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How are Pythagoras' theorem and Fermat's last theorem related?
Pythagoras' theorem proves that if you draw a square on the longest side (the hypotenuse) of a right-angled triangle, its area is the same as the areas of the squares drawn on the two shorter sides, added together. See 'Pythagoras' theorem' under 'Sources and related links' below.Pythagoras' theorem holds for any right-angled triangle. But of special interest to Fermat were right-angled triangles where all the three sides were whole number lengths. These special lengths are known as Pythagorean triples.Here are some Pythagorean triples:-(3,4,5) (5, 12, 13) (7, 24, 25) (8, 15, 17)In each case, the square of each of the smaller numbers is equal to the square of the largest number.Fermat said that if instead of constructing squares (two dimensional figures) on the sides of right-angled triangles, you constructed cubes (three dimensional analogs of squares), or hypercubes (four dimensional analogs) or higher dimensional cube-analogs, there are no equivalents to the Pythagorean triples. In other words, there are no whole number values for 3, 4 or more dimensional analogs of the square.
What postulate or theorem verifies the congruence of triangles?
sssThere are five methods for proving the congruence of triangles. In SSS, you prove that all three sides of two triangles are congruent to each other. In SAS, if two sides of the triangles and the angle between them are congruent, then the triangles are congruent. In ASA, if two angles of the triangles and the side between them are congruent, then the triangles are congruent. In AAS, if two angles and one of the non-included sides of two triangles are congruent, then the triangles are congruent. In HL, which only applies to right triangles, if the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent.
Are some isosceles triangles equilateral triangles?
All isosceles triangles are not equilateral triangles
How did Pythagoras become so famous?
Because Pythagoras was the first person to prove the pythagorean theorem correct and his philosophy influence all other philosophers after his death, incluing Plato and Aristotle. His Pythagorean School gained influence and respect during the years around 520 BC in Italy. His Society was spread all throughout Europe and Asia.
How is the pythagorean theorem used in modern day times?
The Pythagorean theorem is used for many things today. For example, it can be used for building. Putting in flooring deals with squares and triangles using the Pythagorean Theorem. Some builders use this formula, because they can find the missing sides. The Pythagorean theorem plays an important role in mathematics, too. For example: -It is the basis of trigonometry -using the theorems arithmetic form, it connects algebra and geometry. -It is linked to fractal geometry His theorem is not only important in 2-D geometry, but also in 3-D geometry. Video games environments are drawn in 3-D using all triangles. i got this information from a website called: [See below for the related link to this website]. This website tells you all about how the Pythagorean theorem is used in modern day.
