Proof geometrically that QX and QY are the roots

In summary, the conversation discusses the meaning of QX and QY being roots, how to prove their validity using geometric principles, the relationship between geometric proofs and algebraic proofs, using various geometric principles to prove the roots, and the importance of using both geometric and algebraic proofs for a comprehensive understanding of a mathematical concept.
  • #1
raphael3d
45
0
http://img717.imageshack.us/img717/4...10106at123.png

its a construction from felix klein, around 1900. it should be made without trigonometric functions or complex algebra etc.

the ratios of lengths should be sufficient, but i have only found one similar triangle and then i got stuck.

but is the best strategy to show that the lengths QX and QY are the roots?
 
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  • #2
That is a broken link.
 
  • #3
excuse me sir, here is a the working link:

http://img717.imageshack.us/img717/4029/screenshot20110106at123.png

thank you
 
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FAQ: Proof geometrically that QX and QY are the roots

What does it mean for QX and QY to be the roots?

When we say that QX and QY are the roots, it means that they are the solutions to a given equation or problem. In this case, they are the values that make the equation true when substituted in for the variable.

How can we prove geometrically that QX and QY are the roots?

Geometric proofs involve using visual representations, such as diagrams or shapes, to demonstrate the validity of a statement or equation. In this case, we can use geometric principles, such as the Pythagorean Theorem, to show that QX and QY satisfy the equation and thus are the roots.

What is the relationship between geometric proofs and algebraic proofs?

Geometric proofs and algebraic proofs are both methods of proving mathematical statements. Geometric proofs use visual representations, while algebraic proofs use equations and symbols. They can often be used together to provide a more complete understanding of a mathematical concept.

Can we use any geometric principle to prove that QX and QY are the roots?

Yes, there are a variety of geometric principles that can be used to prove that QX and QY are the roots. Some common ones include the Pythagorean Theorem, properties of similar triangles, and the Law of Cosines. The specific principle used will depend on the given equation or problem.

Why is it important to use both geometric and algebraic proofs?

Using both geometric and algebraic proofs allows for a more thorough understanding of a mathematical concept. Geometric proofs provide a visual representation, helping to visualize and understand the problem, while algebraic proofs provide a more rigorous and formal approach to proving the statement. Together, they provide a comprehensive understanding of the concept.

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