# Alhazen's Billard Problem

1. Dec 29, 2004

### FulhamFan3

Alhazen Billiard Problem

I don't get why this problem is impossible with compass/straightedge construction.

I mean can't you draw a line bisecting the two points and where that line meets the circle is the point on the circle your looking for?

I'm probably understanding this problem wrong.

2. Dec 29, 2004

### dextercioby

It says right there on the page.It would imply extraction of cube root.It's the same as other problems in th history of mathematics and especially the trisection of an angle and the famous Delic problem,the one with the doubling of the cube.
Try searching for this problem to the referenced bibliography (the 3 books mentioned there).I'm sure you'll e given a plausible mathematically rigurous explnation.

Daniel.

3. Dec 29, 2004

### FulhamFan3

I know a cube root extraction is impossible with compass and straightedge. I'm arguing that it isn't necessary for this problem.

4. Dec 29, 2004

### dextercioby

On what grounds??Do you think the guy who posted this reason on 'wolfram' site was an imbecil??Or the guys who wrote the books he inspired from??Maybe so,but you'd better come up with something reliable instead of his bull****.

Daniel.

5. Dec 29, 2004

### Hurkyl

Staff Emeritus
Try it. (Make sure to set up an asymmetric problem so you don't get lucky!)

6. Dec 29, 2004

### Hurkyl

Staff Emeritus
Or maybe, just maybe, FulhamFan3 is trying to learn something? Please tone down your attitude.

7. Dec 29, 2004

### FulhamFan3

I figured out what I was doing wrong that would make my solution invalid. The site has no diagram showing what they did to get that formula. I had no idea how they came up with the formula and I came here to see if someone could explain it. The solution seemed obvious so i didn't see what the deal was. Thanks for not explaning anything and being a dick dex.

8. Dec 29, 2004

### Hurkyl

Staff Emeritus
Everything you need to know to get the formula, you learned in Algebra II! (really!)

Probably the easiest place to begin is to figure out how to express, algebraically, the notion that two chords of a circle are equal in length. You pick how to represent the lines algebraically.