Unimpressive and quirky

[UsuallyPresent]

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).

That means that the total for all 3 angles, summing interior and exterior angles, is always 1080 degrees (360 x 3) no matter what the requirements of the “inside” angles are in that particular geometry.

That property should remain consistent in any 'smooth' realm - IE, no spikes running to plus/minus infinity, no disjointed space (gaps), etc - if I recall my advanced geometry correctly.

 

[Jackie.Hikaru]

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).

That means that the total for all 3 angles, summing interior and exterior angles, is always 1080 degrees (360 x 3) no matter what the requirements of the “inside” angles are in that particular geometry.

Unimpressive Police here! This thread is focused on the unimpressive Y'all need to tone down this impressive math shit alright? Good. Carry on!

 

[Britva415]

Yes, notifications.

This happens to me when I miss the notification and don’t open the thread right away.

It’s like the site thinks, “I already notified you” and stops doing it until I take it upon myself to catch up with the thread.

Which I don’t know to do because I missed the notification.

Vicious cycle!

But once I catch up with the thread, I’ll start seeing notifications again.

I’ve also somehow mistakenly “in-watched” a thread.

 

[Britva415]

Unimpressive Police here! This thread is focused on the unimpressive Y'all need to tone down this impressive math shit alright? Good. Carry on!

Math nerds aren’t quirky?

Ah, there’s an AND in that title.

 

[Bramblethorn]

If you place the vertexes at the maxima of each axis, covering 1/8th of the sphere, you get 90 degree angles.

Pulling the vertexes in closer and the angles shrink down towards the planar normal of 60 degrees as the curvature flattens towards a plane.

I 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.

edit: argh, didn't see @Britva415 's more succinct answer until I'd posted this one. At least we agree!

That's an easy one when you see the trick to it.

Take a little equilateral triangle, small enough that the sphere is approximately flat over that region. As you've said, the angles will be just over 60 degrees, for a total of (180+ε)°.

Expand it until it covers one-eighth of the sphere, and again as you've said, the angles are 90° for a total of 270°.
Expand it further again, until the triangle covers one-half of the sphere, with our three points evenly spaced along an equator. (It's now a perfect circle, but by our definitions it's still a triangle.) Now the angle at each vertex is 180°, for a total of 540°.

But which half of the sphere is the "inside" and which is the "outside" of that triangle?

Any time we draw a triangle on a sphere, we're actually creating two triangles: one "inside", one "outside" the lines, for whichever side we designate as "inside". Normally we're thinking about the smaller triangle, but the larger one is just as valid by spherical-geometry definitions (even though it's a long way from the plane triangles we're used to).

At any vertex, the sum of the interior and exterior angles is 360°. So for any set of three lines that split the sphere into two triangles, the total angle sum of the two is 3*360° = 1080°.

Since the minimum angle sum possible for a triangle on the sphere is 180°, the maximum is (1080-180)° = 900°. Going back to our original tiny equilateral triangle with angles each just over 60°, the partner triangle is an equilateral triangle with angles each just under 300°.

 

[UsuallyPresent]

Math nerds aren’t quirky?

Ah, there’s an AND in that title.

We're not iterating over polydimensional space, fractal spaces, or other truly impressive math. Carry on, we fit.

 

[Kitty_so_frisky]

Since I’ve been in the author’s hangout I’ve learned that my fellow lit authors are an incredibly impressive bunch who have lived incredibly impressive lives and to simply be here among you I feel so fortunate and honored. That said I would love to learn more about you all! Specifically how about we share something entirely unimpressive yet perhaps a bit quirky about ourselves.

I’ll go first! The only Cheetos I eat are hot Cheetos and I always eat them with chopsticks. I guess that’s two facts…

Quirkiness, a Cowboy Bebop reference in tagline AND you eat Cheetos with chopsticks?! You can come to the Sex & Shenanigans thread and sit by me and @UnquietDreams , we were just talking about eating Cheetos and other snacks with chopsticks yesterday!

 

[Jackie.Hikaru]

You can come to the Sex & Shenanigans thread and sit by me and @UnquietDreams , we were just talking about eating Cheetos and other snacks with chopsticks yesterday!

such classy people in this joint!

 

[Bramblethorn]

That property should remain consistent in any 'smooth' realm - IE, no spikes running to plus/minus infinity, no disjointed space (gaps), etc - if I recall my advanced geometry correctly.

It's been a while, but I think the smoothness condition needs to be a little tighter than that: not just "no spikes running to plus/minus infinity", but no spikes at all.

For instance, replace our sphere with an icosahedron (d20), made up of twenty flat equilateral triangles glued together in a ball. For any point not at one of the vertices, the space is locally flat so the sum of angles around a point is exactly 360°. But for a point at one of the vertices, the angle sum is only 300°.

For a more obnoxious example, consider the surface defined by x = r cos θ, y = r sin θ, z = r sin nθ, for some positive integer n. This is continuous, and for any point not at (0,0,0) the angle sum is 360° as usual, or 2π radians. But at (0,0,0)?

The angle sum at a point is equivalent to the limit of (circle circumference/circle radius) as the radius tends to zero.

For a circle of radius r with centre at (0,0,0), the circumference is equal to:

integral from 0 to 2π of sqrt( (dx/dθ)^2 + (dy/dθ)^2 + (dz/dθ)^2)) dθ
= integral from 0 to 2π of sqrt( (r^2 sin^2 θ + r^2 cos^2 θ + r^2 n^2 cos^2 (nθ) ) dθ
= r * integral from 0 to 2n of sqrt(1 + n^2 cos^2 (nθ)) dθ

So the angle sum is equal to:

integral from 0 to 2n of sqrt(1 + n^2 cos^2 (nθ)) dθ

which is clearly larger than 2π, and can be made arbitrarily large by increasing n.

 

[Bramblethorn]

Unimpressive fact about me: when I was a kid I used to eat apples core, seeds and all. I may have thought I was building up a resistance to cyanide, I don't remember for sure.

I loved apricots and cherries, and I would do a thing where I'd carefully split an apricot in half, remove the kernel, and stick a cherry in the hollow before eating it.

 

[TheDickens]

I have bought full-sized candy bars to give out at Halloween for the past 20 years.

I always buy too many and my co-workers look forward to me coming back to work after Halloween.

Legend! To both your trick-or-treaters and your cow-orkers.

(Yea, waaaay late to this thread, but I just happened across it.)

 

[TheDickens]

... sometimes it's best to leave the fantasies in my head rather than exposing them to the blowtorch of reality.

I suspect "the blowtorch of reality" has just become a regular part of my lexicon.

And "captured by a sunbeam" is so beautifully evocative!

To all the Annabelles...

 

[ShelbyDawn57]

I once ran a mile in 5:59. Tons of mile times between 6:00 and 6:10, but only ever got below 6 minutes once.

Impressive. I've had cars that couldn't do that downhill.

 

[MillieDynamite]

I once drove a quarter of a mile in 9.2 seconds. My Pops was really impressed but a bit upset at the piss on the driver's seat.

 

[ShelbyDawn57]

Also, I sort my peanut M&M's by color and eat them in a manner that the number of each color is the same.

AS for quirky...those M&M's once correctly predicted the record of my Texas Longhorns based on team colors, going 13-1 against the actual scores(Texas went 8-6. The M&M's were right 13 of 14 times). Unfortunately I have not been able to recreate that feat, and no, I didn't bet on the games.

 

[MillieDynamite]

A wise man, my adopted Dad, told me don't bet and you'll have no regret. Regrets? Yeah, I have a few.

Also, I sort my peanut M&M's by color and eat them in a manner that the number of each color is the same.

AS for quirky...those M&M's once correctly predicted the record of my Texas Longhorns based on team colors, going 13-1 against the actual scores(Texas went 8-6. The M&M's were right 13 of 14 times). Unfortunately I have not been able to recreate that feat, and no, I didn't bet on the games.

 

[Steadfast421]

Regrets? Yeah, I have a few

But then again, too few to mention.

 

[gunhilltrain]

I can tell a lot about New York subway cars just by looking at them - the year built, the builder, the class number (actually a contract number), and so forth. The one in my avatar is an R-32, ran on the B division, built by the defunct Budd Company in Philadelphia. There were about 600 of them, and they were in service from 1965 to the last ones about two years ago. Now I have to explain the difference between the A and B divisions, but I'be gone on long enough.

 

[Jackie.Hikaru]

I can tell a lot about New York subway cars just by looking at them - the year built, the builder, the class number (actually a contract number), and so forth. The one in my avatar is an R-32, ran on the B division, built by the defunct Budd Company in Philadelphia. There were about 600 of them, and they were in service from 1965 to the last ones about two years ago. Now I have to explain the difference between the A and B divisions, but I'be gone on long enough.

There's a hiking route near where I live where you'll find a cafe nestled in a sunny hillside right above a beautiful rail bridge. Whenever I walk by, I always see a gaggle of people sitting on the edge of the cafe's terrace or on the grassy hillside below the cafe, coffee or beer in hand, many with fancy telephoto cameras worth more than my car set up on tripods, and a generally jovial atmosphere. When a train comes through the tunnel and traverses the rail bridge, the cameras snap away, the engineer sounds the train whistle (or is it horn?) a few times and waves at the people at the cafe, and the people wave back. And long after the train is gone, smiles are still broad as can be.

Every time I see this transpire, I think, dang, being a trainspotter seems like such a great thing to be.

 

[EdgySubMic]

For many years, I travelled internationally a lot for my job. At some point, whenever visiting a larger city and having spare time, I got into a habit of finding an expensive high-quality book about one of the many subjects my mother was fascinated by. I saw it as a way to say thanks for all the years and for the fact that she still looked after some of my things, even though I had already been living alone for many years. I'd give her a new book at least twice a year, sometimes more often, and I did not need a special occasion such as a birthday or so to do it. She (almost) never asked for something specific, but there was one specialist exception to that. After she told me that one, I duly went hunting, but failed to find anything for many months. These days, I'd buy one from Amazon as a stand-in, but no Amazon was to be spotted back then....

One day, I had a whole day to myself in a large but otherwise boring city in Germany. The place had been bombed into utter oblivion during WW2 and there was nothing much historical left there to go see. It was all just 1950's and 1960's "we need something up by yesterday" concrete box "architecture". Very ugly and sad, really. Anyway, this was an excellent opportunity to hunt down every single book store I could locate, looking for that one elusive book. The weather was bad and I had no car, so, apart from using some public transport, I walked for miles, and miles, and miles, going into at least six stores without any luck. By the evening, I was cold, very wet, and my feet really hurt badly, despite me being an avid hiker – when not wearing the wrong type of shoes, that is.

The weekend after that trip, I went to see my parents. I had no present, but also did not need to have one. For one, she did not know about the trip and, anyhow, I did not bring something every time. It turned out that. in my absence, she had done something very minor in effort, but extremely annoying to me. It was like she had assumed that I was still living with her and she had completely overlooked that I'd have to deal with what she did while I was away on my own for weeks or months. I considered her idea "utterly stupid", and asked her to kindly reverse it – not expressing my actual opinion. She refused, even though it would have taken her less than five minutes to comply. The fight escalated. Finally, I blurted out how I'd had an absolutely awful day looking for the kind of book she'd asked for, only to get this kind of nonsense "in return". She was very visibly shocked, as she suddenly understood the mismatch, and immediately relented, but I never really forgave her and I never again went book hunting for her. I did still bring along some other minor stuff, but no more expensive books. She died a few years later.

To this day, when I go into a major book store, I sometimes go and see if I can find that one book. And Amazon won't do...

 

[Candy_Kane54]

If you watch the order in which I eat the different foods on my plate you will know which are my favorites and which are not. I will always finish the least liked food item first and my favorite food item last.

 

[SinclairGroupLLP]

I have edited more than half of my stories on my laptop while in the bathtub. It's one of the few places where I can just sit and not be distracted by anything. Completely unimpressive, other than the fact that I haven't managed to electrocute myself yet (no, it's not plugged in).

 

[Erozetta]

I have edited more than half of my stories on my laptop while in the bathtub. It's one of the few places where I can just sit and not be distracted by anything. Completely unimpressive, other than the fact that I haven't managed to electrocute myself yet (no, it's not plugged in).

Same.

 

[nice90sguy]

I eat 1/2 bulb of garlic a day. I'm healthy, but a little lonely

 

[Erozetta]

Legend! To both your trick-or-treaters and your cow-orkers.

(Yea, waaaay late to this thread, but I just happened across it.)

I had a kid and his dad track me down a couple years after my husband and I moved the last time. That was a little unnerving, but the kid was sweet and very excited to have found me again. ('Cause apparently I'm the only one who does full sized chocolate and fruit candy and he loved Skittles.)