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Thanks - the text I was reading probably did mean 'homeomorphic', so you've given me the answer.
Shapes that have the same Euler Characteristic could be turned into each other by the right set of manipulations, whereas those that have a different Euler Characteristic cannot?
I'm after a short, simple but correct explanation for children ~10 years old of why the Euler Characteristic is a 'basic idea in topology' (as I've read). It's for use as a 'by the way, you might be interested to know...' insight into more advanced maths to conclude an exercise of counting faces, vertices and edges of common 3D shapes, and discovering that they usually have an Euler Characteristic of 2 (The only exception I've been able to think of among common 3D shapes is a cylinder, which I think has 3 faces, 0 vertices and 2 edges, so an Euler Characteristic of 1.).
Thanks for your help!
Thank you - the forum already seems like a friendly place!
A while ago, I made up this thought experiment
Imagine that you are playing this game:
You and 9 other players are asked to vote "200" or "300" by secret ballot. When all 10 of you have voted, everyone who chose "200" gets an equal share of £200, and everyone who voted "300" gets an equal share of £300. Your goal is to maximise the amount of money you get. Imagine there is no way of working together with other players, or finding out how they have voted. All you can do is to guess what they will do.
The dilemma is of course whether to go for the larger 300 prize, or whether to assume that this is what most players will do, thereby making the 200 prize a better option. That reasoning can be regressed infinitely...
I set up this web page to enable people actually to play the game, and I wondered whether anyone here would be interested in giving it a go? You can play the game by clicking this link and filling out the 1-question survey (optionally also saying why you made the choice you did).
(Just to be clear, nobody playing this game is really going to get any prizes. This is only an exercise in finding out what people would do. Thanks for you help with the experiment!)
BTW - is there a formal game theory approach to determining the optimal strategy? I'd be interested to know, but please be aware that I studied maths to 17 years of age and that was a long time ago. So I'm unlikely to follow a high-level explanation, unfortunately!
Thank you zetafunc. Ah, I think I've just seen how it works.
If I wanted to get both fractions over a common denominator in order to compare them, I can do this:
a/b = da/bd
c/d = bc/bd
so my original a/b ? c/d------------ (where '?' means 'what is the relationship between?' - I don't know if there's a formal maths symbol for that?)
becomes da/bd ? bc/bd
= da ? bc
So that's how and why it works (I think)!
I have two arms, but I also have two fore-arms
2+ (2x4) = 10 so I have 10 arms
10 is certainly an odd number of arms to have, but 10 is also an even number
The only number I know of that is both odd and even is infinity
So I must have an infinite number of arms....
Someone showed me a trick for determining which of 2 fractions is larger (where this isn't obvious). It works on examples I've tried, but I've not been able to think of a general proof to show it always works. Can anyone help?
The assertion is:
If a/b <c/d, then da<bc
For example - is 6/8 < 5/6?
da = 6*6 = 36
bc = 8*5 = 40
da<bc, therefore a/b <c/d (and 6/8 < 5/6).
Thanks for your help & I hope this is a fun thing to think about!
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