Triangular number and Pythagorean triple: Difference between pages

Latest revision as of 13:38, 30 March 2017

In mathematics, a Pythagorean triple is a set of three positive integers which satisfy the equation (make the equation work):

[math]\displaystyle{ x^2 + y^2 = z^2 }[/math]

This equation is known as the Diophantine equation, and is related to Pythagoras' theorem. The lowest Pythagorean triple is [3, 4, 5] because:

[math]\displaystyle{ 3^2 + 4^2 = 9 + 16 = 25 = 5^2 }[/math]

So, [math]\displaystyle{ 3^2 + 4^2 = 5^2 }[/math]

The next highest triple is [5, 12, 13] then [7, 24, 25], and so on. There is an infinite number of Pythagorean triples.

A Pythagorean Triple always consists of:

• all even numbers, or

• two odd numbers and an even number.

A Pythagorean Triple can never be made up of all odd numbers or two even numbers and one odd number.

Template:Math-stub

no:Pythagoras’ læresetning#Pytagoreiske tripler

@@ Line 1: / Line 1: @@
-[[File:Triangular number 10 as sum of gnomons.svg|thumb|Ten pebbles arranged into a triangle]]
+In [[mathematics]], a '''Pythagorean triple''' is a set of three [[Positive number|positive]] [[integer|integers]] which satisfy the [[equation]] (make the equation work):
-A '''triangular number''' is a number that is the sum of all of the [[natural number]]s up to a certain number. For example, 10 is a triangular number because {{math|1=1 + 2 + 3 + 4 = 10}}.                                   The first [[25 (number)|25]] triangular numbers are:1, 3, 6, 10, 15, 21,  28, 36, 45, 55, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, and 351.
+:<math>x^2 + y^2 = z^2</math>
+This equation is known as  the [[Diophantine equation]], and is related to [[Pythagoras' theorem]].
+The lowest '''Pythagorean triple''' is [3, 4, 5] because:
+:<math>3^2 + 4^2 = 9 + 16 = 25 = 5^2</math>
+: So, <math>3^2 + 4^2 = 5^2</math>
+The next highest triple is [5, 12, 13] then [7, 24, 25], and so on.
+There is an [[infinite]] number of Pythagorean triples.
-A triangular number is calculated by the equation:
+A Pythagorean Triple always consists of:
-<math>\frac{n(n+1)}{2}</math>  .
+•	all even numbers, or
+•	two odd numbers and an even number.
+A Pythagorean Triple can never be made up of all odd numbers or two even numbers and one odd number.
 {{math-stub}}
-[[Category:Integer sequences]]
+[[Category:Mathematics]]
+[[no:Pythagoras’ læresetning#Pytagoreiske tripler]]

Triangular number and Pythagorean triple: Difference between pages

Latest revision as of 13:38, 30 March 2017

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