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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,476

**Hi;**

**This problem was posted and solved in another thread by Fistfiz. **

**http://www.mathisfunforum.com/viewtopic … 75#p233175**

**We are given that ABCD is a square and P and Q are midpoints. We need the ratio of BEFG to ABCD.Let's see what can be done with geogebra.**

**1) Turn off the xy axes.**

**2) Use the regular polygon tool to draw the square ABCD. Label it as in the diagram below.**

**3) Use the midpoint tool to create points P and Q.**

**4) Use the line segment tool to draw AP,BP,CQ and BQ.**

**5) Use the intersect tool to create points E, F, and G.**

**6) Use the polygon tool and click on points B, E, F and G. Poly2 will be created.**

**7) Go into options and increase rounding to 15 digits.**

**8) Type in the input bar, n = poly2 / poly1.**

**9) Immediately in the Algebra pane you will see under the heading Number, n= .266666666666666...**

**This is the fraction 4 / 15 which you can guess at or take to Alpha.**

**9) Drag point D up and down to generate as many squares as you like. What do you notice about n? Stays the same, doesn't it? We are done with geogebra.**

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

Nice!

A couple of things:

- there's a bogus space between "poly" and "1" in 7)...I tripped myself up by being lazy and copy/pasted your input, which led to an error.

- your steps' numbering has two sixes.

Btw, Excel gives the fraction if you format the input cell in Excel as 'Fraction'.

And yes, you can drag D up and down for dimension changes - and all over the place for different orientations - and n stays the same.

"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: 86,476

Hi phrontister;

Sorry about the typos. Thanks for looking at the program.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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