Fox 334

This is more like a google search than a geometry problem, but it is nice to have a reference in our blog as well. Good luck to those who want to try!

http://www.8foxes.com/

Fox 306 - Solution

To see the animation below, you will need any of the following browsers:
Chrome, Firefox, Opera, Safari, or IE Explorer 9.0.

Bleaug converts Fox 306 to Fox 302 by "folding" twice. I have seen translation, rotation, similarity, etc., but haven't seen anything like this before. Enjoy and please do respect to human intelligence!

Fox 302 - Solution

To see the animation below, you will need any of the following browsers:

Chrome, Firefox, Opera, Safari, or IE Explorer 9.0.

Bleaug teases the human intelligence, saying:

"I know that analytic solution to this Fox 302 is obvious (although cumbersome). Here is an alternative geometric demonstration. Use Home/PageUp/PageDown/End keys/ or mouse wheel to go though demo steps."

Do enjoy!

Fox 306

Answer is not confirmed yet.

http://www.8foxes.com/

Fox 160 - Solutions

Three distinct solutions were found for Fox 160.

The solution commented out by Julian deserves to be presented here. We often had questions inspired from the "things" we observe around us. Julian's solution is the other way. It uses a very casual observation from real-life for the solution. That's perspective lines converge linearly. See the solution below:
by Julian: This one has a simple, intuitive proof. Imagine a long, hollow square-prism. Something like a cardboard tube with a square cross-section. Imagine lines connecting the diagonally-opposite corners of the opposite ends. Due to the symmetry of the tube these four lines will meet at a single point half-way along it.

Now imagine looking through the tube from one end to the other. You see two squares: a large square at the near end, and a smaller square at the far end. By subtly changing the direction the tube is pointing, the far square may move off centre so that the construction looks like the problem diagram. This will not alter the fact that the four lines meet at a single point. QED!

Analytic Geometry by Bob Ryden:

Observe that proving DH implies CG as well (due to rotation). Neat!

Similarity of Triangles by Giannno:

http://www.8foxes.com/

Fox 299

http://www.8foxes.com/

Fox 155

Fox 162

http://www.8foxes.com/

Fox 161

Thy heart yearns to fly in the heavens,
Yet there are knots pulling thou,
to the darketh corners.
- Ninja fox

Fox 160

http://www.8foxes.com/

Fox 158

http://www.8foxes.com/Home/158

Fox 153

Think simple.
Math has nothing to do with numbers.
Try to see the connections.

http://www.8foxes.com/Home/153

Fox 116

Uniqueness!
Uniqueness!
Whole universe is crying out for uniqueness.
Once you see it,
you'll forget your uniqueness.
http://www.8foxes.com/

Fox 114

Simple, elegant.