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Author Topic: Math oddities  (Read 8901 times)

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Offline ReanimateMagnus

Re: Math oddities
« Reply #25 on: May 19, 2011, 08:26:40 PM »
In Euclidean geometry, the Pythagorean theorem no longer always works. For the instance if you stand on the north pole and draw a line down the prime meridian and then one down the 90th meridian either east or west it doesn't matter. Then go to the equator and draw a line that connects the two. You just created a triangle with all 90 degree angles.

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Re: Math oddities
« Reply #26 on: May 19, 2011, 08:39:40 PM »
Except that, by definition, is non-Euclidean geometry. 

Offline ReanimateMagnus

Re: Math oddities
« Reply #27 on: May 19, 2011, 10:22:26 PM »
yeah I wanted to edit that T_T

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Re: Math oddities
« Reply #28 on: May 19, 2011, 10:29:02 PM »
Well, the 'problem' is that, in order to prove the statement 'the sum of the angles in a triangle = 180 degrees' to be true (which isn't the Pythagorean theorem, by the way - that's distance), you have to use the Parallel Postulate.  Once you toss that and start going into non-Euclidean spaces, triangles can have more than 180 degrees (elliptic geometry) or less than 180 degrees (hyperbolic geometry, which is useful when dealing with things like gravity wells).

Offline ReanimateMagnus

Re: Math oddities
« Reply #29 on: May 19, 2011, 10:34:25 PM »
I was just pointing something out...I don't need a "lesson" on Lobachevskian geometry.

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Re: Math oddities
« Reply #30 on: May 19, 2011, 10:41:42 PM »
Well, then, consider the explanation a courtesy for those others reading the thread.  Perhaps if you get approved, we can have a conversation about the analytic and algebraic topology of locally Euclidean parameterization of infinitely differentiable Riemannian manifolds.

Offline ReanimateMagnus

Re: Math oddities
« Reply #31 on: May 19, 2011, 10:49:10 PM »
Well the Riemannian manifolds were only really applicable for advanced physics and general relativity and would be no where if it wasn't for Gauss.

Offline Trieste

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Re: Math oddities
« Reply #32 on: May 19, 2011, 10:57:44 PM »
I have no idea how I followed that conversation, but I did, and I can tell you with absolute certainty that you have moved quite a bit beyond the scope of the topic of this thread. <3

At the very least, take your Gauss, your Reimann, and your Lobachevski to a thread dedicated to WHOA-ARE-YOU-EVEN-SPEAKING-ENGLISH-ANYMORE mathematics, please.

(But it's mean to make Euclid sit outside and cry, y'all. ;) )

Offline ReanimateMagnus

Re: Math oddities
« Reply #33 on: May 19, 2011, 11:00:37 PM »
I have no idea how I followed that conversation, but I did, and I can tell you with absolute certainty that you have moved quite a bit beyond the scope of the topic of this thread. <3

At the very least, take your Gauss, your Reimann, and your Lobachevski to a thread dedicated to WHOA-ARE-YOU-EVEN-SPEAKING-ENGLISH-ANYMORE mathematics, please.

(But it's mean to make Euclid sit outside and cry, y'all. ;) )

I'm sorry, but this made me smile. If my wife wasn't sleeping, I might have laughed out loud. ^__^ Sorry, I wont post here anymore.

Offline Trieste

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Re: Math oddities
« Reply #34 on: May 19, 2011, 11:04:43 PM »
No worries! Just make a new thread for the new topic. :)

Offline Oreo

Re: Math oddities
« Reply #35 on: May 19, 2011, 11:44:28 PM »
I came across these recently and found them fun oddities:

9x9+7=88
98x9+6=888
987x9+5=8888
9876x9+4=88888
98765x9+3=888888
987654x9+2=8888888
9876543x9+1=88888888
98765432x9+0=888888888


1x1=1
11x11=121
111x111=12321
1111x1111=1234321
11111x11111=123454321
111111x111111=12345654321
1111111x1111111=1234567654321
11111111x11111111=123456787654321
111111111x111111111=123456787654321


1x9+2=11
12x9+3=111
123x9+4=1111
1234x9+5=11111
12345x9+6=111111
123456x9+7=1111111
1234567x9+8=11111111
12345678x9+9=111111111
123456789x9+10=1111111111


1x8+1=9
12x8+2=98
123x8+3=987
1234x8+4=9876
12345x8+5=98765
123456x8+6=987654
1234567x8+7=9876543
12345678x8+8=98765432
123456789x8+9=987654321
« Last Edit: May 20, 2011, 12:09:58 AM by Oreo »

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Re: Math oddities
« Reply #36 on: May 20, 2011, 12:06:41 AM »
No worries! Just make a new thread for the new topic. :)

It's not something I'd be likely to discuss in a thread anyways, mostly because I wouldn't want to risk any head-splodeys from an unwary passer-through.

(For what it's worth, I was quoting a line from Tom Lehrer's 'Lobachevsky' - a bit of a shout-out to any math person with a sense of humor.)

Offline ReanimateMagnus

Re: Math oddities
« Reply #37 on: May 20, 2011, 06:57:27 AM »
(For what it's worth, I was quoting a line from Tom Lehrer's 'Lobachevsky' - a bit of a shout-out to any math person with a sense of humor.)

I guess I don't have a sense of humor then ^_^ I'll have to look up Tom Lehrer then.

I show this to my students

1/9=.1111(these are repeating of course)
2/9=.2222
3/9=.3333
4/9=.4444

1/11=.0909
2/11=.1818
3/11=.2727
4/11=.3636
When I was a kid this was how I always remembered those fractions.

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Re: Math oddities
« Reply #38 on: May 20, 2011, 11:24:21 AM »
I guess I don't have a sense of humor then ^_^ I'll have to look up Tom Lehrer then.

I suspect you'll like it.  He is a (now retired) Harvard math professor who had a brief run as a satirical pianist.  A number of his songs are actually educational in nature, and a few songs that made it to the Electric Company.

Offline Oreo

Re: Math oddities
« Reply #39 on: May 20, 2011, 03:31:57 PM »
I was always able to remember my 9's times with this. The answer always began with one less number than the multiplier and the two added up to 9.

2x9=18 (1+8=9)
3x9=27 (2+7=9)
4x9=36 (3+6=9)
5x9=45 (4+5=9)
6x9=54 (5+4=9)
7x9=63 (6+3=9)
8x9=72 (7+2=9)
9x9=81 (8+1=9)

Offline Falanor

Re: Math oddities
« Reply #40 on: May 20, 2011, 10:52:30 PM »
I figured someone here might find this amusing...

Offline ReanimateMagnus

Re: Math oddities
« Reply #41 on: May 21, 2011, 11:46:33 PM »
I love that picture btw.

Offline kckolbe

Re: Math oddities
« Reply #42 on: May 22, 2011, 05:23:37 PM »
Here's one I've always liked:

Proving that .999 (repeating) is equal to 1

.333 = 1/3
.666 = 2/3
.999 = 3/3
.999 = 1

Offline ReanimateMagnus

Re: Math oddities
« Reply #43 on: June 05, 2011, 06:47:12 PM »
Didn't I already post that? Oh well maybe not.

Offline frogman

Re: Math oddities
« Reply #44 on: June 15, 2011, 05:59:48 AM »
Did you know that... 7 x 13 = 28

There's another version with vacuum sales.  Ingenius... ;D

Offline frogman

Re: Math oddities
« Reply #45 on: June 15, 2011, 06:32:12 AM »
For a serious math oddity, though, how about the St. Petersburg Paradox:

You pay a flat fee to enter a lottery where a fair coin is flipped repeatedly until a tails appears, thus ending the game.  The pot starts at $1, and the pot doubles every time a heads appears.  You win whatever is in the pot once the game ends.  For example, if the first flip is tails, then you win $1.  If you gets heads and then tails, you win $2.  Heads, heads, tails = $4.  Heads, heads, heads, tails = $8.  And so on.  So the question is how much should you be willing to pay to enter this lottery?

To determine this, you need to find the expected payout.  The expected value is found by taking the probability of each outcome, multiplying that probability by what you would win, and adding all the probability payoffs together.  In other words, there's a 1/2 chance that you will get tails on the first flip, thus getting $1.  There's a 1/4 chance that you will get heads on the first flip and tails on the second, thus getting $2.  The chance decreases as you continue the string of getting heads in a row, but that's compensated by doubling the pot.  So mathematically, that's expressed as the following:

E(x) = (1/2 x 1) + (1/4 x 2) + (1/8 x 4) + (1/16 x 8) + (1/32 x 16) + ...

Once you get far out there, the chances of getting that payoff are very miniscule, but it's compensated for by the enormous payoff.  As you can see from simplifying the math above, there's an interesting pattern:

E(x) = 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + ...

This mathematical expression converges to infinity, meaning that if you keep adding 1/2 forever, so the total will keep growing without ever stopping.  So we see that the expected earnings of the St. Petersburg Paradox is an infinite amount.  Thus, you should be willing to spend everything you have on this game, because your probable earnings are infinite.  Would you be willing to risk everything?  Mathematically, it seems that you should!

Note: the math here is correct (unless I mistyped something), but obviously something doesn't seem right here because who do you know would actually be willing to risk everything?  There are answers to explain this paradox (some more mathematical than others), but it's nonetheless a cool mathematical oddity that I thought people would enjoy. 
 

Offline Oreo

Re: Math oddities
« Reply #46 on: June 15, 2011, 06:40:59 AM »
Did you know that... 7 x 13 = 28

There's another version with vacuum sales.  Ingenius... ;D
Gotta love Abbott and Costello.

Offline ReanimateMagnus

Re: Math oddities
« Reply #47 on: June 15, 2011, 06:47:50 PM »

Offline Kuroneko

Re: Math oddities
« Reply #48 on: June 16, 2011, 01:09:51 AM »
I think my brain just asploded ...

Offline frogman

Re: Math oddities
« Reply #49 on: June 16, 2011, 06:31:21 AM »
I think my brain just asploded ...

In a base 4 number system, 2 + 2 = 10.  In base 3, it's 11. :-)