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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

This problem was posed in another thread:

Three runners start on the same spot of a circular track. They are called B,C and D. The ratio of their speeds is 3:5:7 respectively. We assume a constant speed around the track and they run in a clockwise fashion.

How many times will C and D lap B before they all meet up at the same point? Where is this first point of triple intersection?

Let's solve as best we can it using no math or programming, just with geogebra.

1)Use the circle with radius tool to draw a circle with the center at the origin and with a radius of 5. Color it a light brown.

2)Put 3 points on the circle called B,C and D.

3) Color them and enlarge to size 5.

4) Set the Algebra pane in object properties of B to

Cartesian coordinates.

increment .05

speed .3

repeat decreasing

5) Set the Algebra pane in object properties of C to

Cartesian coordinates.

increment .05

speed .5

repeat decreasing

6) Set the Algebra pane in object properties of D to

Cartesian coordinates.

increment .05

speed .7

repeat decreasing

7)Drag B,C and D to coordinates (0,5) and now hide the axes. Get this as accurate as possible by dragging or inputting the values. All 3 points should appear as one.

8)In the algebra pane select B,C and D, right click and click animation on.

The picture below shows that a triple intersection is about to occur at 180° from the start position. How many times did someone lap someone else?

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Hi Bobby,

A nice graphical solution method!

*Last edited by phrontister (2012-02-04 02:12:17)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Hi phrontister;

Very good! Glad you liked it. Did you see what we did with it over here:

http://www.mathisfunforum.com/viewtopic … 91#p200691

Post #1253

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Hi Bobby,

Yes, I saw the posts about this puzzle there.

Other than referring to a hair style I didn't know what 'braids' meant, and so I looked it up.

When I read some of the blurb about 'braid theory' my eyes glazed over and my brain went into a deep trance, but luckily just before it was too late to revive me my cuckoo clock went berserk and woke me up!

I'm much wiser now and was happy just to play Geogebra.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

A's comments are my own thoughts on the mathematical and scientific community in general. Play with geogebra and you will be way ahead of him.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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