Triangular inequality - Revision history

DavidB4-bot: /* top */Spelling/Grammar Check & Cleanup, typos fixed: smaller then → smaller than

2016-09-20T05:49:04Z

top: Spelling/Grammar Check & Cleanup, typos fixed: smaller then → smaller than

JonathanG: dead-end fix

2009-06-27T17:17:24Z

dead-end fix

Sunda62: fix category name

2009-06-10T17:06:54Z

fix category name

JY23: cat

2009-04-26T01:05:00Z

cat

Sunda62: stub

2009-04-16T02:36:10Z

stub

New page

In a triangle ABC, any side is smaller then the sum of the other two sides. However, if the three points are aligned, then there may be equality, but it's never possible that ''AC'' > ''AB'' + ''BC''.

This generalizes in mathematics to the '''triangle inequality''': in a space where the notion of distance between two points (''d(x,y)'') is defined, the following inequality must hold:
: <math>\forall x,y,z, d(x,z) \le d(x,y) + d(y,z)\,</math>

← Older revision		Revision as of 05:49, September 20, 2016
Line 1:		Line 1:
−	In a [[triangle]] ABC, any side is smaller ~~then~~ the sum of the other two sides. However, if the three points are aligned, then there may be equality, but it's never possible that ''AC'' > ''AB'' + ''BC''.	+	In a [[triangle]] ABC, any side is smaller than the sum of the other two sides. However, if the three points are aligned, then there may be equality, but it's never possible that ''AC'' > ''AB'' + ''BC''.

	This generalizes in mathematics to the '''trianglar inequality''': in a space where the notion of distance between two points (''d(x,y)'') is defined, the following inequality must hold:		This generalizes in mathematics to the '''trianglar inequality''': in a space where the notion of distance between two points (''d(x,y)'') is defined, the following inequality must hold:

@@ Line 1: / Line 1: @@
-In a triangle ABC, any side is smaller then the sum of the other two sides. However, if the three points are aligned, then there may be equality, but it's never possible that ''AC'' > ''AB'' + ''BC''.
+In a [[triangle]] ABC, any side is smaller then the sum of the other two sides. However, if the three points are aligned, then there may be equality, but it's never possible that ''AC'' > ''AB'' + ''BC''.
-This generalizes in mathematics to the '''triangle inequality''': in a space where the notion of distance between two points (''d(x,y)'') is defined, the following inequality must hold:
+This generalizes in mathematics to the '''trianglar inequality''': in a space where the notion of distance between two points (''d(x,y)'') is defined, the following inequality must hold:
 : <math>\forall x,y,z, d(x,z) \le d(x,y) + d(y,z)\,</math>
 [[Category:Mathematics]]

← Older revision		Revision as of 17:06, June 10, 2009
Line 4:		Line 4:
	: <math>\forall x,y,z, d(x,z) \le d(x,y) + d(y,z)\,</math>		: <math>\forall x,y,z, d(x,z) \le d(x,y) + d(y,z)\,</math>

−	[[Category:~~Math~~]]	+	[[Category:Mathematics]]

← Older revision		Revision as of 01:05, April 26, 2009
Line 3:		Line 3:
	This generalizes in mathematics to the '''triangle inequality''': in a space where the notion of distance between two points (''d(x,y)'') is defined, the following inequality must hold:		This generalizes in mathematics to the '''triangle inequality''': in a space where the notion of distance between two points (''d(x,y)'') is defined, the following inequality must hold:
	: <math>\forall x,y,z, d(x,z) \le d(x,y) + d(y,z)\,</math>		: <math>\forall x,y,z, d(x,z) \le d(x,y) + d(y,z)\,</math>
		+
		+	[[Category:Math]]