Monday, September 27, 2010
Tuesday, September 21, 2010
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.
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!
Thursday, September 16, 2010
Tuesday, September 7, 2010
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!
Monday, August 23, 2010
Friday, August 6, 2010
Fox 305
Yet again,
try to see the goodness,
see the beauty,
surrounding you.
Forget about the numbers, summations, subscripts.
Leave behind the accounts, stocks, papers, statistics.
Just leave yourselves to the arms of an ocean,
full of love and compassion.
Drift away with the blowing wind...
-- Dervish Fox
Monday, August 2, 2010
Fox 54 - Discussion
Bob Ryden provided a solution below. This has been the first attempt to solve this fox. His solution has not been confirmed yet, but it is published here to start the discussion. Wanna say somethin', comment it out!
Let the radius of the spheres = 1.
Inside is a tetrahedron whose vertices are the centers
of the spheres. Its edge length = 2
and its volume = (1/8) √3
On each face of the tetrahedron, build a triangular prism.
Volume of each prism = (1/2) 2 (√3) 1
Total volume of four prisms = 4√3
On each edge of the tetrahedron, build a cylindrical sector.
The angle of the sector = 360 – 90 – 90 – dihedral angle of the tetrahedron
= 360 – 90 – 90 – arccos (1/3) = approx. 109.47°
Length of each cylindrical sector = 2, radius = 1
Total volume of the six sectors
Finally, there are pieces of the four original spheres that are not covered by any of the above. The four pieces together make one complete sphere, V = (4/3)π.
Total volume is the sum
tetrahedron + 4 prisms + 6 cylindrical sectors + sphere
= approx. 23.52
Inside is a tetrahedron whose vertices are the centers
of the spheres. Its edge length = 2
and its volume = (1/8) √3
On each face of the tetrahedron, build a triangular prism.
Volume of each prism = (1/2) 2 (√3) 1
Total volume of four prisms = 4√3
On each edge of the tetrahedron, build a cylindrical sector.
The angle of the sector = 360 – 90 – 90 – dihedral angle of the tetrahedron
= 360 – 90 – 90 – arccos (1/3) = approx. 109.47°
Length of each cylindrical sector = 2, radius = 1
Total volume of the six sectors
= 6 π (1^2) 2 (109.47 / 360) ≈ 11.46
Finally, there are pieces of the four original spheres that are not covered by any of the above. The four pieces together make one complete sphere, V = (4/3)π.Total volume is the sum
tetrahedron + 4 prisms + 6 cylindrical sectors + sphere
= approx. 23.52
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