Thread: Zeus' altar.

Make Zeus' altar double as big using equal parts of it enclosing a hollow altar of the original. What I have so far is-
Where a equals the divisor of a cube, so that if a = 2, the cube is divided into 8 parts, more straightforward that a is the number of squares along a side:

6a^2 + 12a + 8

A phrase in it which you will probably use in it. I have a lightning bolt of a headache and can't finish it.

What? Let's guess Mr. Zeus has a cubic alter?

If the original has volume a^3, the new one will need volume b^3 - a^3 = 2a^3 for some b. A little algebra suggests b^3 = 3a^3, which probably could have been guessed.

What's the answer? How many times do you have to divide a cube to form another one around the former? It's somewhere between 7 and 8.

Originally Posted by Zeus

Make Zeus' altar double as big using equal parts of it enclosing a hollow altar of the original. What I have so far is-
Where a equals the divisor of a cube, so that if a = 2, the cube is divided into 8 parts, more straightforward that a is the number of squares along a side:

6a^2 + 12a + 8

A phrase in it which you will probably use in it. I have a lightning bolt of a headache and can't finish it.

Your wording is almost as obscure as that of Apollo. If you mean divide the original cubical altar into equal sub-cubes such that they can be reassembles into an altar who's enclosed volume is double that of the original we would have



where is the side of the new alter and the side of the original. But this is imposible since would have to be an rational multiple of and so imply that is rational

CB

I'm sorry. It would work if rectangle sided shapes were used. Then a decimal divisor could be used. Can you get that?

Originally Posted by Zeus

I'm sorry. It would work if rectangle sided shapes were used. Then a decimal divisor could be used. Can you get that?

No if the altar is a cube the volume of the big altar built from congruent bricks produced by a dissection of the original alter must always be a rational multiple of the volume of the original altar, but it is not.

CB