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Math oddities

Started by Kurzyk, April 06, 2011, 06:16:45 PM

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ReanimateMagnus

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.

Oniya

Except that, by definition, is non-Euclidean geometry. 
"Language was invented for one reason, boys - to woo women.~*~*~Don't think it's all been done before
And in that endeavor, laziness will not do." ~*~*~*~*~*~*~*~*~*~*~Don't think we're never gonna win this war
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ReanimateMagnus

yeah I wanted to edit that T_T

Oniya

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).
"Language was invented for one reason, boys - to woo women.~*~*~Don't think it's all been done before
And in that endeavor, laziness will not do." ~*~*~*~*~*~*~*~*~*~*~Don't think we're never gonna win this war
Robin Williams-Dead Poets Society ~*~*~*~*~*~*~*~*~*~*~*~*~*~Don't think your world's gonna fall apart
I do have a cause, though.  It's obscenity.  I'm for it.  - Tom Lehrer~*~All you need is your beautiful heart
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ReanimateMagnus

I was just pointing something out...I don't need a "lesson" on Lobachevskian geometry.

Oniya

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.
"Language was invented for one reason, boys - to woo women.~*~*~Don't think it's all been done before
And in that endeavor, laziness will not do." ~*~*~*~*~*~*~*~*~*~*~Don't think we're never gonna win this war
Robin Williams-Dead Poets Society ~*~*~*~*~*~*~*~*~*~*~*~*~*~Don't think your world's gonna fall apart
I do have a cause, though.  It's obscenity.  I'm for it.  - Tom Lehrer~*~All you need is your beautiful heart
O/O's Updated 5/11/21 - A/A's - Current Status! - Writing a novel - all draws for Fool of Fire up!
Requests updated March 17

ReanimateMagnus

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.

Trieste

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. ;) )

ReanimateMagnus

Quote from: Trieste 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. ;) )

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.

Trieste

No worries! Just make a new thread for the new topic. :)

Oreo

#35
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

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She spins magic and moonlight in her meadows and streams, and seeks deep inside me,
and touches my dreams. - Harry Chapin

Oniya

Quote from: Trieste on May 19, 2011, 11:04:43 PM
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.)
"Language was invented for one reason, boys - to woo women.~*~*~Don't think it's all been done before
And in that endeavor, laziness will not do." ~*~*~*~*~*~*~*~*~*~*~Don't think we're never gonna win this war
Robin Williams-Dead Poets Society ~*~*~*~*~*~*~*~*~*~*~*~*~*~Don't think your world's gonna fall apart
I do have a cause, though.  It's obscenity.  I'm for it.  - Tom Lehrer~*~All you need is your beautiful heart
O/O's Updated 5/11/21 - A/A's - Current Status! - Writing a novel - all draws for Fool of Fire up!
Requests updated March 17

ReanimateMagnus

Quote from: Oniya on May 20, 2011, 12:06:41 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.

Oniya

Quote from: ReanimateMagnus on May 20, 2011, 06:57:27 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.
"Language was invented for one reason, boys - to woo women.~*~*~Don't think it's all been done before
And in that endeavor, laziness will not do." ~*~*~*~*~*~*~*~*~*~*~Don't think we're never gonna win this war
Robin Williams-Dead Poets Society ~*~*~*~*~*~*~*~*~*~*~*~*~*~Don't think your world's gonna fall apart
I do have a cause, though.  It's obscenity.  I'm for it.  - Tom Lehrer~*~All you need is your beautiful heart
O/O's Updated 5/11/21 - A/A's - Current Status! - Writing a novel - all draws for Fool of Fire up!
Requests updated March 17

Oreo

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)

She led me to safety in a forest of green, and showed my stale eyes some sights never seen.
She spins magic and moonlight in her meadows and streams, and seeks deep inside me,
and touches my dreams. - Harry Chapin

Falanor

I figured someone here might find this amusing...

ReanimateMagnus

I love that picture btw.

kckolbe

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
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ReanimateMagnus

Didn't I already post that? Oh well maybe not.

frogman

Did you know that... 7 x 13 = 28

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

frogman

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. 

Oreo

Quote from: frogman 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
Gotta love Abbott and Costello.

She led me to safety in a forest of green, and showed my stale eyes some sights never seen.
She spins magic and moonlight in her meadows and streams, and seeks deep inside me,
and touches my dreams. - Harry Chapin

ReanimateMagnus


Kuroneko

I think my brain just asploded ...
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frogman

Quote from: Kuroneko on June 16, 2011, 01:09:51 AM
I think my brain just asploded ...

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