The Möbius Strip pinned down!

[Uncwilly]

Originally Posted by Orgasmic Troll

wrong em boyo, if you cut it in the middle you get ONE loop (you add an edge)

That was the starting point that Retina asked us to consider. He wanted to know the answer to the next step. That is what my answer refered to. Just to confirm, I did the physical test. I stand by my statement.

[mfgoode]

Originally Posted by Uncwilly

I have done this before: You get 2 linked rings I forget what happens when you cut a mobius strip in thirds.

Well it all depends what is meant by a twist in the initial Mobius band.

Does the first twist in the original Mo/band have a half twist or a full twist.?

By half I mean a 180* twist. By a full twist I mean a 360 Twist which would be equivalent to two half twists.

ASFAIK it is the half twist that is used in making the Mo/Band.
In this case on cutting down the middle will only give a single loop with two twists

If one speaks of an initial half twist then cutting it down the centre line will yield one larger loop with two half twists.

So after the first cutting down the middle if we proceed with cutting the second single band obtained, with two half twists, we will get two loops interlocked like the links of a chain.

This is what Uncwilly got by experiment. He probably did a full 360* twist initially to create the Mo/Band. If that is the case then he will get two loops as he stated in the very first cutting into half.

If one cuts the band in one third of the width the Mo/ band will open into a large band linked with a smaller one. The larger band will be twice as big as the original band and will have two twists where as the smaller band will be the same size as the original with a single twist like the original.

Since we are on this interesting topic maybe you will like to check the Net on Borromean rings which form the coat of arms of the Italian family Borromeo.

They are three rings all interlocked with each other. If you cut just one of the rings then all three will come loose. I made one years ago for my sons out of silver bangles my maid wears. Really fascinating, both the rings and my maid!

Mally

[Uncwilly]

Originally Posted by mfgoode

Well it all depends what is meant by a twist in the initial Mobius band.

Does the first twist in the original Mo/band have a half twist or a full twist.?

By half I mean a 180* twist. By a full twist I mean a 360 Twist which would be equivalent to two half twists.

ASFAIK it is the half twist that is used in making the Mo/Band.
In this case on cutting down the middle will only give a single loop with two twists

If one speaks of an initial half twist then cutting it down the centre line will yield one larger loop with two half twists.

So after the first cutting down the middle if we proceed with cutting the second single band obtained, with two half twists, we will get two loops interlocked like the links of a chain.

This is what Uncwilly got by experiment. He probably did a full 360* twist initially to create the Mo/Band. If that is the case then he will get two loops as he stated in the very first cutting into half.

If one cuts the band in one third of the width the Mo/ band will open into a large band linked with a smaller one. The larger band will be twice as big as the original band and will have two twists where as the smaller band will be the same size as the original with a single twist like the original.

PLEASE read the first post in this thread!
The assumption is that one takes a Mobius strip and cuts it. THIS is the starting point for the question.
As to the twists, a Mobius is well defiend: http://en.wikipedia.org/wiki/Möbius_strip

I stand by my intial response.

[mfgoode]

[QUOiTE=Uncwilly;113938]PLEASE read the first post in this thread!
The assumption is that one takes a Mobius strip and cuts it. THIS is the starting point for the question.
As to the twists, a Mobius is well defiend: http://en.wikipedia.org/wiki/Möbius_strip

I stand by my initial response.[/QUOTE]



Hey! Hey! Uncwilly! Hold your horses man, or I should I say your reindeers?

It’s no use getting hysterical posting your answers in bold colored print. It’s bad for the nerves. You may not even live as long as me if you carry on in this fashion.

If we don’t agree on religious beliefs it does not make it necessary to disagree in Mathematics!

A Mobius band is well defined as per your URL. Now you said you actually made one and tried it out and that’s where the trouble started as your solution if you meant the first cut (and this is very AMBIGUOUS) in your post means you got two interlocked bands. This is in variance with OT's answer, so I examined it and found that OT is absolutely right and you are wrong! The answers don’t tally. OT also mentioned it

I cannot read your closed mind so I wondered if you have made one half twist or a full one. Now go back and read my last post again. You will find that if the band is made initially with a full twist (two half twists) the result will be two interlocked bands. So I stand by my statement too. Try it!

Its not the egoist God Almighty stand that counts it is what is the TRUTH!?

BTW: The Mobius is made of a HALF TWIST! As per your URL>

"A model can easily be created by taking a paper strip and giving it a half-twist, and then merging the ends of the strip together to form a single strip"

Mally :Coffee:

[R.D. Silverman]

Originally Posted by mfgoode

Well it all depends what is meant by a twist in the initial Mobius band.

Does the first twist in the original Mo/band have a half twist or a full twist.?

In your case, there is a choice.

You can either be a half wit or a full twit. You qualify for both.

[mfgoode]

Originally Posted by R.D. Silverman

In your case, there is a choice.

You can either be a half wit or a full twit. You qualify for both.

Thank you for your humour RDS. I woud direct you to the Dumb Jokes thread to improve on your unpleasantness. Your comment was uncalled for. It is a personal jab to me and I take it as an insult so I hope I get away in replying in the same coin, but I will make it more subtle. Just sustitute 'i' in twit for 'a'. Got it RDS? Thats what you are. Forget the wat part of it!

And with a full twist I coin it 'Goode's band' and it has remarkable topological properties. It jumps the first cut straight into the second cut. Oh I forgot that you have not gone deep into topology. Sorry!

Mally

[davieddy]

There is a thread for this sort of banter in "Soap box".
I forget who started it.

[Orgasmic Troll]

Originally Posted by Uncwilly

That was the starting point that Retina asked us to consider. He wanted to know the answer to the next step. That is what my answer refered to. Just to confirm, I did the physical test. I stand by my statement.

huh, I thought I posted a reply to this admitting that I read too quickly and that you were right.

Well, here it is.

[Orgasmic Troll]

Originally Posted by mfgoode

Thank you for your humour RDS. I woud direct you to the Dumb Jokes thread to improve on your unpleasantness. Your comment was uncalled for. It is a personal jab to me and I take it as an insult so I hope I get away in replying in the same coin, but I will make it more subtle. Just sustitute 'i' in twit for 'a'. Got it RDS? Thats what you are. Forget the wat part of it!

And with a full twist I coin it 'Goode's band' and it has remarkable topological properties. It jumps the first cut straight into the second cut. Oh I forgot that you have not gone deep into topology. Sorry!

Mally

.

[mfgoode]

Originally Posted by Orgasmic Troll

.

Keep away from the night clubs in Chicago (theres more there than piano playing) and get down to serious studies

Mally

[davieddy]

Originally Posted by mfgoode

Keep away from the night clubs in Chicago (theres more there than piano playing)

And there was I thinking it was a computer keyboard in Mumbai