Rectangle Triangles

Rectangle Triangles (using MathML)

Integer triangles and respective smallest angles.
$4^{2} + 3^{2} = 5^{2}$	$3^{2} + 4^{2} = 5^{2}$	${36,87}^{o}$
	$5^{2} + 12^{2} = 13^{2}$	${22,62}^{o}$
$8^{2} + 15^{2} = 17^{2}$		${28,07}^{o}$
	$7^{2} + 24^{2} = 25^{2}$	${16,26}^{o}$
	$9^{2} + 40^{2} = 41^{2}$	${12,68}^{o}$
$12^{2} + 35^{2} = 37^{2}$		${18,92}^{o}$
	$11^{2} + 60^{2} = 61^{2}$	${10,39}^{o}$

Trigonometric Functions

More Rectangle Triangles (without MathML)

"i" is a non-negative integer.
(3+2i)²+[2(i+1)(i+2)]² =[1+2(i+1)(i+2)]²	13²+84²=85²	15²+112²=113²
(4+4i)²+[(2i+1)(2i+3)]² =[2+(2i+1)(2i+3)]²	16²+63²=65²	20²+99²=101²
Nothing new here: 9²+12²=15² 15²+36²=39²	21²+72²=75²	27²+120²=123²

Add-On (with images)

Both perpendicular sides of any integer rectangle triangle have lengthes related by the following equation:

where N is an integer (check the following graph).

See also the proofs (with java).

Home.

Created by XEmacs.

MathML inside!