
USAP PAETE Discussion Forums for the people of Paete, Laguna, Philippines

View previous topic :: View next topic 
Author 
Message 
adedios SuperPoster
Joined: 06 Jul 2005 Posts: 5060 Location: Angel C. de Dios

Posted: Sat Sep 16, 2006 4:15 pm Post subject: (Math) Infinity 


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://wwwgroups.dcs.stand.a.....inity.html
http://www.firstscience.com/SI.....inity1.asp
The Archimedes Palimpsest
http://newsservice.stanford.e.....s116.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 

Back to top 


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

Posted: Sat Oct 06, 2007 10:08 am Post subject: A Prayer for Archimedes 


Week of Oct. 6, 2007; Vol. 172, No. 14
A Prayer for Archimedes
A longlost 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 

Back to top 


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

Posted: Sat Jan 12, 2008 6:26 am Post subject: Small Infinity, Big Infinity 


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 

Back to top 




You can post new topics in this forum You can reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot vote in polls in this forum

Powered by phpBB © 2001, 2005 phpBB Group
