Alhazen's Billard Problem: Solving a Geometric Puzzle with Algebra

  • Thread starter FulhamFan3
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In summary, the Alhazen Billiard Problem involves constructing a line that bisects two given points on a circle using only a compass and straightedge. However, this is impossible to do due to the extraction of cube root, similar to other problems in the history of mathematics. The argument arises whether or not this extraction is necessary for the problem. Additionally, it is suggested to search for explanations in the referenced bibliography and to use knowledge from Algebra II to understand the problem.
  • #1
FulhamFan3
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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.
 
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  • #2
FulhamFan3 said:
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.

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
I know a cube root extraction is impossible with compass and straightedge. I'm arguing that it isn't necessary for this problem.
 
  • #4
FulhamFan3 said:
I know a cube root extraction is impossible with compass and straightedge. I'm arguing that it isn't necessary for this problem.

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
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?

Try it. (Make sure to set up an asymmetric problem so you don't get lucky!)
 
  • #6
On what grounds?

Or maybe, just maybe, FulhamFan3 is trying to learn something? Please tone down your attitude.
 
  • #7
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
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.
 

FAQ: Alhazen's Billard Problem: Solving a Geometric Puzzle with Algebra

What is Alhazen's Billard Problem?

Alhazen's Billard Problem is a mathematical problem that involves finding the path of a billiard ball bouncing off the walls of a rectangular billiard table with no pockets.

Who was Alhazen?

Alhazen, also known as Ibn al-Haytham, was a renowned Arab scientist and mathematician who lived in the 10th and 11th centuries. He is often referred to as the father of optics and is credited with making significant contributions to the fields of mathematics, physics, and astronomy.

What is the main goal of Alhazen's Billard Problem?

The main goal of Alhazen's Billard Problem is to determine the ideal placement of a billiard ball on a billiard table so that it will pass through a specific point after a certain number of bounces.

Why is Alhazen's Billard Problem significant?

Alhazen's Billard Problem is significant because it is considered to be one of the earliest examples of a mathematical optimization problem. It also demonstrates the connection between mathematics and real-world applications, such as billiards and optics.

What are some real-world applications of Alhazen's Billard Problem?

Alhazen's Billard Problem has been used to design solar panels, create efficient lighting systems, and develop more accurate satellite imaging techniques. It also has applications in game theory and computer graphics.

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