1. Pythagorean theorem

1.1. Definition

In mathematics, the Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that 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 on the other two sides.

This theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation: ¹

\[a^2 + b^2 = c^2\]

Another technical notation is: a²+b²=c².

1.2. Visual representation

The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

Picture of a2+b2=c2

The following picture is integrated in SVG format in the page as HTML:

1.3. Values

	1	2	3	4	5	6	7	8	9	10
1	1,41
2	2,24	2,83
3	3,16	3,61	4,24
4	4,12	4,47	5,00	5,66
5	5,10	5,39	5,83	6,40	7,07
6	6,08	6,32	6,71	7,21	7,81	8,49
7	7,07	7,28	7,62	8,06	8,60	9,22	9,90
8	8,06	8,25	8,54	8,94	9,43	10,00	10,63	11,31
9	9,06	9,22	9,49	9,85	10,30	10,82	11,40	12,04	12,73
10	10,05	10,20	10,44	10,77	11,18	11,66	12,21	12,81	13,45	14,14

Exercise: if a=3 and b=5, then c=... ?

c = √34 ≈ 5,83

2. Script

2.1. Python

from math import sqrt

try:
    a = float(input('Value of a = '))
    b = float(input('Value of b = '))
    c2 = a ** 2 + b ** 2
    print('c = %.2f' % sqrt(c2))
except ValueError:
    print('Invalid value')

2.2. JavaScript

var a = parseFloat(prompt('Value of a =', '2')),
    b = parseFloat(prompt('Value of b =', '3'));
alert('c = ' + Math.sqrt(a*a + b*b));

2.3. Other languages to implement

Python
JavaScript
C++
Java

3. See also

4. Notes

Judith D. Sally; Paul Sally (2007). "Chapter 3: Pythagorean triples". Roots to research: a vertical development of mathematical problems. American Mathematical Society Bookstore. p. 63. ISBN 978-0-8218-4403-8. ↩

Attached documents

264px-pythagorean.svg.png
image/png (8.1 kB)

Revision #1 was last modified by gitbra
on 2024-11-30 at 00:00:00 — 3c1e56c0e9981455