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

Graphical analogs of 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:

Equation Image.

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

GNUPLOT graph.

See also the proofs (with java).


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