What is Pythagorean triplet
Answers
Answer:
A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Such a triple is commonly written, and a well-known example is. If is a Pythagorean triple, then so is for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime.
Answer:
A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule:
a2 + b2 = c2
Example: The smallest Pythagorean Triple is 3, 4 and 5.
Let's check it:
32 + 42 = 52
Calculating this becomes:
9 + 16 = 25
Yes, it is a Pythagorean Triple!
Triangles
Pythagoras
When a triangle's sides are a Pythagorean Triple it is a right angled triangle.
pythagoras squares a^2 + b^2 = c^2
See Pythagoras' Theorem for more details.
Example: The Pythagorean Triple of 3, 4 and 5 makes a Right Angled Triangle:
triangle 3 4 5
triangle 3 4 5 lego
Here are two more Pythagorean Triples:
5, 12, 13 9, 40, 41
5, 12, 13 Triangle 9, 40, 41 Triangle
52 + 122 = 132 92 + 402 = 412
25 + 144 = 169 (try it yourself)
And each triangle has a right angle!
List of the First Few
Here is a list of the first few Pythagorean Triples (not including "scaled up" versions mentioned below):
(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) ... infinitely many more ...
Scale Them Up
The simplest way to create further Pythagorean Triples is to scale up a set of triples.
Example: scale 3, 4, 5 by 2 gives 6, 8, 10
Which also fits the formula a2 + b2 = c2:
62 + 82 = 102
36 + 64 = 100
If you want to know more about them read Pythagorean Triples - Advanced
Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10
Pythagoras Theorem
Right Angled triangles
Pythagorean Triples - Advanced
Triangles
Proof that a Triangle has 180°
Step-by-step explanation: