Australian Politics Forum - Relationship to mathematics

Jovial Monk

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Relationship to mathematics
May 2^nd, 2018 at 6:37pm

Maths seems to be a lot of peoples’ least favorite school subject, yet maths can be beautiful.

Who knew geometry could be put on graph paper? Analytical geometry does that.

Algebra an early bugbear for some but it is an elegant way to structure a problem to arrive at a solution. An offshoot is matrix mathematics.

The real hate or fear I think is induced by calculus. Two types of calculus, the differential calculus and the integral calculus.

There is also Boolean arithmetic and Boolean calculus. You might remember sets and Venn diagrams.

The weirdest offshoot of maths is topology.

To a topologist a vinyl record/CD/DVD and a teacup are exactly the same. Anybody know why?

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lee Gold Member Offline Australian Politics Posts: 19440 Gender:	Re: Relationship to mathematics Reply #1 - May 2^nd, 2018 at 6:48pm And then there is simple subtraction and some can't do something as elementary as that.
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Jovial Monk Gold Member Offline Dogs not cats! Posts: 50505 Gender:	Re: Relationship to mathematics Reply #2 - May 2^nd, 2018 at 6:49pm Another ad hom.
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Jovial Monk Gold Member Offline Dogs not cats! Posts: 50505 Gender:	Re: Relationship to mathematics Reply #3 - May 2^nd, 2018 at 6:51pm So, a vinyl record and a teacup, how can they possibly be considered the same thing? Told you topology was weird. You can probably find the answer on google, but try without that.
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Jovial Monk Gold Member Offline Dogs not cats! Posts: 50505 Gender:	Re: Relationship to mathematics Reply #4 - May 2^nd, 2018 at 7:04pm Topologists consider things in terms of sides and edges. That is what is known as a clue.
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Jovial Monk

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Re: Relationship to mathematics
Reply #5 - May 2^nd, 2018 at 7:09pm

OK, a teacup and a record are identical to a topologist because they are two surfaces (top and bottom, inside and outside) and two edges, one in the spindle hole, one formed by the teacup handle and one edge on the outside.

Most should know this one: Can you have a strip of paper (or road or railway etc) that has only one surface and one edge?

I reckon something will be ringing a bell for most.

Any bells getting louder anywhere?

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« Last Edit: May 2^nd, 2018 at 7:41pm by Jovial Monk »

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Jovial Monk Gold Member Offline Dogs not cats! Posts: 50505 Gender:	Re: Relationship to mathematics Reply #6 - May 2^nd, 2018 at 7:36pm Let you think about that. You have probably heard that “Angles on one side of a straight line always add to 180 degrees.” This was the fifth axiom of Euclid. Is it true always?
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Jovial Monk

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Re: Relationship to mathematics
Reply #7 - May 2^nd, 2018 at 7:56pm

Get a strip of paper, preferable not too wide or too long just for convenience sake. Some glue, sticky tape ready to hand.

Hold both ends close together and give one end a half twist so what was the top side is now the bottom side. Fasten the two ends together.

You now have a bit of paper that has only one side. True! Sides are separated by edges but the strip has only one edge!

Don’t believe me? Put the strip down, put a pen to it and start drawing a line on the strip, keep moving it towards the pen, keep going—and eventually you will come to where you started the line. No edges crossed—the strip has only one side! You could test it has only one edge in a similar way. Magic! No—maths!

Can anyone name the name of the strip we made? Cudgel those brains!

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Jovial Monk

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Re: Relationship to mathematics
Reply #8 - May 2^nd, 2018 at 8:33pm

Poor neglected Möbius strip

If you glued two together, and assuming you could pass some paper through the 4th (or whatever) dimension, you would make a Klein bottle, a bottle with no inside or outside!

Something easier, get a pair of scissors and cut the strip in half lengthwise, like you drew the line on the one surface. See what results.

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Jovial Monk Gold Member Offline Dogs not cats! Posts: 50505 Gender:	Re: Relationship to mathematics Reply #9 - May 2^nd, 2018 at 8:37pm That leaves our poor neglected straight line. Can you have a straight line with more than 180°? Can you have a straight line with less than 180°? Anyone?
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Aussie

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Re: Relationship to mathematics
Reply #10 - May 2^nd, 2018 at 9:05pm

Jovial Monk wrote on May 2^nd, 2018 at 7:56pm:

Get a strip of paper, preferable not too wide or too long just for convenience sake. Some glue, sticky tape ready to hand.

Hold both ends close together and give one end a half twist so what was the top side is now the bottom side. Fasten the two ends together.

You now have a bit of paper that has only one side. True! Sides are separated by edges but the strip has only one edge!

Don’t believe me? Put the strip down, put a pen to it and start drawing a line on the strip, keep moving it towards the pen, keep going—and eventually you will come to where you started the line. No edges crossed—the strip has only one side! You could test it has only one edge in a similar way. Magic! No—maths!

Can anyone name the name of the strip we made? Cudgel those brains!

I made my strip of paper....and then....found your 'instructions' incapable of understanding or applying.
Huh

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Jovial Monk Gold Member Offline Dogs not cats! Posts: 50505 Gender:	Re: Relationship to mathematics Reply #11 - May 2^nd, 2018 at 9:14pm If you have made your Mobius Strip, having given one side a half twist, draw a line along its length, keep doing that—you will arrive at your starting point without having crossed an edge—the strip has only one side!
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Aussie Gold Member Offline OzPolitic Posts: 39477 Gender:	Re: Relationship to mathematics Reply #12 - May 2^nd, 2018 at 9:19pm Jovial Monk wrote on May 2^nd, 2018 at 9:14pm: If you have made your Mobius Strip, having given one side a half twist, draw a line along its length, keep doing that—you will arrive at your starting point without having crossed an edge—the strip has only one side! Far car! Observe!
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Jovial Monk Gold Member Offline Dogs not cats! Posts: 50505 Gender:	Re: Relationship to mathematics Reply #13 - May 2^nd, 2018 at 9:25pm Exactly what I said. Hmmm I thought everyone would have come across the Mobius strip at school. Start drawing a line along the length of the strip, keep going, you will come back to your starting point!
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Aussie Gold Member Offline OzPolitic Posts: 39477 Gender:	Re: Relationship to mathematics Reply #14 - May 2^nd, 2018 at 9:47pm I followed your instructions. First....my strip of paper was two inches long, half an inch wide. Nowhere did you tell me get some sticky tape and do what is shown in the video. So....no I will have another go. And in the mean time....
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