Math Problems

[mithrand1r]

Originally posted by Jonathan
Are you thinking about a Klein bottle ? A bottle that where you cannot determine what is the inside and what is the outside?

A colourful picture of a Klein bottle
a Klein bottle cut in two

A love triangle? The love between FF, Ruinel and SGH for instance is way hotter than 180°

Are you thinking about a Klein bottle ? A bottle that where you cannot determine what is the inside and what is the outside?

I was not thinking of a Klein bottle, but I think that that is an acceptable answer.

I was thinking of a Mobius strip.

A love triangle? The love between FF, Ruinel and SGH for instance is way hotter than 180°

Good try.

This however is not what I was thinking about. I do give you extra points for a creative answer though.

[Janny]

What's a Mobius strip?
And is not a solid sphere one sided?
A Klein bottle isn't a real world shape! I mean, if you define real world as 3D. Isn't that just straying into the work of Escher?

[Count Comfect]

A triangle on a sphere (say, on Earth, the N Pole, and two points on the equator) can have a lot more than 180 degrees.

[mithrand1r]

Originally posted by Count Comfect
A triangle on a sphere (say, on Earth, the N Pole, and two points on the equator) can have a lot more than 180 degrees.

Excellent.

That is one example of a trangle that is not 180°.

It is considered to be part of the Riemansan (sp?) space.
[Triangle has more than 180°.]

The other type of space is Lobechevsky (sp?).
[Triangle has less than 180°.]

Euclidian space.
[Triangle has exactly 180°.]
This is probably what most people had in elementary and/or secondary school.

[Janny]

Hmm, visually I can see a triangle ina sphere with many degrees, but when I try and visualise the same thing flat it reverts to just 180.
But on the plus side, I know about Euclid and Riemann. 2 from 3's okay.

[mithrand1r]

Originally posted by Janny
What's a Mobius strip?
And is not a solid sphere one sided?
A Klein bottle isn't a real world shape! I mean, if you define real world as 3D. Isn't that just straying into the work of Escher?

A sphere is techniqually two sided. Think of a Basketball filled with air. You touch the outside of the sphere, but the air presses on the inside fo the sphere.


Ask Dr. Math

Topics in Geometry

The Mobius Strip

[Janny]

But a solid sphere doesn't have an inside to have an edge on!?

My first instinct on making that strip was 'look, 2 edges, count them! one, two!'
Then I traced my finger around. I feel duped, like (was it) Euclid's proof that root two is irrational.

[Khamûl]

Originally posted by Jonathan
Math Problems (Admins, merge this thread with that?)

Sure, why not?

Btw, I would have suggested a Mobius strip, but I didn't get here in time. As for the rest of this stuff... my head hurts.

[mithrand1r]

Originally posted by Janny
But a solid sphere doesn't have an inside to have an edge on!?

My first instinct on making that strip was 'look, 2 edges, count them! one, two!'
Then I traced my finger around. I feel duped, like (was it) Euclid's proof that root two is irrational.

Good point about a solid sphere. I think, IIRC, that when refering to objects they do not consider solids. But I may be mistaken on this point.

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What is the minimum number of colors necessary to color any map? (ie. So that an area of one color does not touch another area of the same color.)

Bonus points if you can provide a mathematical proof for your answer.

[Count Comfect]

Four. On a plane.
Seven (IIRC) on a toroid.

And I can't prove it, so there Without a supercomputer, that is.

[mithrand1r]

Originally posted by Count Comfect
Four. On a plane.
Seven (IIRC) on a toroid.

And I can't prove it, so there Without a supercomputer, that is.

I can't prove it, either. (at least not from memory )

I should have specified on a plane, but I thought map would be sufficient.

[Janny]

Sorry you've lost me. I don't understand what you mean in the question (blanket coat the whole page? With a stipple effect maybe? ) Also what is IIRC?

[mithrand1r]

Originally posted by Janny
Sorry you've lost me. I don't understand what you mean in the question (blanket coat the whole page? With a stipple effect maybe? ) Also what is IIRC?

IIRC = If I Remember Correctly

If you look at a globe (as one example of a map).
What is the minimum number of colors needed for each country not to touch adjacent countries that have the same color.

Otherwise I am unclear by your question.

What is a stipple effect?

[Janny]

Sorry, I was suggesting you paint the map just one colour. A stipple effect is the uneven effect you can get when you paint ceilings...
I don't understand what your asking about the map.

[Janny]

Here's a nice one, dead easy but nice. How many legs does the average human being have?

[Count Comfect]

By the way, if you have a standard mathematical proof of the 4 color theorem, you're a genius. I believe they've actually only proved it by a combined brute force/theory method using a computer for all the examples the theory didn't cover.

[mithrand1r]

Originally posted by Janny
Here's a nice one, dead easy but nice. How many legs does the average human being have?

A little under two.

==========================

You have been convicted of violating a law in Mathmatica. Your sentance is as follows:

You are given 100 marbles (50 black, 50 white) and two bags (each bag can easily contain the 100 given marbles.

All of the marbles are to be divided in to the two bags in any manner of your choosing. After the bags are sufficiently mixed you are to choose a marble, without looking, from one of the bags.

If you select a white marble you are sent free.

If you select a black marble you are sentanced to 10 years hard labor.

How can you maximize your chances of being sent free?

[Count Comfect]

Put a single white marble in one bag and the other 99 in the other. So you have a (.5 * 1) + (.5 * 49/99) chance of getting a white one, which is almost .75.
I can't think of a better.

[mithrand1r]

Originally posted by Count Comfect
Put a single white marble in one bag and the other 99 in the other. So you have a (.5 * 1) + (.5 * 49/99) chance of getting a white one, which is almost .75.
I can't think of a better.

Correct!

What is the next number in this series?

41, 43, 47, 53, ???

[Janny]

61
Can't work out a formula tho... second row of differences, is it quadratic?