Student Activities for Theorem 15: Converse of Pythagoras` Theorem
... lesson. This theorem stated that the square on the hypotenuse in a right-angled triangle is equal to the sum of the squares on the other two sides. Today we want to explore whether the theorem holds true in reverse. In other words: Suppose the three sides of a triangle are such that the square of th ...
... lesson. This theorem stated that the square on the hypotenuse in a right-angled triangle is equal to the sum of the squares on the other two sides. Today we want to explore whether the theorem holds true in reverse. In other words: Suppose the three sides of a triangle are such that the square of th ...
Demonstrative Math 800
... A circle is bisected by any diameter The base angles of an isosceles triangle are equal Two triangles are congruent if they have two angles and one side in each respectfully equal. ...
... A circle is bisected by any diameter The base angles of an isosceles triangle are equal Two triangles are congruent if they have two angles and one side in each respectfully equal. ...
Physics of Music
... and its total length was always a nice and easy fraction such as a half, two-thirds, three-quarters and so on. Since medieval times, the notes formed by these ratios have been called respectively the octave, fifth and forth. They are collectively known as the perfect consonances. More on these in a ...
... and its total length was always a nice and easy fraction such as a half, two-thirds, three-quarters and so on. Since medieval times, the notes formed by these ratios have been called respectively the octave, fifth and forth. They are collectively known as the perfect consonances. More on these in a ...
Pythagorean Treasury
... much clearer understanding of Pythagoras’ Theorem than the Egyptians, although they still could not understand why such sets of triples existed. They had no idea how to produce a general proof. ...
... much clearer understanding of Pythagoras’ Theorem than the Egyptians, although they still could not understand why such sets of triples existed. They had no idea how to produce a general proof. ...
Looking for Pythagoras!!!
... 8. At Error’s evergreen farm, the taller trees are braced by a wire extending from 2 feet below the top of the tree to a stake in the ground. What is the tallest tree that can be braced with a 25-food wire staked 15 feet from the base of the tree? ...
... 8. At Error’s evergreen farm, the taller trees are braced by a wire extending from 2 feet below the top of the tree to a stake in the ground. What is the tallest tree that can be braced with a 25-food wire staked 15 feet from the base of the tree? ...
Document
... If we think about a right triangle we know of course that one of the angles is a right angle. We also know that the other two angles are acute angles (why?). In fact we know that the other two angles are complementary angles. Therefore there is a relationship between the sizes of the angles that the ...
... If we think about a right triangle we know of course that one of the angles is a right angle. We also know that the other two angles are acute angles (why?). In fact we know that the other two angles are complementary angles. Therefore there is a relationship between the sizes of the angles that the ...
RZC-Factsheet-Geometry (Revision)
... and we can use the tips in (a). c. We’re given the diameter? The angle subtended by any point on the circumference is 90°. 2. Use variables to represent appropriate unknown angles/lengths. Form equations (e.g. using Pythagoras, or comparing lengths) to find the values of these variables. 3. Look out ...
... and we can use the tips in (a). c. We’re given the diameter? The angle subtended by any point on the circumference is 90°. 2. Use variables to represent appropriate unknown angles/lengths. Form equations (e.g. using Pythagoras, or comparing lengths) to find the values of these variables. 3. Look out ...
Pythagoras and the Pythagoreans
... What is known of the Pythagorean school is substantially from a book written by the Pythagorean, Philolaus (fl. c. 475 BCE) of Tarentum. However, according to the 3rd-century-AD Greek historian Diogenes Laërtius, he was born at Croton. After the death of Pythagoras, dissension was prevalent in Ital ...
... What is known of the Pythagorean school is substantially from a book written by the Pythagorean, Philolaus (fl. c. 475 BCE) of Tarentum. However, according to the 3rd-century-AD Greek historian Diogenes Laërtius, he was born at Croton. After the death of Pythagoras, dissension was prevalent in Ital ...
Euclidean and Non-Euclidean Geometries: Development and History
... http://geometryalgorithms.com/history.htm ...
... http://geometryalgorithms.com/history.htm ...
Proof that 2is irrational - Biblical Christian World View
... I). Irrational numbers cannot be written as the ratio of two integers. Their decimal expansions are infinite, without pattern, but given by some rule so that we can say that the expansion represents a point at a definite distance from 0 on the number line. Irrational numbers are non-rational or non- ...
... I). Irrational numbers cannot be written as the ratio of two integers. Their decimal expansions are infinite, without pattern, but given by some rule so that we can say that the expansion represents a point at a definite distance from 0 on the number line. Irrational numbers are non-rational or non- ...
The Pythagorean Theorem and Irrational Numbers
... means b 2 is even so b is even. But therein lies our contradiction. The numbers a and b cannot both be even!!! If they are, then their gcd is obviously larger than 1 because a and b have a common divisor of 2. CONTRADICTION! Therefore, the original assumption, that we could a write 2 as with a and b ...
... means b 2 is even so b is even. But therein lies our contradiction. The numbers a and b cannot both be even!!! If they are, then their gcd is obviously larger than 1 because a and b have a common divisor of 2. CONTRADICTION! Therefore, the original assumption, that we could a write 2 as with a and b ...
LevelUp 6-8 Unit 4 STUOBS Word document
... I know that the tangent at any point on a circle is perpendicular to the radius at that point I can explain why the perpendicular from the centre to the chord bisects the chord I know the definition of a circle and the names of its parts; explain why inscribed regular polygons can be constructed by ...
... I know that the tangent at any point on a circle is perpendicular to the radius at that point I can explain why the perpendicular from the centre to the chord bisects the chord I know the definition of a circle and the names of its parts; explain why inscribed regular polygons can be constructed by ...
Converse of Pythagoras
... A pupil has 7 sticks of different lengths as shown. If he picks three of them and forms a triangle, how many different triangles can he form? How many of these triangles will be right angled? 5cm ...
... A pupil has 7 sticks of different lengths as shown. If he picks three of them and forms a triangle, how many different triangles can he form? How many of these triangles will be right angled? 5cm ...
Pythagorean Treasury Powerpoint - 8.1 ~ A collection of teaching
... of Samos in the Eastern Aegean in about 570 B.C. He travelled extensively throughout Egypt, Mesopotamia and India absorbing much mathematics and mysticism. He eventually settled in the Greek town of Crotona in southern Italy. ...
... of Samos in the Eastern Aegean in about 570 B.C. He travelled extensively throughout Egypt, Mesopotamia and India absorbing much mathematics and mysticism. He eventually settled in the Greek town of Crotona in southern Italy. ...
![pythagoreantreasury[1]](http://s1.studyres.com/store/data/008460234_1-b0fb1826394697cba2511ff556bba420-300x300.png)
pythagoreantreasury[1]
... of Samos in the Eastern Aegean in about 570 B.C. He travelled extensively throughout Egypt, Mesopotamia and India absorbing much mathematics and mysticism. He eventually settled in the Greek town of Crotona in southern Italy. ...
... of Samos in the Eastern Aegean in about 570 B.C. He travelled extensively throughout Egypt, Mesopotamia and India absorbing much mathematics and mysticism. He eventually settled in the Greek town of Crotona in southern Italy. ...
sin(A) = cos(A) = x tan(A) = csc(A) = 1 = sec(A
... contain the soul of an ancestor. New initiates into the brotherhood were only permitted to hear the voice of Pythagorus and not see him. After several years of purification they were allowed to see him. It was believed that an understanding of the kosmos can be achieved through reason and observati ...
... contain the soul of an ancestor. New initiates into the brotherhood were only permitted to hear the voice of Pythagorus and not see him. After several years of purification they were allowed to see him. It was believed that an understanding of the kosmos can be achieved through reason and observati ...
Elementary matematical ideas, theorems from the Ancient Greece
... Elementary matematical ideas, theorems from the Ancient Greece In this time the greatest mathematicians were Thales of Miletos, Pythagoras of Samos, Aristoteles of Strageria and Euclides of Alexandria in chronological sequence. They also were philosophers except for Euclides. Thales is the first wel ...
... Elementary matematical ideas, theorems from the Ancient Greece In this time the greatest mathematicians were Thales of Miletos, Pythagoras of Samos, Aristoteles of Strageria and Euclides of Alexandria in chronological sequence. They also were philosophers except for Euclides. Thales is the first wel ...
SIMILARITY a = b + c
... Two figures are similar if one is the image of the other under a transformation from the plane into itself that multiplies all distances by the same positive scale factor, k - SIMILAR TRIANGLES Triangle ABC is similar to the triangle DEF. Facts about similar triangles: ...
... Two figures are similar if one is the image of the other under a transformation from the plane into itself that multiplies all distances by the same positive scale factor, k - SIMILAR TRIANGLES Triangle ABC is similar to the triangle DEF. Facts about similar triangles: ...
Area of a regular pentagon
... 4. Consider how you will use trigonometry and Pythagoras to solve for the area of the triangles. 5. Use the rules that we have learnt in geometry to find angles that you will need to use. 6. Now work through finding sides of the triangles, to get their areas, etc… ...
... 4. Consider how you will use trigonometry and Pythagoras to solve for the area of the triangles. 5. Use the rules that we have learnt in geometry to find angles that you will need to use. 6. Now work through finding sides of the triangles, to get their areas, etc… ...
Thales 625-545, one of seven Sages of Greece 1) Rejected myth
... 1) Escaped a tyrant of Samos, in Croton established a secret esoteric society (type of orphics), opened a school, called themselves “Mathematikoi”; -knowledge, study, learning, lesson, science (in Latin and English, until 1700 mathematics meant astrology); polymath; common meals, exercises, r ...
... 1) Escaped a tyrant of Samos, in Croton established a secret esoteric society (type of orphics), opened a school, called themselves “Mathematikoi”; -knowledge, study, learning, lesson, science (in Latin and English, until 1700 mathematics meant astrology); polymath; common meals, exercises, r ...
Pythagoras and the Language of Nature
... Pythagoras and the Language of Nature Walking past the village blacksmith's shop, the pleasant ring of hammers striking an anvil catches your attention. It's music in harmony. Going into the shop, you find that the lower notes that you hear are produced by heavy hammers, while the higher notes are c ...
... Pythagoras and the Language of Nature Walking past the village blacksmith's shop, the pleasant ring of hammers striking an anvil catches your attention. It's music in harmony. Going into the shop, you find that the lower notes that you hear are produced by heavy hammers, while the higher notes are c ...
Pythagorean Triples Historical Context: Suggested Readings
... Investigation integral solutions to the equation a2 + b2 = c2, where these solutions also are the sides of a right triangle. ...
... Investigation integral solutions to the equation a2 + b2 = c2, where these solutions also are the sides of a right triangle. ...
Parry A
... 6.5: We did what we need to do with congruence testing with right triangles already. We did the HL. This chapter also includes LL (SAS), HA and LA (both AAS). Pythagoreans: 1 represented logic because reason could produce only one consistent body of truths 2 stood for man 3 stood for woman 4 stood f ...
... 6.5: We did what we need to do with congruence testing with right triangles already. We did the HL. This chapter also includes LL (SAS), HA and LA (both AAS). Pythagoreans: 1 represented logic because reason could produce only one consistent body of truths 2 stood for man 3 stood for woman 4 stood f ...
. cba= +
... the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. ...
... the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. ...
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.