Is anyone else fascinated by basic geometric shapes?

Page 3 of 4 [ 50 posts ] Go to page Previous 1, 2, 3, 4 Next

Previous topic | Next topic

Daewoodrow
Pileated woodpecker

Joined: 21 Feb 2008
Age: 36
Gender: Male
Posts: 182
Location: Canterbury, England

29 Apr 2008, 9:40 pm

KateShroud wrote:

Daewoodrow wrote:

A tesseract can't exist at present, because the inside occupies more space than the outside. It is four dimensional, several objects of matter occupying the same space. (yes, I know what some of you are inevitably thinking! Vworp!) If that effect is achievable, it is out of the realms of modern science. But to say it is "not real" is somewhat of a mistake.

A tesseract was used in the novel for time travel, not just space travel. I believe folding space is certainly possible, even though we can't do it yet, but time travel is not. Of course time exists, but much of our understanding of time is a man-made construct.

Well generally speaking A Tesseract represents neither time nor space, but it can be used to symbolise either time, or a four dimensional object in space, the latter being more physically plausable than the former. Personally I believe time obeys laws similar to space, in that I think it has multiple dimensions, but I think we are locked to the space plane and therefore incapable of comprehending the dimensionality of time. Much like an hour (in the hypothetical sense that it should be conscious) could not possibly comprehend a metre.

_________________
Umquam sentio nex?

Daewoodrow
Pileated woodpecker

Joined: 21 Feb 2008
Age: 36
Gender: Male
Posts: 182
Location: Canterbury, England

29 Apr 2008, 9:42 pm

Odin wrote:

slowmutant wrote:

If a hypercube exists in 4 dimensions, how can it be rendered by three dimensional beings like ourselves?

A rotating hypercube:

A practical Hypercube:

_________________
Umquam sentio nex?

Odin
Veteran
Veteran

Joined: 12 Oct 2006
Age: 39
Gender: Male
Posts: 2,475
Location: Moorhead, Minnesota, USA

29 Apr 2008, 9:48 pm

I love geometry, especially as it is applied to physics.

POP QUIZ!! !

Is the sum of the angles of a triangle in a negatively-curved space more than, less than, or equal to 180 degrees? :nerdy:

_________________
My Blog: My Autistic Life

Daewoodrow
Pileated woodpecker

Joined: 21 Feb 2008
Age: 36
Gender: Male
Posts: 182
Location: Canterbury, England

29 Apr 2008, 9:51 pm

No idea. I'm a Biologist/Forensic Scientist, not a mathematician!

_________________
Umquam sentio nex?

lotus
Pileated woodpecker

Joined: 8 Dec 2007
Age: 45
Gender: Female
Posts: 183

29 Apr 2008, 9:52 pm

No of course..... Wait! Is that a rhombus? :lol:

Odin
Veteran
Veteran

Joined: 12 Oct 2006
Age: 39
Gender: Male
Posts: 2,475
Location: Moorhead, Minnesota, USA

29 Apr 2008, 9:59 pm

Who has a copy of Euclid's Elements? I have an unabridged copy I bought when I was 14 and instantly fell in love with it. It has a clear, logical elegance that transcends time.

_________________
My Blog: My Autistic Life

pakled
Veteran
Veteran

Joined: 12 Nov 2007
Age: 67
Gender: Male
Posts: 7,015

29 Apr 2008, 10:01 pm

Here's something to bend your minds around, if you want to play with geometry.

Topmod (a topological modeler)

http://www-viz.tamu.edu/faculty/ergun/r ... nload.html

I use something called Wings 3d to make models out of various primitives. You can find it at

http://www.wings3.com

they're both free...

KateShroud
Veteran
Veteran

Joined: 1 Feb 2008
Age: 39
Gender: Female
Posts: 1,159
Location: Austin, Texas, United States, north America, Earth, Milky Way Galaxy

29 Apr 2008, 10:02 pm

If I knew exactly what a negatively curved space looked like, I might be able to give a definitive answer. I learned though that the angles of every triangle must add up to 180 degrees.

Odin
Veteran
Veteran

Joined: 12 Oct 2006
Age: 39
Gender: Male
Posts: 2,475
Location: Moorhead, Minnesota, USA

29 Apr 2008, 10:28 pm

KateShroud wrote:

If I knew exactly what a negatively curved space looked like, I might be able to give a definitive answer. I learned though that the angles of every triangle must add up to 180 degrees.

A clue: A sphere (such as the earth's surface) is a positive space. Imagine a right triangle with one point at the north pole and the other two points and the right angle on the equator. The answer for a negitive space is the opposite for the answer in a positive space. A flat, or Euclidean space is where the angles of a triangle add up to 180 degrees and parallel lines never meet.

one more clue: In a positive space parallel lines always meet (think of line of longitude on a globe, they all meet at the poles) and in a negitive space parallel lines always get farther away from each other.

_________________
My Blog: My Autistic Life

Odin
Veteran
Veteran

Joined: 12 Oct 2006
Age: 39
Gender: Male
Posts: 2,475
Location: Moorhead, Minnesota, USA

29 Apr 2008, 10:29 pm

pakled wrote:

The second link doesn't work.

_________________
My Blog: My Autistic Life

Odin
Veteran
Veteran

Joined: 12 Oct 2006
Age: 39
Gender: Male
Posts: 2,475
Location: Moorhead, Minnesota, USA

29 Apr 2008, 10:35 pm

one more thing to help:

"Hyperbolic" = negitive curvature

"Elliptic" = positive curvature

_________________
My Blog: My Autistic Life

Icheb
Veteran
Veteran

Joined: 23 Sep 2007
Age: 60
Gender: Male
Posts: 1,918
Location: Switzerland

30 Apr 2008, 2:29 am

Daewoodrow wrote:

Robert Heinlein's short story "- And He Built A Crooked House -" is about a tesseract-shaped house that collapses in on itself and traps the occupants inside.

_________________
"If you're using half your concentration to look normal, then you're only half paying attention to whatever else you're doing." - Magneto in "X-Men: First Class"

sim
Veteran
Veteran

Joined: 19 Apr 2008
Age: 35
Gender: Male
Posts: 512
Location: an uneven circle

30 Apr 2008, 2:49 am

Odin wrote:

one more thing to help:

"Hyperbolic" = negitive curvature

"Elliptic" = positive curvature

good, simple explanation. I'm going to go pickup that copy of the Elements sitting around in my school's library that nobody seems to touch.

Also: Less than!

I read something about it in Roger Penrose's "Guide to the laws of the universe", but didn't really remember much having to do with the relations of hyperbolic angles... *palms the side of my head* There's something to learn!

TallyMan
Veteran
Veteran

Joined: 30 Mar 2008
Gender: Male
Posts: 40,061

30 Apr 2008, 3:22 am

Odin wrote:

slowmutant wrote:

If a hypercube exists in 4 dimensions, how can it be rendered by three dimensional beings like ourselves?

A rotating hypercube:

While we can't directly picture a four dimensional object, think of it this way...

In the same was as a three dimensional cube can be drawn as a wire diagram on a flat sheet of paper so the four dimensional hypercube can be rendered in three dimensions. Think of the former as the two dimensional shadow of a three dimensional cube and the latter (above) as the three dimensional shadow of a four dimensional hypercube.

KateShroud
Veteran
Veteran

Joined: 1 Feb 2008
Age: 39
Gender: Female
Posts: 1,159
Location: Austin, Texas, United States, north America, Earth, Milky Way Galaxy

30 Apr 2008, 5:28 pm

Odin wrote:

one more thing to help:

"Hyperbolic" = negitive curvature

"Elliptic" = positive curvature

Now I'm compelled to ask, would the image of the hyperbolic be described as like the curved surface found on the inside of a hollow globe? I'm assuming this since you described a positive curvature as like the outside of the globe.

pakled
Veteran
Veteran

Joined: 12 Nov 2007
Age: 67
Gender: Male
Posts: 7,015

30 Apr 2008, 9:31 pm

sorry..ok, working backward from the site (actually being there...

http://www.wings3d.com/

ok..tested it from inside the post...should work fine.

Page 3 of 4 [ 50 posts ] Go to page Previous 1, 2, 3, 4 Next

Jump to:

Is anyone else fascinated by basic geometric shapes? Post Reply New Topic

Is anyone else fascinated by basic geometric shapes?