Distance Functions - Objects distant and near from...

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Sites for teachers Sites for parents Terms of use Awards Interactive Activities CTK Exchange CTK Wiki Math CTK Insights - a blog What Is What Arithmetic/Algebra Geometry Probability Outline Mathematics Make an Identity Book Reviews Stories for Young Eye Opener Analog Gadgets Inventor's Paradox Did you know?. .. Proofs Math as Language Things Impossible Visual Illusions My Logo Math Poll Cut The Knot! MSET99 Talk Other Math sites Front Page Movie shortcuts Personal info Privacy Policy Guest book News sites Recommend this site Games to relax Sites for teachers Sites for parents G o o g l e Web CTK Search Attention: A once a year event! The Third Millennium International Mathematical Olympiad will take place on Sunday, 1 March, 2009 from 4-7 p.m. (EST) Join nearly one million students from more than 50 countries that participated in the Olympiad since its inception in 2001. The 9th Olympiad is completely online. Completely free. For grades 5 to 12. Check the details . Just think of this. One thousand years ago a person of a completely different culture conceived a notion that would probably be endorsed today by nearly every one. Physical proximity is unfortunately often not a reflection of moral or intellectual proximity. Are we any different from those born in the distant past of one thousand years ago? You do feel quite close and involved when they share their thoughts and emotions with you, do not you? Well, by now you are probably near wondering whether a discussion on human nature is a sensible topic for a mathematical page. Have I strayed too far from the topic I want to discuss? I plan to discuss the mathematical notion of distance. You may or may not remember that the most customary notion of the distance is somehow related to the Pythagorean Theorem. But having read the introduction you won't be surprised to learn that mathematicians study other distances as well. However, once they realized what is actually important about the notion of distance, they managed to distill its three most significant properties. These are the axioms of distance. A function dist(A,B) of two variables defined on a set ( Metric Space ) M is called a distance (between A and B), provided Let's consider several examples. 1. M = R, the set of all real numbers. dist(a, b) = |a - b|, where
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This note was uploaded on 05/04/2011 for the course MATH 73 taught by Professor Danberwick during the Spring '09 term at University of California, Berkeley.

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Distance Functions - Objects distant and near from...

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