Maths SoW - Thinking Skills @ Townley
... Algebra Cards – find value of each card when x = 30, which ones are the same value when x = 20, what does 2x mean, put in order from smallest to largest when x = 12 (or which one would be in the middle), which three could be the angles in a triangle when x = 38. Non-algebraic linking activity such ...
... Algebra Cards – find value of each card when x = 30, which ones are the same value when x = 20, what does 2x mean, put in order from smallest to largest when x = 12 (or which one would be in the middle), which three could be the angles in a triangle when x = 38. Non-algebraic linking activity such ...
Pythagorean Triples Challenge - Virtual Commons
... 1. From the Pi Mu Epsilon Journal, 1993 (used with permission from Steve Miller): For a < b < c positive integers, if gcd(a, b) = 1 and a2 + b2 = c2, then we say (a, b, c) is a primitive Pythagorean. If both a and c are primes, we call it a prime primitive Pythagorean triple. (i) If (a, b, c) is a p ...
... 1. From the Pi Mu Epsilon Journal, 1993 (used with permission from Steve Miller): For a < b < c positive integers, if gcd(a, b) = 1 and a2 + b2 = c2, then we say (a, b, c) is a primitive Pythagorean. If both a and c are primes, we call it a prime primitive Pythagorean triple. (i) If (a, b, c) is a p ...
On Euclidean and Non-Euclidean Geometry by Hukum Singh DESM
... which is not containing the given point (e) Two straight lines in a plane are either parallel or intersecting (f) The sum of the angles of a triangle is 180◦ The five Euclid’s Postulates are [1], [3] (a) A straight line can be drawn from any point to any other point (b)A finite straight line can be ...
... which is not containing the given point (e) Two straight lines in a plane are either parallel or intersecting (f) The sum of the angles of a triangle is 180◦ The five Euclid’s Postulates are [1], [3] (a) A straight line can be drawn from any point to any other point (b)A finite straight line can be ...
Document
... =~ is a binding operator and means: perform the following action on this variable. The operation tr/// translates each character from the first set of characters into the corresponding character in the second set: acgt ...
... =~ is a binding operator and means: perform the following action on this variable. The operation tr/// translates each character from the first set of characters into the corresponding character in the second set: acgt ...
Topic 1: Combinatorics & Probability
... You should know most of these already. Although there’s a couple you may not have used (e.g. intersecting chord theorem). ...
... You should know most of these already. Although there’s a couple you may not have used (e.g. intersecting chord theorem). ...
Slides - Dr Frost Maths
... You should know most of these already. Although there’s a couple you may not have used (e.g. intersecting chord theorem). ...
... You should know most of these already. Although there’s a couple you may not have used (e.g. intersecting chord theorem). ...
Core - The New Indian Model School, Dubai
... emergence of a fresh thought process in imparting a curriculum which would restore the independence of the learner to pursue the learning process in harmony with the existing personal, social and cultural ethos. The Central Board of Secondary Education has been providing support to the academic need ...
... emergence of a fresh thought process in imparting a curriculum which would restore the independence of the learner to pursue the learning process in harmony with the existing personal, social and cultural ethos. The Central Board of Secondary Education has been providing support to the academic need ...
Full text
... The authors define the notion of an independent Pythagorean number and they prove that there exist infinitely many primitive Pythagorean numbers that are not independent (Theorem 10, p. 40). According to that definition (Definition 2, p. 40), a Pythagorean number is called independent if it cannot b ...
... The authors define the notion of an independent Pythagorean number and they prove that there exist infinitely many primitive Pythagorean numbers that are not independent (Theorem 10, p. 40). According to that definition (Definition 2, p. 40), a Pythagorean number is called independent if it cannot b ...
Topic 1 - Dr Frost Maths
... Forming circles around regular polygons By circumscribing a regular polygon, we can exploit circle theorems. [IMC 2003 Q22] The diagram shows a regular dodecagon (a polygon with twelve equal sides and equal angles). What is the size of the marked angle? ...
... Forming circles around regular polygons By circumscribing a regular polygon, we can exploit circle theorems. [IMC 2003 Q22] The diagram shows a regular dodecagon (a polygon with twelve equal sides and equal angles). What is the size of the marked angle? ...
Prime Numbers in Music Tonality
... to the fundamental pitch of the instrument. To him and others, this could only be explained as a consonant blending, an effect that they were the same sound in different places. “It is one of the amazing phenomena of acoustics that the 2/1 of a tone, the doubling of its cycles, gives a tone which we ...
... to the fundamental pitch of the instrument. To him and others, this could only be explained as a consonant blending, an effect that they were the same sound in different places. “It is one of the amazing phenomena of acoustics that the 2/1 of a tone, the doubling of its cycles, gives a tone which we ...
Bloom`s Taxonomy applied to understanding the Pythagorean
... 2. Would the Pythagorean Theorem hold true in three dimensions? If so, what would it say and how would it work? If not, why? 3. Use the Pythagorean Theorem to explain why the graph of x 2 y 2 r 2 is a circle. 4. Create a story problem the solution of which involves use of the Pythagorean Theorem ...
... 2. Would the Pythagorean Theorem hold true in three dimensions? If so, what would it say and how would it work? If not, why? 3. Use the Pythagorean Theorem to explain why the graph of x 2 y 2 r 2 is a circle. 4. Create a story problem the solution of which involves use of the Pythagorean Theorem ...
The Pythagorean Theorem
... The Pythagorean Theorem • Greek Mathematician, Pythagoras, proved this theorem. • Applies to right triangles. • Many different proofs exist, including one by President Garfield. ...
... The Pythagorean Theorem • Greek Mathematician, Pythagoras, proved this theorem. • Applies to right triangles. • Many different proofs exist, including one by President Garfield. ...
Section 7 * 2 The Pythagorean theorem & Its converse
... Section 7 – 2 The Pythagorean theorem & Its converse Objectives: To use the Pythagorean Theorem To use the Converse of the Pythagorean Theorem ...
... Section 7 – 2 The Pythagorean theorem & Its converse Objectives: To use the Pythagorean Theorem To use the Converse of the Pythagorean Theorem ...
5-85 Pythagorean Triples
... Substitute your new triples into the Pythagorean formula. Which one works? ...
... Substitute your new triples into the Pythagorean formula. Which one works? ...
Exam Review
... A triangle’s three perpendicular bisectors are concurrent. Know what is, and how to construct a triangle’s circumcircle. All of theorem 2.2.1 (chords of circles). A triangle’s three angle bisectors are concurrent. Know what a triangle’s incircle is, how it’s center is found and how the incircle woul ...
... A triangle’s three perpendicular bisectors are concurrent. Know what is, and how to construct a triangle’s circumcircle. All of theorem 2.2.1 (chords of circles). A triangle’s three angle bisectors are concurrent. Know what a triangle’s incircle is, how it’s center is found and how the incircle woul ...
Thales and His Semicircle Theorem Historical Context: Suggested
... mythos (i.e. understanding the world via traditional stories) to logos (i.e. understanding the world via reasoning). In fact, Aristotle stated: “To Thales the primary question was not what do we know, but how do we know it.” Thales is usually credited with being responsible for five theorems in geom ...
... mythos (i.e. understanding the world via traditional stories) to logos (i.e. understanding the world via reasoning). In fact, Aristotle stated: “To Thales the primary question was not what do we know, but how do we know it.” Thales is usually credited with being responsible for five theorems in geom ...
Chapter 9 Slides
... 4. All right angles are equal 5. Given a line k and a point P not on the line, there exists one and only one line m through P that is parallel to k ...
... 4. All right angles are equal 5. Given a line k and a point P not on the line, there exists one and only one line m through P that is parallel to k ...
The Establishment of Equal Temperament
... tune. In fact, some keys still sounded better than others. Both of these temperaments allowed for the freedom to modulate between all twelve keys while upholding the character of the keys. One of the greatest treasures that came from the Baroque era amidst the tuning and temperament controversies w ...
... tune. In fact, some keys still sounded better than others. Both of these temperaments allowed for the freedom to modulate between all twelve keys while upholding the character of the keys. One of the greatest treasures that came from the Baroque era amidst the tuning and temperament controversies w ...
Study Advice Services
... Remember to check that your calculator is in degrees if you are using degrees or in radians if you are using radians. This can normally be altered via the mode button. Depending on your calculator you may need to type in either 2nd/shift sin 30 or 30 2nd/shift sin to get the value of sin1 30 . ...
... Remember to check that your calculator is in degrees if you are using degrees or in radians if you are using radians. This can normally be altered via the mode button. Depending on your calculator you may need to type in either 2nd/shift sin 30 or 30 2nd/shift sin to get the value of sin1 30 . ...
Prezentacja programu PowerPoint
... THALES' LIFE • The dates of Thales' life are not exactly known but are roughly established by a few datable events mentioned in the sources. According to Herodotus, Thales predicted the solar eclipse of May 28, 585 BC. Diogenes Laërtius quotes saying that Thales died at the age of 78 during the 58t ...
... THALES' LIFE • The dates of Thales' life are not exactly known but are roughly established by a few datable events mentioned in the sources. According to Herodotus, Thales predicted the solar eclipse of May 28, 585 BC. Diogenes Laërtius quotes saying that Thales died at the age of 78 during the 58t ...
Pythagoras and President Garfield
... The President's Proof There are many proofs to the Pythagorean theorem. President James Garfield developed his own proof in The Journal of Education (Volume 3 issue161) in 1876. President Garfield studied math at Williams College (in Williamstown, MA) and taught in the public school in Pownal, Vermo ...
... The President's Proof There are many proofs to the Pythagorean theorem. President James Garfield developed his own proof in The Journal of Education (Volume 3 issue161) in 1876. President Garfield studied math at Williams College (in Williamstown, MA) and taught in the public school in Pownal, Vermo ...
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.