Food & Drink0 min ago
one or two sided shape
My son has some maths homework concerning polygons.
My question concerns henagons (or monogons) and digons.
I may be a bit thick here, but how on earth can you have a one or two sided shape??? Surely the minimum number of sides needed to make a shape is three (triangle)?
I would be interested to see a one or two sided shape.
Thanks in advance to the more intelligent on here who will probably make me look like a walley for asking this question.....
My question concerns henagons (or monogons) and digons.
I may be a bit thick here, but how on earth can you have a one or two sided shape??? Surely the minimum number of sides needed to make a shape is three (triangle)?
I would be interested to see a one or two sided shape.
Thanks in advance to the more intelligent on here who will probably make me look like a walley for asking this question.....
Answers
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My descriptions are only valid in Euclidean geometry. ie. in a flat, two dimensional plane.
When you get into spherical geometry it gets more complicated.
http://en.wikipedia.org/wiki/Henagon
When you get into spherical geometry it gets more complicated.
http://en.wikipedia.org/wiki/Henagon
My goodness - unless your son's a maths undergraduate non euclidian geometry's a bit tough for homework!
The thing is that a couple of thousand years ago there was a pretty bright guy called Euclid - He wrote a book called the Elements which contained all there was to know about Geometry.
This had 5 "axioms" things that couldn't be proved - you had to accept and all geometry rested on them.
They were common sense things like things like "all right angles are equal"
This lasted for 2,000 years until some mathematicians started looking at the last or 5th one that said "if you have two straight lines parallel to each other they never meet". They scratched their beards (all mathematicians had beards in the 19th Century) and said "what if that wasn't true?"
They assumed that all geometry would fall apart into a mess if you did this but lo and behold it did not.
For a while these strange geometries where parallel lines meet were just the playthings of mathematicians until Albert Einstein came up with General Relativity as it turns out these non-Euclidian geometries are just the things you need to describe the shape of the Universe.
You can't really visualise non-Euclidian objects like henagons but you can work with them using rules a bit like working with higher dimensions:
You may not beable to visualise 4D space but you can work out the distance between two ponts with Pythagorus squaring all 4 distances and taking the square root.
Same in non-Euclidean Geometry
No I certainly don't think it's a "Wally question"!
The thing is that a couple of thousand years ago there was a pretty bright guy called Euclid - He wrote a book called the Elements which contained all there was to know about Geometry.
This had 5 "axioms" things that couldn't be proved - you had to accept and all geometry rested on them.
They were common sense things like things like "all right angles are equal"
This lasted for 2,000 years until some mathematicians started looking at the last or 5th one that said "if you have two straight lines parallel to each other they never meet". They scratched their beards (all mathematicians had beards in the 19th Century) and said "what if that wasn't true?"
They assumed that all geometry would fall apart into a mess if you did this but lo and behold it did not.
For a while these strange geometries where parallel lines meet were just the playthings of mathematicians until Albert Einstein came up with General Relativity as it turns out these non-Euclidian geometries are just the things you need to describe the shape of the Universe.
You can't really visualise non-Euclidian objects like henagons but you can work with them using rules a bit like working with higher dimensions:
You may not beable to visualise 4D space but you can work out the distance between two ponts with Pythagorus squaring all 4 distances and taking the square root.
Same in non-Euclidean Geometry
No I certainly don't think it's a "Wally question"!
Thanks for all the answers chaps. Even though Im non the wiser at least I know it wasnt a 'wally' question...
Jake, lol, my son isnt a maths undergraduate, it was just a bit of work concerning the names of polygons but it got ME thinking a bit about one and two sided figures, which I'd heard about before.
I like to think that Im reasonably educated but there are some seriously intelligent people on this site....
Jake, lol, my son isnt a maths undergraduate, it was just a bit of work concerning the names of polygons but it got ME thinking a bit about one and two sided figures, which I'd heard about before.
I like to think that Im reasonably educated but there are some seriously intelligent people on this site....
Wrong thread I think, T&S. I assuem you wanted this one:
http://www.theanswerb.../Question1103617.html
http://www.theanswerb.../Question1103617.html
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