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(Math) Infinity

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

PostPosted: Sat Sep 16, 2006 4:15 pm    Post subject: (Math) Infinity Reply with quote






Week of Sept. 16, 2006; Vol. 170, No. 12

Touring the Poles
Ivars Peterson

A classic brainteaser concerns a hunter out to bag a bear. The hunter walks 1 mile south. He then turns left and walks 1 mile east, then turns left again and walks 1 mile north. He ends up back where he started and spots a bear. What color is the bear?

The obvious answer is "white." If you're at the North Pole and you go south along any meridian, turn left and go 1 mile east along a circle of latitude, then 1 mile north, you end up where you started. And you're more likely to find a polar bear there than any other kind.

But, if you ignore the requirement of seeing a bear, there are infinitely many possible solutions—if you look for additional starting points near the South Pole. The South Pole itself isn't a solution because the only direction in which you can go to start with is north.

In fact, there is "an infinity of infinitely many solutions," Eli Maor of Loyola University Chicago points out in the September issue of Math Horizons. "And this is in addition to the one obvious solution, the North Pole."

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

Questions to explore further this topic:

Brain Teaser: The Hunter and the Bear

http://www.metacafe.com/watch/....._the_bear/

1. Walking in Circles
Taken from:

http://www.automationnotebook......_2005.html

A classic puzzle describes the hunter who walks a mile south, turns and walks a mile east, turns again and walks a mile north. He is surprised to find himself right back where he started. He then shoots a bear. What color is the bear? The answer is usually given as “white”, because the hunter must have started his 3 mile walk at the North Pole. Can you find some other places on the globe where you could follow those same directions and end up at your starting point?
Hint: No polar bears near any of those places!

SOLUTION:

Walking in Circles Other than at the north pole, there are quite a few other places on the globe where you can walk a mile south, a mile east, a mile north, and be back where you started. For example: If you were 1.159 miles north of the south pole (anywhere on that circle), then when you walk the one mile south you would be 0.159 mile from the pole. This is exactly the right distance (radius) from the pole, so that your "one mile east" trek will take you exactly once around the pole. Then, of course, when you turn and walk your "one mile north" you will be retracing your steps from the first leg of your journey. Now consider starting at 1.08 miles north of the south pole. This would offer you the opportunity to loop the south pole twice before retracing your steps. These distances are an interesting progression. 1.159 is more accurately 1 plus (1 over 2pi). 1.08 is 1 plus (1 over 4pi), the list goes on for 3 trips around the pole, start at 1 + (1 over 6pi) miles, and so forth. For each of these distances from the south pole,technically there are an infinite number of starting points along the circle. But you won't see any bears this close to the south pole!


What is infinity?

http://www.solipsys.co.uk/new/.....athematics
http://www.bbc.co.uk/radio4/sc.....ers5.shtml
http://mathforum.org/dr.math/f.....mbers.html
http://www.math.cornell.edu/~a.....tynew.html
http://www.csmonitor.com/class.....ep2402.pdf
http://en.wikipedia.org/wiki/Infinite

Is there really such a thing as "infinity"?

http://www.math.toronto.edu/ma.....inity.html

What is this thing we call infinity: A view from cognitive science

http://cogsci.ucsd.edu/~batali/cogsci1/nunez.pdf

History of Infinity

http://www.npr.org/templates/s.....Id=1464156
http://www.mathacademy.com/pr/...../index.asp
http://www-groups.dcs.st-and.a.....inity.html
http://www.firstscience.com/SI.....inity1.asp

The Archimedes Palimpsest

http://news-service.stanford.e.....s-116.html

Infinity: A class activity

http://www.heartofmath.com/fir.....m_Ch03.pdf

Working with Infinity:
A Mathematical Perspective


http://www.pbs.org/wgbh/nova/a.....inity.html

Contemplating Infinity:
A Philosophical Perspective


http://www.pbs.org/wgbh/nova/a.....ating.html
http://www.colostate.edu/Colle.....finity.pdf

Infinite Secrets (NOVA)

http://www.pbs.org/wgbh/nova/archimedes/

GAMES

http://www.niehs.nih.gov/kids/brnumber.htm
http://www.funbrain.com/brain/.....Brain.html
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adedios
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Joined: 06 Jul 2005
Posts: 5060
Location: Angel C. de Dios

PostPosted: Sat Oct 06, 2007 10:08 am    Post subject: A Prayer for Archimedes Reply with quote

Week of Oct. 6, 2007; Vol. 172, No. 14

A Prayer for Archimedes

A long-lost text by the ancient Greek mathematician shows that he had begun to discover the principles of calculus.

Julie J. Rehmeyer

For seventy years, a prayer book moldered in the closet of a family in France, passed down from one generation to the next. Its mildewed parchment pages were stiff and contorted, tarnished by burn marks and waxy smudges. Behind the text of the prayers, faint Greek letters marched in lines up the page, with an occasional diagram disappearing into the spine.

For the full article:

http://sciencenews.org/article.....thtrek.asp
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adedios
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Joined: 06 Jul 2005
Posts: 5060
Location: Angel C. de Dios

PostPosted: Sat Jan 12, 2008 6:26 am    Post subject: Small Infinity, Big Infinity Reply with quote

Week of Jan. 12, 2008; Vol. 173, No. 2

Small Infinity, Big Infinity
Infinity can be big or bigger, countable or not
Julie J. Rehmeyer

Infinity is bigger than any number. But saying just how much bigger is not so simple. In fact, infinity comes in infinitely many different sizes—a fact discovered by Georg Cantor in the late 1800s.

For the full article:

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