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(Math) Topology

 
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adedios
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Joined: 06 Jul 2005
Posts: 5060
Location: Angel C. de Dios

PostPosted: Sun Sep 24, 2006 7:10 am    Post subject: (Math) Topology Reply with quote






Science News
Week of Sept. 23, 2006; Vol. 170, No. 13

Euler's Bridges
Ivars Peterson

The East Prussian city of Königsberg (now part of Russia and known as Kaliningrad) straddles both banks of the River Pregel and an island, called Kneiphof, located right where the river divides into two branches. In the 18th century, seven bridges spanned various segments of the river, connecting different parts of the city.

These bridges were the subject of a well-known puzzle at the time: Could a person follow a path through the city that crosses each of the bridges only once, then returns to the starting point?

For the full article:

http://sciencenews.org/article.....thtrek.asp

*************************************************************

Questions to explore further this topic:

What is topology?

http://mcraefamily.com/MathHel.....sIntro.htm
http://pass.maths.org/issue10/.....index.html
http://www.questacon.edu.au/ht.....logy_.html
http://www.indiana.edu/~minimal/maze/topology.html
http://neil-strickland.staff.s.....urble.html
http://www.math.uwaterloo.ca/P.....logy.shtml
http://en.wikipedia.org/wiki/Topology
http://math.pepperdine.edu/kiga/topology.html

Leonard Euler and the Bridges of Königsberg

http://mathforum.org/isaac/problems/bridges1.html

What are the various topological types?

http://www.geom.uiuc.edu/zoo/toptype/

What are the building blocks for surfaces?

http://www.geom.uiuc.edu/zoo/features/

What is a torus?

http://www.mathsisfun.com/geometry/torus.html
http://www.geom.uiuc.edu/zoo/toptype/torus/
http://en.wikipedia.org/wiki/Torus

What is the volume of a torus?

http://whistleralley.com/torus/torus.htm

What is a maze?

http://www.gwydir.demon.co.uk/jo/maze/
http://www.rit.edu/~dbsgsh/MAZES1.pdf
http://en.wikipedia.org/wiki/Maze

What are the different types of mazes?

http://www.amazeingart.com/maz.....types.html

A short history of mazes

http://www.mazemaker.com/history_mazes.htm
http://plus.maths.org/issue14/features/budd/

Mazes and topology

http://plus.maths.org/issue14/.....index.html

Topology of the alphabet

http://britton.disted.camosun......rt_sol.pdf

Colors and Maps

http://www.sciencenewsforkids......se0202.asp

What is a Klein bottle?

http://www.kleinbottle.com/wha.....bottle.htm
http://en.wikipedia.org/wiki/Klein_bottle
http://www.geometrygames.org/TorusGames/
http://www.math.hmc.edu/~gu/cu.....klein.html

What is knot theory?

http://www.math.utah.edu/~best.....knots.html
http://www.c3.lanl.gov/mega-ma...../knot.html
http://www.42brghtn.mistral.co.....tmenu.html

What are flexagons?

http://www.aa42.com/Mathemagic.....exagon.htm
http://www.enarsson.nu/Flexagon/
http://math.dartmouth.edu/~lee.....xagon.html

What is the Euler characteristic?

http://www.math.utah.edu/~best.....euler.html

GAMES

http://www.questacon.edu.au/ht.....idges.html
http://rainydayplayhouse.net/alexwarp/alexwarp.htm
http://www.questacon.edu.au/ht.....uzzle.html
http://www.questacon.edu.au/ht.....mages.html
http://www.questacon.edu.au/html/mobius_strip.html
http://www.questacon.edu.au/ht.....clips.html
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