Document
... (roughly 'the broad') derived either from the width of his shoulders, the results of training for wrestling, or from the size of his forehead. Although Plato made no important mathematical discoveries himself, his belief that mathematics provides the finest training for the mind was extremely import ...
... (roughly 'the broad') derived either from the width of his shoulders, the results of training for wrestling, or from the size of his forehead. Although Plato made no important mathematical discoveries himself, his belief that mathematics provides the finest training for the mind was extremely import ...
document
... Chant)-monophonic line remains Theory practices were written and passed on from Ptolemy (2nd Century)Boethius (c.480-524) in to the Middle Ages ...
... Chant)-monophonic line remains Theory practices were written and passed on from Ptolemy (2nd Century)Boethius (c.480-524) in to the Middle Ages ...
PHYSICAL THEORY OF MUSIC
... Furthermore, we thought that we could elaborate more on what would happen if we separated the octave in 10 «equal» parts instead of 12.In that case, the frequencies ratio of the two sequential sounds would be the tenth root of 2. We did that because we noticed that the ratio of the first and the sev ...
... Furthermore, we thought that we could elaborate more on what would happen if we separated the octave in 10 «equal» parts instead of 12.In that case, the frequencies ratio of the two sequential sounds would be the tenth root of 2. We did that because we noticed that the ratio of the first and the sev ...
I1 Pythagoras` Theorem and Introduction Trigonometric Ratios
... Very little is known of the life of Pythagoras, but he was born on the island of Samos and is credited with the founding of a community at Crotona in Southern Italy by about 530 BC. The community had religious and political purposes, but also dealt with mathematics, especially the properties of whol ...
... Very little is known of the life of Pythagoras, but he was born on the island of Samos and is credited with the founding of a community at Crotona in Southern Italy by about 530 BC. The community had religious and political purposes, but also dealt with mathematics, especially the properties of whol ...
Year 9 Curriculum Overview Spring Half Term 2
... derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs ...
... derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs ...
Year-9-Curriculum-Overview-Spring-Half-Term-2
... derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs ...
... derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs ...
Pythagoras and His Vibrating Strings
... up to it every morning when your alarm clock goes off. You may never take headphones out of your ears and get more than your moneys worth out of your iPod. Most couples have “their song”, and music is played at weddings, church services, funerals, restaurants, elevators, shopping malls, and is set t ...
... up to it every morning when your alarm clock goes off. You may never take headphones out of your ears and get more than your moneys worth out of your iPod. Most couples have “their song”, and music is played at weddings, church services, funerals, restaurants, elevators, shopping malls, and is set t ...
Ancient Music
... started in Iraq. By the time this harp was first made almost 5000 years ago, Iraq had already enjoyed more than 2000 years of history. ...
... started in Iraq. By the time this harp was first made almost 5000 years ago, Iraq had already enjoyed more than 2000 years of history. ...
Pythagorean triples from fractions
... 2. Find the sum of their reciprocals, simplifying fractions where appropriate. 3. The numerator and the denominator give the first two numbers in your Pythagorean triple. Substitute these numbers into Pythagoras’ Theorem to find the third number. E.g. ...
... 2. Find the sum of their reciprocals, simplifying fractions where appropriate. 3. The numerator and the denominator give the first two numbers in your Pythagorean triple. Substitute these numbers into Pythagoras’ Theorem to find the third number. E.g. ...
Lecture 4. Pythagoras` Theorem and the Pythagoreans
... beautiful and harmonious and postulated that some scientific law may have caused this to happen. He went to the blacksmiths and took a look at their tools. He discovered that it was because the anvils were “simple ratios of each other, one was half the size of the first, another was 2/3 the size, an ...
... beautiful and harmonious and postulated that some scientific law may have caused this to happen. He went to the blacksmiths and took a look at their tools. He discovered that it was because the anvils were “simple ratios of each other, one was half the size of the first, another was 2/3 the size, an ...
Bringing some science to music
... Each tone is separated by a “semitione” Also “half tone” or “half step”. ...
... Each tone is separated by a “semitione” Also “half tone” or “half step”. ...
Chapter 3: The Beginnings of Greek Mathematics Greeks were not
... Chapter 3: The Beginnings of Greek Mathematics Greeks were not confined to a neighborhood or the Aegean and the Peloponnesis. They ranged far and wide including present day Italy and Sicily and many lived in North Africa including Egypt. This is of course before the expansion of the Roman Empire (Pu ...
... Chapter 3: The Beginnings of Greek Mathematics Greeks were not confined to a neighborhood or the Aegean and the Peloponnesis. They ranged far and wide including present day Italy and Sicily and many lived in North Africa including Egypt. This is of course before the expansion of the Roman Empire (Pu ...
2 Chants Ancient Roo.. - Paul Ayick Vintage Brass
... In order to fully understand the origins of plainsong or chant, actually all of Western music, one must go back to the ancient Greeks. In approximately 500 B.C. Pythagoras, perhaps history’s first music theorist and other ancient Greek scientists developed the system of scales (modes) and division o ...
... In order to fully understand the origins of plainsong or chant, actually all of Western music, one must go back to the ancient Greeks. In approximately 500 B.C. Pythagoras, perhaps history’s first music theorist and other ancient Greek scientists developed the system of scales (modes) and division o ...
Slide 1
... did not seem to write down any of his teachings. Members of his community were bound not to disclose to outsiders anything taught by Pythagoras or discovered by others in the brotherhood.[2 pp 86-88] At the age of 60 he married one of his students a women named Theno who was in her late teens or ear ...
... did not seem to write down any of his teachings. Members of his community were bound not to disclose to outsiders anything taught by Pythagoras or discovered by others in the brotherhood.[2 pp 86-88] At the age of 60 he married one of his students a women named Theno who was in her late teens or ear ...
shape 2 (H F) - School
... Talk me through how you went about drawing and labelling this triangle for this problem. How can you use Pythagoras’ theorem to tell whether an angle in a triangle is equal to, greater than or less than 90 degrees? ...
... Talk me through how you went about drawing and labelling this triangle for this problem. How can you use Pythagoras’ theorem to tell whether an angle in a triangle is equal to, greater than or less than 90 degrees? ...
Lecture 06 Part II a little more history of science
... • They are dissonant if they do not. • BUT whether or not a harmony is pleasing is a matter of personal taste, as there are consonant and dissonant harmonies, both of which are pleasing to the ears of some and not others. • Pythagoras did not subscribe to the last statement. • Pythagoras tried to de ...
... • They are dissonant if they do not. • BUT whether or not a harmony is pleasing is a matter of personal taste, as there are consonant and dissonant harmonies, both of which are pleasing to the ears of some and not others. • Pythagoras did not subscribe to the last statement. • Pythagoras tried to de ...
Pythagoras and His Theorem Historical Context: Suggested
... Students unfortunately remember only the phrase “a2 + b2 = c2” and do not “see” any of the geometry involved (e.g. a relationship between areas). Yet, the Pythagorean Theorem encompasses many other interesting aspects and connections. Though known and used prior to Pythagoras’ time, the Theorem is c ...
... Students unfortunately remember only the phrase “a2 + b2 = c2” and do not “see” any of the geometry involved (e.g. a relationship between areas). Yet, the Pythagorean Theorem encompasses many other interesting aspects and connections. Though known and used prior to Pythagoras’ time, the Theorem is c ...
Pythagoras` Theorem c =a +b - Strive for Excellence Tutoring
... Example 3: How to create a Pythagorean Triad Step 1: Choose any odd number for your “s” value and then square it. We will choose “72 = 49” for this example. Step 2: Find 2 consecutive numbers that add up to the squared value in step 1. ...
... Example 3: How to create a Pythagorean Triad Step 1: Choose any odd number for your “s” value and then square it. We will choose “72 = 49” for this example. Step 2: Find 2 consecutive numbers that add up to the squared value in step 1. ...
Teaching Plan 1B
... TEACHING PLAN 2B Stage 8 Learning Objectives Chapter 11 Pythagoras’ Theorem ...
... TEACHING PLAN 2B Stage 8 Learning Objectives Chapter 11 Pythagoras’ Theorem ...
1_M2306_Hist_chapter1
... • According to the Pythagoras theorem, the diagonal of the unit square is not a rational number • Discovery of incommensurable lengths (not measurable as integer multiple of the same unit) • Irrational numbers ...
... • According to the Pythagoras theorem, the diagonal of the unit square is not a rational number • Discovery of incommensurable lengths (not measurable as integer multiple of the same unit) • Irrational numbers ...
storyboard - WordPress.com
... perfect numbers. Pythagoreans contributed to our understanding of angles, triangles, areas, proportion, polygons, and polyhedra. Pythagoras also related music to mathematics. He had long played the seven string lyre, and learned how harmonious the vibrating strings sounded when the lengths of the st ...
... perfect numbers. Pythagoreans contributed to our understanding of angles, triangles, areas, proportion, polygons, and polyhedra. Pythagoras also related music to mathematics. He had long played the seven string lyre, and learned how harmonious the vibrating strings sounded when the lengths of the st ...
Pythagorean Theorem
... Mathematics • The Pythagoreans wrote many geometric proofs, but it is difficult to ascertain who proved what, as the group wanted to keep their findings secret. They did not write anything down until the very end. Unfortunately, this vow of secrecy prevented an important mathematical idea from ...
... Mathematics • The Pythagoreans wrote many geometric proofs, but it is difficult to ascertain who proved what, as the group wanted to keep their findings secret. They did not write anything down until the very end. Unfortunately, this vow of secrecy prevented an important mathematical idea from ...
Chapter 6: Pythagoras` Theorem
... Pythagoras • Pythagoras lived in the sixth century BC. • He travelled the world to discover all that was known about Mathematics at that time. • He eventually set up the Pythagorean Brotherhood – a secret society which worshipped, among other things, numbers. • Pythagoras described himself as a phi ...
... Pythagoras • Pythagoras lived in the sixth century BC. • He travelled the world to discover all that was known about Mathematics at that time. • He eventually set up the Pythagorean Brotherhood – a secret society which worshipped, among other things, numbers. • Pythagoras described himself as a phi ...
Pythagoras
Pythagoras of Samos (US /pɪˈθæɡərəs/; UK /paɪˈθæɡərəs/; Greek: Πυθαγόρας ὁ Σάμιος Pythagóras ho Sámios ""Pythagoras the Samian"", or simply Πυθαγόρας; Πυθαγόρης in Ionian Greek; c. 570 – c. 495 BC) was an Ionian Greek philosopher, mathematician, and has been credited as the founder of the movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of Samos, and traveled, visiting Egypt and Greece, and maybe India, and in 520 BC returned to Samos. Around 530 BC, he moved to Croton, in Magna Graecia, and there established some kind of school or guild.Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which bears his name. However, because legend and obfuscation cloud his work even more than that of the other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important. It was said that he was the first man to call himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato, and through him, all of Western philosophy.