Top Answer

Since the 4th century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right triangle the square of the hypotenuse (the longest side, opposite the right angle) is equal to the sum of the squares of the other two sides.

.

In other words, given a right-triangle with side lengths a and b, and a hypotenuse of length c, then

a2 + b2 = c2

Example:

Given a right-triangle with side a = 3 and side b = 4, what is the hypotenuse (side c)?

Solution: a2 + b2 = c2

32 + 42 = c2

(3 x 3) + (4 x 4) = c2

9 + 16 = c2

25 = c2

c = √25

c = 5.

(Note that c can't equal -5 because c is the length of the hypotenuse of the triangle and length must be positive.)

The importance of the theorem goes way beyond triangles, in fact the Pythagorean theorem is the basis for the definition of distance between two points in space of any dimension of size 2 or more.

(There is a related link to 81 different proofs of this theorem.)

Euler Improvement

The mathematician George Euler improved the Pythagoras theorem to apply to all triangles using the cosine of the included angle:

a2 + b2 -2abcosT= c2

where T is the angle between a and b and cos the goniometric function.

(The cosine of 90Â° is 0 which makes this the Pythagoras theorem.)

Example

IF BC=A=5CM=base of right angle, and AB=B=6CM the perpendicular and AC=C=the hypotenuse.

(HYP)2=(BASE)2+(PERP)2

C2=A2+B2

So we have:

C2=25+36

C2=61

Now we use the square root property but take the positive square root.

So C is approximately equal to 7.81 CM

Generalizing the theorem to higher dimensions

The Pythagorean Theorem works in higher dimensions too. If you have three legs, each one in a different dimension, and each at right angles to the other two, the hypotenuse joining these three lines has a length which equals sqrt(a2+b2+c2). You can't have four mutually right legs in three dimensions, but you can in four dimensions, in which case h=sqrt(a2+b2+c2+d2) and so on.

a squared + b squared = c squared. You square a and square b, and them together and find the square root of that number. that = c

A2 + B2 = C2

🙏

0🤨

0😮

0😂

0Loading...

The Pythagorean theorem is a2 + b2 = c2

Oh yes, the Pythagorean Theorem has been proven.

The Pythagorean theorem uses the right triangle.

There are 19 various aspects of Pythagoras theorem. Pythagorean Theorem (1) Pythagoras Theorem(2) Pythagorean Theorem (3) Pythagorean Theorem (4) Pythagoras Theorem(5) Pythagorean Theorem(6) Pythagrean Theorem(7) Pythagoras Theorem(8) Pythagorean Theorem (9) Hyppocrates' lunar Minimum Distance Shortest Distance Quadrangular Pyramid (1) Quadrangular Pyramid (2) Origami Two Poles Pythagoras Tree(1) Pythagoras Tree(2) Theorem by Pappus

See below for the related link for proof of the pythagorean theorem

the standard form of the Pythagorean Theorem is :a2 + b2 = c2

You can use pythagorean theorem twice to find the diagonal of a cube

they use pythagorean theorem to determine altitude and ground distance

The Greek, Babylonian, Indian, and Chines knew and used the Pythagorean Theorem.

The Pythagorean theorem gets its name from the ancient Greek mathematician Pythagoras. He was one of the first to offer proof of the theorem.

?

pythagorean theorem was named from a greek mathemition called pythagorus (I think that's how you spell it)

When the Scarecrow gets his brains, he recites the Pythagorean Theorem.

The Pythagorean Theorem allows the mathematician to determine the value of the hypotenuse. The converse of the Pythagorean Theorem manipulates the formula so that the mathematician can use the values to determine that if the triangle is a right triangle.

Since the Pythagorean theorem is named after the Greek mathematician Pythagoras, it was reasonable to assume that he is the first person to have it.

In the Pythagorean Theorem b is not twice a. The formula is [ a squared + b squared = c squared].

The Pythagorean theorem is actually the law of cos, where the angle is 90.

Architects use the Pythagorean theorem to check distances, heights, etc...that cant be measured

The difference in the distance formula and the pythagorean theorem is that the distance formula finds the distance between two points while the pythagorean theorem usually finds the hypotenuse of a right triangle.

You would use the Pythagorean Theorem when you are trying to determine the length of a side on a right triangle.ORYou might use the Pythagorean Theorem if you are carpenter or builder. A carpenter might use the Pythagorean Theorem to find the length of the hypotenuse (longest side of the triangle) or the length of the wall or roof. Use can use this methed or theorem in any building situation.

pythogorous

Pythagoras.

Pythagoras

Pythagoras

because it was