May 02, 2006

1 equals 2


Albert Eistein once said, "The only thing that interferes with my learning is my education." That's the buga-boo.

My students did not believe me when I told them that, using Algebra, I could prove that 1 equals 2.

Picking up a stubby piece of chalk, I aproached the black board and scrawled the proof below. Then I asked the students to consider each step very carefully.


I challenged them to prove me wrong. Can you?

Posted by roadapples at 12:04 PM | Comments (10)

April 30, 2006

rubik's cube


While at the teacher store yesterday, I happened upon a toy that I had not played with since my youth. It is a puzzle that filled with me great frustration at the time. I never could solve the cube and I swore I would never play with the damn thing again. What became of it is a mystery to me now.

I took the multicolored cube down from the shelf and studied it. At $10.99, the price had quadrupled over the years. The sticker on the outside of the box indicated that this was the twenty fifth-year anniversary edition. I wonder how many are sitting in landfills discarded over the years. I bought it. Took it home. My daughter promptly twisted it till there were no two adjacent facelets that matched then handed it to me.

I worked till almost midnight with the blasted thing. I followed the directions on the folded up paper with the tiny font that came with it. I came close several times but each time it would get the best of me.

I found one mistake in the directions right away. In Step One, the third sentence refers to a blue-green edge. It should say yellow-green. After I found that, I had trouble trusting the rest of the steps.

Turning to my trusty Mac, I did a Google for solutions to the cube. I found 50,000 entries. They were all more confusing than the instructions that came with it but I did find out that, with 10,000 hours of practice, I could eventual solve the cube in a blazing 12 seconds. Somehow I don't see that happening. That much time would certainly put a crimp in my naptime.

This morning, I gave it another go. I was wide-awake and alert. The instructions started to make sense. In an hour I had it solved. I can now rest knowing that I too have mastered the mysterious cube. Why I can do this in two days at the age of 60 when I could never seem to do it at 30, is also a mystery.

The number of websites with bragging rights to Rubik's Cube is now 50,001.

If you need help solving your cube, check out this site. I did not find it until after I solved my cube so I did not need to use It. But it looks interesting. If you try it, let me know if the site is useful.

In case you lost your copy of the sloution that came with the rubic cube, here they are:
page 1
page 2
page 3

Posted by roadapples at 08:05 AM | Comments (5)