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Why was the Pythagorean theorem regarded as a statement about areas?
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∙ 11y ago
Pythagoras' theorem states that for any right angle triangle the square of its hypotenuse is equal to the squares of its 2 sides:-
a2+b2 = c2 whereas a and b are the sides of the triangle with c being its hypotenuse or longest side
Wiki User
∙ 11y ago
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When did Greece invent the Pythagorean theorem?
The Pythagorean theorem was, oddly enough, first postulated by a Greek named Pythagoras of Samos, in the 6th century BC or so. It basically described the relationship among the three sides of a triangle and the areas of the same. There is some thought that Babylonian mathematicians well before the time of Pythagoras knew of the relationship, but he's the guy who got his name on the theorem.
Why is Pythagorean theorem important in geometry?
It finds the third side of the right triangle when the two sides are available. That helps to figure out the circumference of the triangle, it also helps find the length of the diagonal of the square or a rectangle. It helps finding areas and circumpherences of polygons, it helps with construction of polygons, etc... Generally it is one of the most basic and fundamental theorems.
Why is the right angle triangle theorem named after Pythagorean when Egyptian were using it to build the great pyramids 1500 year before he was born?
Because he produced a general theorem. The Egyptians knew that a 3-4-5 triangle gave a right angle.Additional Information:A possible explanation is that although the ancients knew that in a right angle triangle 32+42 = 52 Pythagoras also suggested that pi*1.52+pi*22 = 2.52 (the three sides as areas of a circle) but because no one knew then and even today knows the true value of pi so it became to be known as Pythagoras' Theorem.
How this pythagorean theorem made?
The Pythagorean Theorem was not made, it was discovered by an ancient Greek philosipher named Pythagoras. "A greek phylosopher proposed a theory that when two squares are drawn with a common corner and their sides are perpendicular to each other then a third square whose side connects to the corners of the adjacent sides of the first two squares will have an area that is equal to the sum of areas of the first two squares. let square1 be Area1 = X x X = X^2 square2 be Area2 = Y x Y = Y^2 Square3 be Area3 = H x H = H^2 the sides are X, Y, H form the triangle whose 90 deg angle is between X and Y. He states that the sum of the squares of these sides = the square of the thid side. He is actually reffering to the areas of the three squares. "From...(ENAC)
Where can you find the Phythagoras Theorem?
The Pythagorean Theorem refers to the mathematical relationship between the three sides of any right triangle. "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). In other words, if you know the length of two of the sides (the two legs), then the length of the third side (the hypotenuse) can be determined using the following formula: a2 + b2 = c2
Whats the theorem used for right triangles?
The Pythagorean Theorem is a statement about triangles containing a right angle. The Pythagorean Theorem states that:"The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides."
What are the other areas of maths besides geometry that make use of the Pythagorean Theorem?
Trig., Calculus.
What does the Pythagorean theorem tell you about the areas of the square?
The square of the hypotenuse of right triangle is equal to the sum of the squares of the two adjacent sides.
When did Greece invent the Pythagorean theorem?
The Pythagorean theorem was, oddly enough, first postulated by a Greek named Pythagoras of Samos, in the 6th century BC or so. It basically described the relationship among the three sides of a triangle and the areas of the same. There is some thought that Babylonian mathematicians well before the time of Pythagoras knew of the relationship, but he's the guy who got his name on the theorem.
Can you state the Pythagorean Theorem not just the formula?
In a right-angled triangle the area of the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides.
What does the Pythagorean Theorem state?
The sum of the areas of the two squares on the legs of a triangle (a and b), where the angle between sides a and b is 90 degrees, equals the area of the square on the hypotenuse (c). a2 + b2 = c2
Who is Pythagoras and Euclid?
Pythagoras and Euclid are both mathematicians. Pythogoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides-that is, . Euclid is in charge of dicovering Pythagorean Triples, Euclidean geometry and more geometry realated things. Euclid also wrote a book called "Elements" in support of his math.
What is the actual definition of the Pythagorean Theorem?
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).
What is the phythagorean theorem?
If you have two straight lines AB and BC such that the two lines meet at B and AB and BC make 90 degrees with each other then the pythagorean theory (theoram) states that the length of line AC (assume that points A and C are joined by a straight line) then (AC) squared = (AB) squared +(BC) squared
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.
Why is Pythagorean theorem important in geometry?
It finds the third side of the right triangle when the two sides are available. That helps to figure out the circumference of the triangle, it also helps find the length of the diagonal of the square or a rectangle. It helps finding areas and circumpherences of polygons, it helps with construction of polygons, etc... Generally it is one of the most basic and fundamental theorems.
Why is the right angle triangle theorem named after Pythagorean when Egyptian were using it to build the great pyramids 1500 year before he was born?
Because he produced a general theorem. The Egyptians knew that a 3-4-5 triangle gave a right angle.Additional Information:A possible explanation is that although the ancients knew that in a right angle triangle 32+42 = 52 Pythagoras also suggested that pi*1.52+pi*22 = 2.52 (the three sides as areas of a circle) but because no one knew then and even today knows the true value of pi so it became to be known as Pythagoras' Theorem.
