« first day (153 days earlier)      last day (1071 days later) » 

flawr
flawr
09:26
Sounds like a challenge for PPCG: math.stackexchange.com/questions/1218899/…
flawr
flawr
09:38
Formula for primes
In number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. No such formula which is efficiently computable is known. A number of constraints are known, showing what such a "formula" can and cannot be. == Formula based on Wilson's theorem == A simple formula is f ( n ) = ⌊ n ! mod ( ...
 
2 hours later…
flawr
flawr
12:03
crazy images:
nasa.gov/feature/goddard/2017/…
PhiNotPi
PhiNotPi
12:42
@flawr am I misunderstanding how the teleporter works or is there no point to it being toroidal?
Nathan Merrill
Nathan Merrill
@PhiNotPi if it was a square, you could go to the corner
as far as spherical vs toroidal, I have no idea
René Descartes
René Descartes
Is Science the knowledge of what is around us? Please give your opinion. I request you.
PhiNotPi
PhiNotPi
13:00
@NathanMerrill my point was that if you could teleport anywhere, the palace is basically random-access and it doesn't matter how the rooms are physically arranged.
Nathan Merrill
Nathan Merrill
You still get to choose where the teleport goes
and the corner is a marking. It means that you can use it to find your partner
PhiNotPi
PhiNotPi
Okay that makes sense.
Martin Ender
Martin Ender
1
A: Sandbox for Proposed Challenges

MvGRendezvous palace optimization Introduction This comes from a well-liked question on the Math SE by RobAu and a more specific follow-up to that by Danikov. There is a palace which is a grid of n × n rooms, which we will index using two coordinates 0 ≤ x,y < n. The rooms are organized in a toru...

Martin Ender
Martin Ender
13:25
@flawr hey, why does this get starred when you post it? :P
I really wish they'd reach the final stretch goal, but another 90k dollars in 5 days seems unlikely
Nathan Merrill
Nathan Merrill
13:40
Especially because its no longer on the front page of reddit
El'endia Starman
El'endia Starman
13:54
@MartinEnder Well, he linked to the Kickstarter itself...
El'endia Starman
El'endia Starman
14:14
TIL that aircraft often use differential braking to turn.
flawr
flawr
14:29
@MartinEnder oh did you link it before?
probably because you already have enough stars :)
@El'endiaStarman ah, on the floor :)
If you also consider paragliders as aircraft, then differential braking is also applied while flying=)
@MartinEnder oh nice=)
El'endia Starman
El'endia Starman
@flawr Oh, lol, I didn't think to clarify that I meant on the ground. Aircraft do turn by other means in the air. :P
flawr
flawr
Sometims they apparently use differential thrust:
Wikipedia: Flight with disabled controls
Martin Ender
Martin Ender
@flawr yeah a couple of weeks ago when the kickstarter had just started, but like El'endia said I shared an article about it, not the kickstarter itself
flawr
flawr
Ah I must have missed that
 
3 hours later…
Nathan Merrill
Nathan Merrill
17:29
Using a Charge Card to Buy $170 Million Painting
►
The interesting part starts at 2:11
flawr
flawr
18:27
Consider a car with tires enumerated 1 to 4. Let alpha_i be the angle at which the valve of tire i is. Consider four arbitrary reals delta_i. Is it possible to find a finite path on the plane for the car to drive along such that for every tire i the valve is at angle alpha_i + delta_i?
trichoplax
trichoplax
18:40
@MartinEnder All the things in the final stretch goal sound like things they will probably do shortly afterwards whether they reach the target or not, so there's still hope...
PhiNotPi
PhiNotPi
18:52
@flawr So the problem is, given the angles of 4 tires of a car, does a matching path exist for the car?
flawr
flawr
Yep:)
Nathan Merrill
Nathan Merrill
19:13
select the center of a square car
have all tires face towards the center
PhiNotPi
PhiNotPi
20:01
I think the 'matching path' for any wheel configuration has to be a circle. Since the wheels are fixed relative to the car the curvature of the path must be constant, right?
And, if the path is a circle, I think the path of each wheel must also be a circle, and the wheel paths must be concentric.
Which means, in order for a path to exist, lines drawn perpendicular to each wheel must all meet at a single point (the center of the circle).
(Edge case: point at infinity in the case of straight wheels)
@flawr ^
flawr
flawr
20:26
Ah I did not define that: You are allowed to turn the steering wheel!
Nathan Merrill
Nathan Merrill
20:48
we need a better definition than that: Does the steering wheel turn the two front wheels the same angle?
is each wheel independent?
flawr
flawr
Hm I didn't think about that. Actually we would need the axis of all the wheels to meet in one point, otherwise we would have slipping.
So either the axis are parallel or they meet in one point.
El'endia Starman
El'endia Starman
21:20
@flawr Real cars avoid wheel slippage via differential gears.
The way I interpret the question is: given a square, can this square be translated and rotated such that the paths traced out by the vertices have lengths equal to given values, modulo 2*pi?
flawr
flawr
@El'endiaStarman I mean sideways slip
@El'endiaStarman yep, exactly
El'endia Starman
El'endia Starman
@flawr Oh, I see, yeah.
My gut is that any modulo will suffice.
 
2 hours later…
PhiNotPi
PhiNotPi
23:25
@El'endiaStarman how is this the same question?
Nvm, I misinterpreted the original problem, angle of the wheel = the pitch, not the yaw
El'endia Starman
El'endia Starman
23:45
Yeah, that's what I understood from him mentioning the valves on the tires.
El'endia Starman
El'endia Starman
23:58
I think this strategy suffices: angle the "car" to some degree and then rotate it around some point. Pick the angle such that the distances from each vertex to the rotation point have irrational ratios with respect to each other. As you rotate the car around that given point, there will be some point (ha!) where the distances traveled modulo 2*pi give the desired angles.

« first day (153 days earlier)      last day (1071 days later) »