Is a ball a one sided dice or an infinite sided dice?

I get what you're saying now. :2thumbsup:

 

for shits and giggles

3d 7d 100d

 

There are lots of features of dice I like to use to confuse students, which makes them think. This one actually demonstrates some good mathematical properties:

Why does a 12 sided die have 12 possible number outcomes but 2 6 sided dice have only 11?

The answer involves the fact that you actually gain 24 possible outcomes (6*6=36 permutations) and in fact you are going from a 1 dimensional range out outcomes 1 to 12 to a 2 dimensional field of outcomes that is 6 by 6, with 1,1 in one corner and 6,6 in the other corner.

Now if you ask if this changes the probability and why, that gets even more interesting. The best way to solve that is to have them draw the grid, where each point = x+y at that point. you get this

2 3 4 5 6 7
3 4 5 6 7 8
4 5 6 7 8 9
5 6 7 8 9 10
6 7 8 9 10 11
7 8 9 10 11 12

as you can see, 7 which lies on the diagonal between 1,6 and 6,1 is the most likely, while the numbers on the matching ends of the range are the least likely. 1,1 and 6,6 can only occur in one way.

Using this you can derive a lot of properties of dice. if n is the number of sides on the dice , then for a pair of dice 1+n is the most likely number. 2 and 2n are the least likely. There are n ways to get the most likely number and n^2 total possible outcomes, meaning the probability of the most likely number is n/n^2 or 1/n. The probability of the least likely numbers is 1/n^2. The number of ways of getting any number in the range of possible outcomes 2 to 2n is the most likely number (n+1) minus the number in question (b), so n+1-b, so the probability of any in range 2 to 2n is (1+n-b)/(n^2). I could go into how it works for dice that don't match, but i realize I'm already boring everyone. I just like that this can all be extracted from that grid.

 

One side to it.

If it truly is a ball that is, it should not be made of hexagons but instead be made of a smooth surface.

 

Hmmm, I don't necessarily disagree with this, but I disagree with your examples

There are a lot of other limits on sex partners. I bet most people would be fine if their girlfriend had slept with a few guys before they got together but would be at least surprised if they found out she had been with 500 or something.....

Same for religion, a lot of people are deists but also incorporate other religions or philosophies into their approach to religion.

Come to think of it I completely disagree with that, absolutes do not exist in the physical world, only our discussion of them

This is more interesting than the dice to me

 

I don't find maths boring Pablo

Painfully confusing though.....

 

you would need to play under glass, looking up. because the number touching surface would be more true ..

 

Numerical things are always generalizations. The real world is analog and numbers are digital. But there are patterns that hold pretty well.

 

...specially when alcohol is involved

 

If you took a microscope and looked at a normal ball, you would eventually get close enough to see that there are "sides", but they would most likely be randomly placed and lack consistency in the shape of each face. It would not be infinite, but it would be a pretty high number of sides, and the numbers you would have to write on each side would be to small to be distinguishable.

This is talking about actual matter based spheres though. Theoretically a sphere has but one face.

 

True, and eventually you would get down to a size where the fibers and crystals became molecules, atoms, subatomic particles, these things tend to either exist in a sort of probability field and/or are separated by distances millions of times their own size. That's why I say the geometric generalization holds, because if it doesn't then a 6 sided dice has immense complexity as well.

 

a ball is neither a single sided die nor infinitely sided. it has a finite surface area