Pythagorean Theorem
The Pythagorean Theorem is used to find the missing length of a side of a right triangle.
Here are some pythagorean triplets, or sides to right triangles:
| (3,4,5) | (5,12,13) | (7,24,25) | (8,15,17) | (9,40,41) |
| (11,60,61) | (12,35,37) | (13,84,85) | (15,112,113) | (16,63,65) |
| (17,144,145) | (19,180,181) | (20,21,29) | (20,99,101) | (21,220,221) |
| (23,264,265) | (24,143,145) | (25,312,313) | (27,364,365) | (28,45,53) |
| (28,195,197) | (29,420,421) | (31,480,481) | (32,255,257) | (33,56,65) |
| (33,544,545) | (35,612,613) | (36,77,85) | (36,323,325) | (37,684,685) |
| (39,80,89) | (39,760,761) | (40,399,401) | (41,840,841) | (43,924,925) |
| (44,117,125) | (44,483,485) | (48,55,73) | (48,575,577) | (51,140,149) |
| (52,165,173) | (52,675,677) | (56,783,785) | (57,176,185) | (60,91,109) |
| (60,221,229) | (60,899,901) | (65,72,97) | (68,285,293) | (69,260,269) |
| (75,308,317) | (76,357,365) | (84,187,205) | (84,437,445) | (85,132,157) |
| (87,416,425) | (88,105,137) | (92,525,533) | (93,476,485) | (95,168,193) |
| (96,247,265) | (100,621,629) | (104,153,185) | (105,208,233) | (105,608,617) |
| (108,725,733) | (111,680,689) | (115,252,277) | (116,837,845) | (119,120,169) |
| (120,209,241) | (120,391,409) | (123,836,845) | (124,957,965) | (129,920,929) |
| (132,475,493) | (133,156,205) | (135,352,377) | (136,273,305) | (140,171,221) |
| (145,408,433) | (152,345,377) | (155,468,493) | (156,667,685) | (160,231,281) |
| (161,240,289) | (165,532,557) | (168,425,457) | (168,775,793) | (175,288,337) |
| (180,299,349) | (184,513,545) | (185,672,697) | (189,340,389) | (195,748,773) |
| (200,609,641) | (203,396,445) | (204,253,325) | (205,828,853) | (207,224,305) |
| (215,912,937) | (216,713,745) | (217,456,505) | (220,459,509) | (225,272,353) |
| (228,325,397) | (231,520,569) | (232,825,857) | (240,551,601) | (248,945,977) |
| (252,275,373) | (259,660,709) | (260,651,701) | (261,380,461) | (273,736,785) |
| (276,493,565) | (279,440,521) | (280,351,449) | (280,759,809) | (287,816,865) |
| (297,304,425) | (300,589,661) | (301,900,949) | (308,435,533) | (315,572,653) |
| (319,360,481) | (333,644,725) | (336,377,505) | (336,527,625) | (341,420,541) |
| (348,805,877) | (364,627,725) | (368,465,593) | (369,800,881) | (372,925,997) |
| (385,552,673) | (387,884,965) | (396,403,565) | (400,561,689) | (407,624,745) |
| (420,851,949) | (429,460,629) | (429,700,821) | (432,665,793) | (451,780,901) |
| (455,528,697) | (464,777,905) | (468,595,757) | (473,864,985) | (481,600,769) |
| (504,703,865) | (533,756,925) | (540,629,829) | (555,572,797) | (580,741,941) |
| (615,728,953) | (616,663,905) | (696,697,985) |
Do you notice any patterns?
Knowing what the pythagorean theorem is can help you in many ways. If can help you find distances between two points, it can help you find the height of things in the sky, or how far you are away from something.
Proofs you can do yourself to show you how the Theorem works.