UsuallyPresent
Literotica Guru
- Joined
- Aug 23, 2019
- Posts
- 7,019
Grape jelly on scrambled eggs here.Quirky? I like marmalade on omelets.
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Grape jelly on scrambled eggs here.Quirky? I like marmalade on omelets.
No. Consider that a triangle has to have straight lines.
two straight lines on a sphere have to be perpendicular to the third in order to be straight.
I was once co-opted by the school orchestra to play the cymbals, but was so bad I was fired after a single performance
We'll call her Annabelle French for the purposes of this memory. She had wavy gold hair that fell to the middle of her back when she wasn't tying it up into a haphazard ponytail, and the blue eyes to go with them. She was tall, and slender, and awkward rather than graceful. She was also frighteningly intelligent - but far, far too kind and warm to be at all smug or bitchy about it. And oh my God could this girl paint.French the language or French....?
AwwHere's to you, Annabelle, wherever you are. I have no doubt you are just as bright and shining as you were when we were young.
This is the best bit of memory-arousal that I've read in weeks.It's thirty years ago and I can still remember the scene, and the... pain, I guess it was, somewhere around where I suppose my heart is.
If that were true, you wouldn’t be able to draw an equilateral triangle with angles close to 60 degrees on the surface of any sphere. This is obviously possible on any sphere, soSpheric geometry's triangles […] two of the angles have to be at least 90 degrees each.
Notifications, you mean?I don't know why new post aren't showing up for me from this thread?
If you place the vertexes at the maxima of each axis, covering 1/8th of the sphere, you get 90 degree angles.If that were true, you wouldn’t be able to draw an equilateral triangle with angles close to 60 degrees on the surface of any sphere. This is obviously possible on any sphere, so
The first part of my statement is correct, and shrinking the triangle may approximate flat space, but never is flat. You can get angles totaling close to 180 degrees, but never 180. Barmablethorn has corrected my error in the second part of my statement.If that were true, you wouldn’t be able to draw an equilateral triangle with angles close to 60 degrees on the surface of any sphere. This is obviously possible on any sphere, so
A good friend is a theoretical physicist. In the hubris that accompanies his advanced degrees, he loved to do this little proof that parallel lines intersext(leaving this typo here because, well, we're on an erotica site). Of course, he use a spherical geometry to do so, not plane geometry.Agreed, but for geometry on curved surfaces we need to define what "straight" means.
The usual interpretation of "straight line" is the shortest path connecting two points. (Give or take some complications to handle the case of line segments that travel more than halfway around the sphere, but let's leave that for now.)
On a sphere, the equivalent to a "straight line" is a great circle, i.e. one whose centre (as defined in 3-D space) coincides with the centre of the sphere. A "triangle" on a spherical surface has three sides which are each segments of great circles.
No. This is not correct.
You might be thinking of the fact that in spherical geometry, unlike plane geometry, it is possible to draw three "straight lines" all perpendicular to one another (forming the 270° triangle that AwkwardMD mentioned earlier). But this does not mean that every set of three lines (great circle segments) has to be mutually perpendicular.
It approaches a maximum possible total of 900 degreesI can't figure out the max angle if you go past the maxima of the angles and put the bulk of the sphere inside the triangle instead of just one eighth of the whole, not that it really matters to this conversation.
You know what’s super interesting about that question? The sum of the inside angle at each vertex and the outside angle at each vertex is still only 360 degrees, no matter what the curvature of the surface is (spherical or hyperbolic).It approaches a maximum possible total of 900 degrees
You can think of it as the triangle enclosed by what otherwise looks like the outside of that equilateral triangle. Each vertex has an angle of something barely less than 300 degrees (360 - 60)
Notifications, you mean?
Or you don’t se new posts at all when you look at the thread?