Sparks of Genius has a lot of challenges for the imagination. What geometrical figure has a circular cross section and a square cross section? Circular, square, and triangular cross sections?
We talked about 3D objects being square from one side and circle from the other—for example a cylinder. But he rejected this approach (though he was able to visualize the form). He considered taking circle and square apart and putting it back together into something like a rounded square but rejected that too as neither square nor circle.
My guess is that your son doesn’t have a solid grasp of the idea of a cross section. Actually, I don’t quite feel good about a cylinder having a square cross section. It’s as though it’s wrong to neglect the idea that a cylinder is round.
Actually, I don’t quite feel good about a cylinder having a square cross section.
Consider a square in front of you with its edges horizontal and vertical. (Say, drawn on your monitor.) Then consider the line running from the top of the square to the bottom of the square that passes through the center of the square. What happens when you rotate the square around that line?
That was also my first impression. But we talked about it a bit longer. I think it clicked when he mentioned how he looked (in imagination) at the form such that the top becomes a straight line (like looking a paper from the side) and the same with the bottom.
Sparks of Genius has a lot of challenges for the imagination. What geometrical figure has a circular cross section and a square cross section? Circular, square, and triangular cross sections?
That book looks interesting. Added it to my wish list. Here is a summary: http://vnthomas1.blogspot.de/2009/06/sparks-of-genius-13-thinking-tools-of.html
We talked about 3D objects being square from one side and circle from the other—for example a cylinder. But he rejected this approach (though he was able to visualize the form). He considered taking circle and square apart and putting it back together into something like a rounded square but rejected that too as neither square nor circle.
My guess is that your son doesn’t have a solid grasp of the idea of a cross section. Actually, I don’t quite feel good about a cylinder having a square cross section. It’s as though it’s wrong to neglect the idea that a cylinder is round.
Consider a square in front of you with its edges horizontal and vertical. (Say, drawn on your monitor.) Then consider the line running from the top of the square to the bottom of the square that passes through the center of the square. What happens when you rotate the square around that line?
That was also my first impression. But we talked about it a bit longer. I think it clicked when he mentioned how he looked (in imagination) at the form such that the top becomes a straight line (like looking a paper from the side) and the same with the bottom.
I think your link didn’t happen correctly.
Thanks for letting me know.