Seventh+Period

64+36=c^2 100=c^2 couldnt find a radical but ... 10=c
 * 2)﻿ Painters use a ladder to paint on a high buildings. A painter has to paint a wall which is 8m high. Painter has to put a ladder 6m away from the base pf the wall to avoid a rack in between. What will the length of the ladder required by the painter to complete his work? ﻿The ladder will be 10m. ﻿How do you know this? ﻿Because when of the pythagorean thereom it is a^2 + b^2 = c^2 8^2+6^2= c^2
 * Ashley an ﻿d Kristen :)
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Pythagoras believed that all relations could be reduced to number relations. As Aristotle wrote: This generalisation stemmed from Pythagoras's observations in music, mathematics and astronomy. Pythagoras noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments. In fact Pythagoras made remarkable contributions to the mathematical theory of music. He was a fine musician, playing the lyre, and he used music as a means to help those who were ill. Pythagoras studied properties of numbers which would be familiar to mathematicians today, such as even and odd numbers, triangular numbers, perfect numbers etc. However to Pythagoras numbers had personalities which we hardly recognise as mathematics today. (Triangle) A&K
 * The Pythagorean ... having been brought up in the study of mathematics, thought that things are numbers ... and that the whole cosmos is a scale and a number.

a2 + b2 = c2 || ||
 * It is called "Pythagoras' Theorem" and can be written in one short equation:
 * external image pythagoras-squares.gif ||

Note: Kristen and Ashley
 * **c** is the **longest side** of the triangle
 * **a** and **b** are the other two sides

(i) The sum of the angles of a triangle is equal to two right angles. Also the Pythagoreans knew the generalisation which states that a polygon with //n// sides has sum of interior angles 2//n// - 4 right angles and sum of exterior angles equal to four right angles. (ii) The theorem of Pythagoras - for a right angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. We should note here that to Pythagoras the square on the hypotenuse would certainly not be thought of as a number multiplied by itself, but rather as a geometrical square constructed on the side. To say that the sum of two squares is equal to a third square meant that the two squares could be cut up and reassembled to form a square identical to the third square. (iii) Constructing figures of a given area and geometrical algebra. For example they solved equations such as //a// (//a// - //x//) = //x//2 by geometrical means. (iv) The discovery of irrationals. This is certainly attributed to the Pythagoreans but it does seem unlikely to have been due to Pythagoras himself. This went against Pythagoras's philosophy the all things are numbers, since by a number he meant the ratio of two whole numbers. However, because of his belief that all things are numbers it would be a natural task to try to prove that the hypotenuse of an isosceles right angled triangle had a length corresponding to a number. (v) The five regular solids. It is thought that Pythagoras himself knew how to construct the first three but it is unlikely that he would have known how to construct the other two. (vi) In astronomy Pythagoras taught that the Earth was a sphere at the centre of the Universe. He also recognised that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realise that Venus as an evening star was the same planet as Venus as a morning star. Kristen ^-^

Read more: [|Pythagoras, Phoenician/Greek Mathematician] []

Read more: [|Pythagoras, Phoenician/Greek Mathematician] []

The //Pythagorean// (or //Pythagoras'//) //Theorem// is the statement that the sum of (the areas of) the two small squares equals (the area of) the big one. In algebraic terms, **a² + b² = c²** where **c** is the hypotenuse while **a** and **b** are the legs of the triangle. The theorem is of fundamental importance in Euclidean Geometry where it serves as a basis for the definition of distance between two points. It's so basic and well known that, I believe, anyone who took geometry classes in high school couldn't fail to remember it long after other math notions got thoroughly forgotten. Zachary and Matthew

He is often refered as a great mathematician luke


 * Pythagoras also investigated the ratios of lengths corresponding to musical harmonies, undertook studies in number theory, and developed methods of geometric proof. Among the results attributed to Pythagoras and his followers is the proof that the number [[image:http://scienceworld.wolfram.com/biography/pimg5.gif width="25" height="36" align="middle"]] (Pythagoras's constant [[image:http://scienceworld.wolfram.com/images/crossrefs/math.gif width="12" height="12" caption="Eric Weisstein's World of Math"]]) is irrational, [[image:http://scienceworld.wolfram.com/images/crossrefs/math.gif width="12" height="12" caption="Eric Weisstein's World of Math"]] usually attributed to [|Hippasus]. [] **
 * By: Kyle,Drew **

Pythagoras’ religious and scientific views were, in his opinion, inseparably interconnected. Religiously, Pythagoras was a believer of [|metempsychosis]. He believed in [|transmigration], or the reincarnation of the soul again and again into the bodies of humans, animals, or vegetables until it became immortal. His ideas of reincarnation were influenced by ancient Greek religion. [|Heraclides Ponticus] reports the story that Pythagoras claimed that he had lived four lives that he could remember in detail,[|[49]] and, according to [|Xenophanes], Pythagoras heard the cry of his dead friend in the bark of a dog.

by unknown

Pythagoras lived in the 500's [|BC], and was one of the first Greek mathematical thinkers. He spent most of his life in the Greek colonies in Sicily and southern Italy. He had a group of followers (like the disciples of [|Jesus]) who followed him around and taught other people what he had taught them. The Pythagoreans were known for their pure lives (they didn't eat [|beans], for example, because they thought beans were not pure enough). They wore their hair long, and wore only simple [|clothing], and went barefoot. Both men and women were Pythagoreans. Pythagoreans were interested in [|philosophy], but especially in [|music] and [|mathematics], two ways of making [|order] out of chaos. Music is noise that makes sense, and mathematics is rules for how the world works.

Pythagoras himself is best known for proving that the Pythagorean Theorem was true. The [|Sumerians], two thousand years earlier, already knew that it was generally true, and they used it in their measurements, but Pythagoras is said to have proved that it would always be true. We don't really know whether it was Pythagoras that proved it, because there's no evidence for it until the time of [|Euclid], but that's the tradition. Some people think that the proof must have been written around the time of Euclid, instead.

By Keyshawn and Timdarius //Each number had its own personality - masculine or feminine, perfect or incomplete, beautiful or ugly. This feeling modern mathematics has deliberately eliminated, but we still find overtones of it in fiction and poetry. Ten was the very best number: it contained in itself the first four integers - one, two, three, and four// [1 + 2 + 3 + 4 = 10] //- and these written in dot notation formed a perfect triangle.//

Read more: [|Pythagoras, Phoenician/Greek Mathematician] [] By:Kody Adams

[|Samos Island] || [|Metapontum] ||
 * ~ Full name || Pythagoras (Πυθαγόρας) ||
 * ~ Born || c. 570 BC
 * ~ Died || c. 495 BC (aged around 75)
 * ~ Era || [|Ancient philosophy] ||
 * ~ Region || Western philosophy ||
 * ~ [|School] || [|Pythagoreanism] ||
 * ~ Main interests || [|Metaphysics], [|Music], [|Mathematics], [|Ethics], [|Politics] ||
 * ~ Notable ideas || [|Musica universalis], [|Golden ratio], [|Pythagorean tuning], [|Pythagorean theorem] ||

{Pythagorean theorem is a relation in Euclidean geometry among the three sides of a right triangle. Pythagoras was the Greek mathematician who is credited for its discovery.-
 * ) ﻿B smiley with a double chin...!!!!!

click on picture it has a caption... The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power. Popular references to Pythagoras' theorem in literature, plays, musicals, songs, stamps and cartoons abound.

In [|mathematics], the **Pythagorean theorem** or **Pythagoras' theorem** is a relation in [|Euclidean geometry] among the three sides of a [|right triangle] (//right-angled triangle//). In terms of areas, it states: > In any right triangle, the area of the square whose side is the [|hypotenuse] (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a [|right angle]). The [|theorem] can be written as an [|equation] relating the lengths of the sides //a//, //b// and //c//, often called the //Pythagorean equation//:[|[1]] where //c// represents the length of the hypotenuse, and //a// and //b// represent the lengths of the other two sides.



All this is information is very interesting keep it up!