h8 modems wrote:yeah meant surface area, sorry.
but still I just can't comprehend that.

Take a cube with a side length of x

The volume of the cube, V=x^3
The surface area of the cube, A=6x^3

On one side of the cube draw a square in the center that has a side length of x/2. Extend this square through the length of the cube to get an object of volume

Vo=[(x^2)/4]*x.

Remove this object from the cube. The volume of cube left is now

V-Vo=x^3-(x^3)/4.

But the surface area of the cube has changed to

A=6x^2 - (2x^2)/4 + (4x^2)/2 = 15x^2/2

So you can see that although the volume of the cube has decreased there has been an addition in surface area. Keep subtracting volumes, causing an increase in surface area and you get the idea. Sorry for the lack elegance.

Jon

steve wrote:Can anybody give me a concise description of Ramsey Number Theory?

It's simple, he just reduces incrementally from 12 to 1.

Josef K wrote:Surely it must have volume? There is solid matter in the structure, if you lowered it into water there would be displacement therefore indicating volume. No?

That picture is just a visual representation of a mathematical construct. When the pattern is extended to infinitesimally small volumes, the resulting total volume converges to zero and the resulting surface area approaches infinity. At least, that is my understanding of it.

Jon

stewie wrote:

steve wrote:Can anybody give me a concise description of Ramsey Number Theory?

It's simple, he just reduces incrementally from 12 to 1.

Good food? - Yes!
+
Expensive food? -Yes!
-
Punters in Glasgow unwilling to pay inflated 'celebrity' prices? - Yes!
=
Amarylis in liquidation.

Done!

Barbo wrote:

Josef K wrote:Surely it must have volume? There is solid matter in the structure, if you lowered it into water there would be displacement therefore indicating volume. No?

That picture is just a visual representation of a mathematical construct. When the pattern is extended to infinitesimally small volumes, the resulting total volume converges to zero and the resulting surface area approaches infinity. At least, that is my understanding of it.

Jon

Sounds similar in principle to Zeno's Achilles paradox, but with distance traveled replaced by total volume.

A little animation that shows the math behind a cardioid pattern.

Barbo wrote:

Josef K wrote:Surely it must have volume? There is solid matter in the structure, if you lowered it into water there would be displacement therefore indicating volume. No?

That picture is just a visual representation of a mathematical construct. When the pattern is extended to infinitesimally small volumes, the resulting total volume converges to zero and the resulting surface area approaches infinity. At least, that is my understanding of it.

Jon

Thanks Jon. You have just, and I'm happy to admit it, confirmed that this theory is beyond me. But if someone were to build the mathematical construct out of plywood, say, it would have volume, no?


only joking.

The cube infinity theory thing only works if you imagine it in a world where matter isn't built of measurable particles and subparticles that are limited to a finite smallness before they stop existing all together. It couldn't be constructed, it is just an exercise in the mathematics of infinity. That makes it cooler.

It is like how no two pieces of matter cannot actually touch because the space in between can be calculated into infinity.

Jack & Jill went up the hill to fetch a pail of water, god knows what happened up there, they came back with a daughter - is an old nursery rhyme. Summarizing: 1+1=3

8 = D