal’s triangle is most commonly used in the binomial theorem so that expressions with two terms such as (x
+ y) to number of powers can be determined easily. However, there are also many other patterns in the triangle. One of
which is the magic 11’s. Each row of the triangle represents the numbers in the powers of 11 - starting from 11 to the
power of 0, which is 1. The numbers in row 4 are 1, 4, 6, 4, and 1, equal to 11 to the power of 4, 14,641.
One other noticeable pattern is the Fibonacci sequence inside Pascal’s triangle. The sum of the diagonals, 1, 1, 2,
3, 5, 8, 13, and so on, represent the Fibonacci numbers where the next number of the sequence can be found by adding
the two previous ones.
Furthermore, triangular numbers can be found inside Pascal’s triangle. Triangular numbers are those that can
be represented in the form of triangular grids of points where the first row contains a single element and the subsequent
contains one more than the previous. Starting from the first slot of the second row going diagonally, the pattern 1, 3, 6,
10, 15, 21, and so forth represent the triangular numbers.
Then what are some applications of Pascal’s triangle that we can use? One prominent example is the binomial
theorem. When expanding a binomial equation, the coefficients for each term can be easily traced from Pascal’s triangle.
For example, if we want to expand (2x +1)3, we would look at the 3rd row, which is 1, 3, 3, and 1. These numbers represent
the coefficients for each term of the equation in order. Therefore, our example will be expanded as 1(2x) 3 + 3(2x)2(1)1 +
3(2x)1(1)2 + (1)3. This stands true for all (x + y)n equations.
Another useful application is dealing with probabilities
of any combinations. If we toss a coin three times, there is one
possibility that will give us three heads (HHH). There are
three that will give us two heads and one tail (HHT, HTH, and
THH). Also, there are three that give us one head and two
tails (HTT, THT, and TTH). Finally, there is only one possibility
for which we would get all tails (TTT). This pattern of 1, 3, 3,
and 1 is illustrated on the 3rd row of the Pascal’s triangle.
Once we become familiar with the numbers of the
triangle, we are able to apply it in numerous different ways.
Once we discover the patterns ourselves, it can become a
useful and fascinating tool for us that have beauty, symmetry,
and practicality.
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November Issue
The Nucleus 2015
American School of Milan
Math as Music
By Francesco Maiocchi
ABSTRACT— This article explores the relationship between math and music. Math and music are a perfect link that is
still alive today. Without this connection we would not be able to understand the art of music and like so, the variety of it
present today, would not exist.
The initial forms of music (Prehistoric music) were
percussion-based, the use of rocks and sticks permitted
people to create sounds. Although this art had not yet
established a particular notation, it was commonly used by
African and Asian tribes in religious ceremonies to
represent animals. Consequently, Egyptians (4000 BCE)
formed new instruments that emitted different sounds to
provoke different moods. Furthermore, the guitar was
created by the Hittites (an ancient Anatolian tribe): the
invention of cords and their vibrations allowed music to
progress greatly. Although, having many creations in the
Prehistoric period, the real influential advancement comes
in Greece (around 600 BCE) with Pythagoras and his
octave scale.
Pythagoras was born in Greece in 570 BCE and
died in 495 BCE. Many of us know him for his famous
theorem (hyp2 = c12+ c22) but, his ideas deeply influenced
Western philosophy and was also the founder of
Pythagoreanism – his movement studying mathematics,
music and astronomy. As I mentioned previously, he
created the octave scale: a key step in the development of
math in music. In music an octave is defined as the pause
between different pitches with half or double its frequency.
This scale permitted musicians, for the first time, to read
music: consequently, musicians could understand music,
therefore developing different kinds that are still alive
today.
The most important, or used, scale is the diatonic
one. The diatonic scale is composed of 7 pitches: F, C, G, D,
A, E, B. It is considered as the “natural scale” meaning that
every piano has these notes. Also this scale is used to tune
instruments only with the perception of your ear: obviously
not as perfect as a piano would tune it. There are many
different “modes” of the diatonic scale, meaning that there
interval sequence differs in tones and semitone (half a
tone). The “Pythagorean scale” is a scale that is obtained
by only having a sequence of perfect fifths: for example, the
diatonic scale.
To help you understand better how music
incorporates mathematics here is a real life example:
Almost once a week you hear an ambulance passing by
your street. As the ambulance gets closer the sound grows
higher and higher but when the ambulance goes away, the
sound becomes lower and lower. But have you ever asked
yourself why? This is because when the ambulance is
nearest to you it breaks the so called “air pockets”
therefore making a higher sound but when it goes away,
you're closer “air pockets” have already been broken
therefore the sound is always lower.
Galileo sustains the nature is a book written in
mathematical symbols: but is it only nature? I believe that
mathematics and music are a perfect link. Pythagoras is a
key player in mathematics, and further developed his
analysis when linking it to such a beautiful art. Greece is a
center of beautiful culture and I am not surprised that
much of Greece’s ideals are still alive today, for example,
democracy. Today in Italy we have a republic which is
slightly different but the basic ideals come from ancient
Greece. Usually I discover that musicians are always good
at math, and, in fact, it is not a coincidence that I play the
drums. In the past few years I developed an analytic
understanding of music that has really helped me achieve
my goals and give amazing performances.
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MATH: Sudoku
By: Giovanna Pinciroli
Solutions:
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PHYSICS
Do Stars Move?
By Giovanna Pinciroli
Abstract: This articles provides a brief explanation of the composition of stars, and then describes its intricate motion.
Have you ever laid down at night, and looked at the multitude of stars that illuminate the sky? If you have, your
feeling certainly was one of admiration, almost one of awe. When laying down, in fact, stars appear fixed, luminous points,
that make up a little fraction of the universe.
Even more interesting that the composition of stars is their motion. Looking at the sky, we stars appear to be
rising and setting, as do the Sun, the Moon, and the planets. When using more accurate instruments, we witness some
stars moving back and forth. So what are the factors causing the motion of stars, and the way we perceive such motion?
After painstaking research, scientists have concluded that stars’ movements are a consequence of both the
Earth’s rotation and movement through its orbit, and of their proper motion through space.
It takes about 24 hours for the Earth to spin on its axis. If you happen to be watching the sky during this time,
you will witness stars rising in the eastern side, and then setting in the western one, just like the sun and the Moon
would do. This general rule, however, is not applicable to all situations. In fact, if you are located close to the north or to
the south pole, Earth’s axis of rotation, you will notice that the great majority of stars rotates 360 degrees around the
pole, instead of rising and setting.
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The Earth’s orbit around the Sun also influences the way we see stars moving. It takes about 365 days - a year
- for the Earth to revolve around the Sun. To understand how our perspective changes during the year, try to imagine
you are running around a soccer field, and you see some buildings in the distance. As you move around the field, the
buildings will appear to shift position, even though they really have not moved from their original spot. The same thing
happens with the Earth - the runner - and the stars - the buildings. As a matter of fact, at the opposite ends of our orbit
- in summer and in winter - stars appear to shift in opposite directions with respect to the background. This occurrence
is called effect parallax, and it is applicable to stars that are as far away as 100 light-years.
The last factor which affects the way we see stars is their own motion through space, called proper motion. This
is dependent on gravity, seen that it is gravity that makes stars revolve around the center of their galaxy. Having said
this, this movement usually is irrelevant to our eyes, because the distance separating the Earth from the stars is
infinitely greater than the average distance travelled by the stars.
Despite their ignorance about the numerous types of motion
undergone by stars, sailors centuries ago were able to effectively
orient themselves thanks to the presence of stars. In fact, by simply
observing the sky as a child would, they identified the stars that were
located in the same position every 24 hours - which we learnt to be the
ones not affected by the Earth’s movement around its orbit - and used
those as reference points.
Is it possible to make a perfect clock?
By Eleonora Pigoli
ABSTRACT—“It all started in 1976 when Canadian physicist William Unruh postulated that the number of particles
visible in a quantum field depends on the acceleration of the observer. Recent discoveries that this theory is true have
brought about discussions of all that regards relativity.”
How many times have you had disagreement with
friends because of time? Your watch says it’s three thirty,
theirs says it’s three thirty. One says you’re late and one
says you are not. This brings up quite an interesting
question. Can we really measure time perfectly? Will we
ever what the ‘proper time’ is with accuracy? The answer
would appear to be no.
It all started in 1976 when Canadian physicist
William Unruh postulated that the number of particles
visible in a quantum field depends on the acceleration of
the observer. Many, like I did, might wonder what on earth
this is supposed to mean. To understand it is important to
realize how time is measured at the most basic level. It all
has to do with particles, specifically muons. These are
elementary particles similar to electrons but much, much
bigger (they are 200 times more massive). Muons tend to
decay into an electron, a muon electron and an
antineutrino. In order to measure time, the rate of decay of
muons is measured. Now, while that might not seem to be
what is going on inside your wristwatch, this is the principle
used to measure time. What is so fascinating about
Unruh’s theory is that because particle visible in a quantum
field change based on the observer’s acceleration, so does
the rate of decay of muons. Because of how we measure
time on a molecular level, this also means that time
changes based on the acceleration of the observer.
Sadly, Unruh never got to prove his theory. All of this was
left at a hypothetical level until now. Physicists from the
university of Nottingham and from the university of Warsaw
teamed up to prove this revolutionary concept. In optimal
laboratory conditions, they analyzed muons to moving along
a straight line. They found that these elementary particles
decay as a result of their interactions with other quantum
fields. According to their calculations, were these muons to
be closed in a vacuum they would not decay. This brings us
back to the concept of quantum fields
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being relative to the observer. If a muon is in a vacuum, so
in a condition similar to that experienced by an observer
with little acceleration, it won’t decay or it will take very
long to do so. If instead, the same muons experiences
interactions between many quantum fields, a condition
viewed by an observer with great acceleration, it will decay
incredibly fast. This brought the Polish-British physicists to
the conclusion that, in a system with great accelerations, it
is impossible to know what the ‘proper time’ is.
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Unruh’s theory goes back to Einstein’s concept of spacetime relativity. Both theories of relativity, special and
general, are based on the assumption that there is a
quantifiable and accurate ‘proper time’. If this is not true
for systems with large accelerations, as the William Unruh
predicted, is the rest of Einstein’s theory still valid? Can we
still speak of relativity of time depending on the observer’s
velocity, if there is no ‘proper time’? This, as well as many
other questions, is what physicist will have to answer now
that the Unruh principle has been proven to be true.
The Solar Neutrino Problem Solved:
a look inside the 2015 Nobel Prize in Physics Winners
By Federica Arcidiaco
ABSTRACT—A brief explanation of the chameleon-like nature of the subatomic particles that won Arthur McDonald and
Takaaki Kajita this year’s Nobel Prize in Physics and how this affects the future of Physics.
The classification and nuclear interactions of all
subatomic particles can be found within the 1970s theory
named the Standard Model. This theory can be considered
to be the basis in order to build more complex and
elaborate models to explain results that differ from what is
stated in the Standard Model. This model can sometimes
be regarded as a theory that encompasses pretty much all
of the experimental predictions concerning the
fundamental particles and how they interact with one
another and it has mainly been successful. However, it also
leaves some physical phenomena unexplained or makes
assumptions which can be proven to be incorrect. In the
early 2000s, a discovery was made by two groups of
scientists on opposite sides of the globe that disproves one
of the most puzzling assumptions made in the Standard
Model. This year, because of their findings concerning
neutrino oscillations, the directors of these two
experiments, Canadian astrophysicist Arthur McDonald
and Japanese physicist Takaaki Kajita, have finally been
chosen to receive one of the greatest honors for a research
scientist: the Nobel Prize.
To fully comprehend why this discovery is so crucial for
the future of physics, it is important to identify what
neutrinos actually are. Neutrinos are subatomic particles
that travel through space and have a neutral electric
charge. These particles are extremely small that their mass
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was long assumed to be negligible or even non existent.
Thousands pass through are bodies every second with very
few actually interacting with our atoms because of their
inferior size. Even though they are extremely small, they are
the second most numerous particle in the universe, second
only to photons (light particles).
Experiments and calculations regarding neutrinos have
been attempted since the 1960s. However, all ended with
the same incorrect conclusion. When calculating the
theoretical amount of neutrinos emitted by the Sun and
gathering data on Earth, the results did not add up.
Approximately two thirds of the neutrinos were always
missing between the time they were emitted by the Sun to
when they reached our planet. Because of their small mass,
scientists assumed that neutrinos disappeared into space,
but scientists McDonald and Kajita proved that this was not
the case.
There are three types of neutrinos in the universe: the
electron, muon and tau neutrinos. The Sun, however, only
produces electron-neutrinos. Therefore, a plausible
solution to what became known as the “Solar Neutrino
Problem” would be that the neutrinos transform into either
muon-neutrinos or tau-neutrinos on their way to Earth
which would explain the deficit of the measured electronneutrinos. This is exactly what scientists Arthur McDonald
and Takaaki Kajita were able to prove throughout their
experiments and why they are the recipients of this year’s
Nobel Prize in Physics.
Takaaki Kajita is a Japanese physicist who has
devoted his whole career as a research scientist to
expanding our knowledge on neutrinos. He directed the
Super - Kamiokande experiment which became operational
in 1996 in a zinc mine, 250km outside of Tokyo. The
Super-Kamiokande consists of a giant detector that was
built 1,000 km under the Earth’s surface. A tank containing
50,000 tones of pure water with more than 11,000 light
detectors on the sides was built to identify the neutrinos
passing through the container. While most of the subatomic
particles would simply pass through the tank, sometimes
they would collide with an atomic nucleus in the water
molecules creating charged particles, depending on the
type of neutrino and what is known as Cherenkov light,
which arises when a particle travels faster than the speed
of light. The shape and size of the light is analyzed to reveal
what type of neutrino collided and where it originated from.
An important discovery that was made was the fact that
there were more muon-neutrinos coming from the Earth’s
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atmosphere than from the crust, hinting that the particles
that had passed through the planet had had more time to
undergo the transformation into tau-neutrinos that could
not be detected by the Super-Kamiokande.
Canadian astrophysicist Arthur B. McDonald, directed
the second experiment, the Sudbury Neutrino Observatory,
which became operational in 1999 and helped to complete
the puzzle started by the Super - Kamiokande and solve
the enigma that had become the Solar Neutrino Problem.
The setup to the experiment was very similar to that of the
Super-Kamiokande. It consisted of a tank filled with 1,000
tones of heavy water (with deuteriums rather than normal
hydrogen atoms), located 2km under the Earth’s surface,
and lined with 9,500 light detectors. This experiment,
however, could also calculate tau-neutrinos and therefore
proved that the sum of all the types of neutrinos was equal
to that which had been theoretically predicted 30 years
earlier.
Therefore, these findings proved that neutrinos undergo
a metamorphosis of sorts as they travel through space and,
in order to be able to achieve these transformations,
neutrinos must have a mass. This ground-breaking
discovery reveals the first apparent discrepancy in the
Standard Model which requires these subatomic particles
to be massless in order to work, and therefore
revolutionizes the world of quantum physics entirely.
Furthermore, these experiments have opened up the rather
hidden and mysterious world of neutrinos which could
change our entire understanding of the history, structure,
and even the future of our universe.
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PHYSICS: Crossword Puzzle
By: Giovanna Pinciroli
HORIZONTAL
VERTICAL
1) This scientist first stated that, within elastic limit, stress is
directly proportional to strain.
3) The degree to which the result of a measurement, calculation,
or specification conforms to the correct value or a standard.
6) Prefix for 10^(-15).
8) The type of energy possessed by a body due to its motion.
9) The physical quantity which is described completely by its
magnitude.
13) The ratio of the size of the image to the size of the object.
14) Force times displacement in the direction of the force.
15) The change in momentum.
2) The type of potential energy which is stored as a result of the
deformation of an elastic object, such as stretching a spring.
4) The transfer of heat by the actual transfer of matter.
5) The S.I. unit for power.
7) The type of expansion occurring when the size of an object is
increased due to the presence of heat.
10) The rate of change in velocity with respect to time.
11) A vector quantity which represents the shortest distance
between the initial and the final position of a moving body.
12) The property of a body to resist a change in its state of rest or
of uniform motion.
19
Watt
5.
Convection
4.
Accuracy
3.
Elastic
2.
Hooke
1.
10.
9.
8.
7.
6.
Acceleration
Scalar
Kinetic
Thermal
Femto
15.
14.
13.
12.
11.
Impulse
Work
Magnification
Inertia
Displacement
STAFF AND CREDITS
CREATORS:
Director and Editor—Giovanna Pinciroli
Layout and Design — Gabriele Calabria
Editor—Francesco Maiocchi
DIRECTORS OF DEPARTMENT:
Biology and Environmental Science—Scintilla Benevolo
Chemistry—Leo Segre
Math—Edoardo Rundeddu
Physics—Federica Arcidiaco
ARTICLES BY:
Andrea Russo
Lucas Peralta
Gabriele Calabria
Leo Segre
Francesco Grechi
Ella Fadool
Ted Yoon
Lisa Kwon
Francesco Maiocchi
Giovanna Pinciroli
Eleonora Pigoli
Federica Arcidiaco
SPECIAL THANKS:
Mr. Bonifacio—Supervisor
Ms. Rizzuto—CAS Coordinator
Mr. Amodio— Publishing
Francesco Grechi—Former Director
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