ramblings

Yesterday one of the Faisal residents showed me how to fold a simple rhombus out of a square piece of paper and then link several of these rhombi together to make various closed solids.

From my research, I have determined that it shouldn’t be too hard to put together a really big solid, but I am wondering how many rhombi are needed…

I gave the geometric solids to Gyosei, who provided the paper, and I don’t have pictures of them.

All of the geometric solids in my research are made of three sided pyramids. Each side of the pyramid is a regular right triangle, with the 90 degree angle at the top. At the apex of the pyramid, three 90 degree angles are formed by the edges.

The simplest one we could make is basically two three sided pyramids attached at their bases, for a six sided object made of right triangles. It requires 3 rhombi.

The next was a cube, which required 6 rhombi.

The next was a shape for which I don’t have a name. It required 12 rhombi.

The next required 30 rhombi.

What’s next?

3, 6, 12, 30, ?

Starting with a rectangular carpet measuring 9 by 12 units, we need to carpet a square room 10 by 10 units and a rectangular hallway 1 by 8 units.

The carpet may be cut into exactly three (3) pieces. One piece measuring 1 by 8. The other two (2) pieces must fit together to make a square 10 by 10.

This problem was presented to us when I was in trigonometry in high school. My instructor said he would give an A for the semester to anyone who could solve it. I knew a good deal when I saw it. I spent three days on the problem, solved it and coasted through the rest of the semester. He made good on his promise, but said he would never make such an offer again.

(thanks to Dude for correcting the original problem. Not 12 x 8…. 12 x 9!!)

Slashdot Math/Logic Riddles

The riddle about sorting coins without being able to see them seems impossible to me… I will ponder it.