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Math Thread

Talk about Math and shit like that

194 posts and 108 image replies omitted. Click reply to view.Talk about Math and shit like that

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Imagine there is an infinite line of light bulbs, each numbered (starting with #1) with its own switch controlling it. Initially all the lights are switched off. You perform a procedure that goes like this: first you go through and flip every switch, turning on all the lights. Then you go back to the beginning and flip every other switch starting with light #2. Then you go through flipping every third switch starting with light #3, and so on for all subsequent numbers. After you've completed this infinite procedure, which of the numbered lights are turned on? Why is this?

>>3641839

The point is to be lazy. and the complicated stuff will be reasonable to deal with eventually. Management skills and a 1000 lightbulbs with a little OCD and you might find a shortcut. At least, that is the optimisic POV. The human side tends to bonk things up and make it worse however. Basically if you realize the dependencies on getting one thing done in that mess that matters, you can zero in on it all.

The point is to be lazy. and the complicated stuff will be reasonable to deal with eventually. Management skills and a 1000 lightbulbs with a little OCD and you might find a shortcut. At least, that is the optimisic POV. The human side tends to bonk things up and make it worse however. Basically if you realize the dependencies on getting one thing done in that mess that matters, you can zero in on it all.

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https://en.wikipedia.org/wiki/Time_dilation

1 sec equals 10 seconds

1 sec equals 10 minutes

1 sec equals 10 hours

1 sec equals 10 days

1 sec equals 10 weeks

1 sec equals 10 months

1 sec equals 10 years

1 sec equals 10 centuries

1 sec equals 10 millenniums

1 sec equals 10 seconds

1 sec equals 10 minutes

1 sec equals 10 hours

1 sec equals 10 days

1 sec equals 10 weeks

1 sec equals 10 months

1 sec equals 10 years

1 sec equals 10 centuries

1 sec equals 10 millenniums

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I'm taking a course in linear control systems this semester and right now we're learning about state space representations of differential equations

I can feel this is Big Shit. If I can really get my head around the concept and get fluent in how it works, I think I'll be able to make major progress in personal math projects of mine

most specifically, one involving matrices of differential equations

I can feel this is Big Shit. If I can really get my head around the concept and get fluent in how it works, I think I'll be able to make major progress in personal math projects of mine

most specifically, one involving matrices of differential equations

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when you manage to derive the closed form solution of a random power series you shat out, from intuition alone

>>3647640

yeah what about it

>>3647640

yeah what about it

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Well well well, looks like I stumbled across the answer to the question posed in the second post itt. "Repulsive curves" provide the solution. Check out the following resources for details.

https://youtu.be/M0RuBETA2f4

https://www.cs.cmu.edu/~kmcrane/Projects/RepulsiveCurves/index.html

>>3647640

>echo chamber

Nah, that's the humanities department. This is hard sciences.

https://youtu.be/M0RuBETA2f4

https://www.cs.cmu.edu/~kmcrane/Projects/RepulsiveCurves/index.html

>>3647640

>echo chamber

Nah, that's the humanities department. This is hard sciences.

>>3647652

1+1 = more water than you really have space for.

1+1 = more water than you really have space for.

>>3649447

integer of substance + (integer of substance) = integer of substance.

But I barely fit all that water into the tank with all that empty space. But its all the same. Let's just call it an echoe chamber despite it being black and white more than what it is.

integer of substance + (integer of substance) = integer of substance.

But I barely fit all that water into the tank with all that empty space. But its all the same. Let's just call it an echoe chamber despite it being black and white more than what it is.

>>3647640

>>3649447

>>3649448

Its complicated ok but lets say you work it out to a base10 you can then set it to a mod10 as the new deritive of the base. There you have the echo chamber scenarios you can make quadratic. They will average as a quotient to the whole dimensional set of XYZ in coordinate fashion. You will have achieved a vector plot doing this likely.

>>3649447

>>3649448

Its complicated ok but lets say you work it out to a base10 you can then set it to a mod10 as the new deritive of the base. There you have the echo chamber scenarios you can make quadratic. They will average as a quotient to the whole dimensional set of XYZ in coordinate fashion. You will have achieved a vector plot doing this likely.

>>3649450

You might not follow me but for me it works out Snug as a bug in an electrical plug.

You might not follow me but for me it works out Snug as a bug in an electrical plug.

>>3649451

and its the same reason why we have trouble touching nucleus without breaking the electron cloud. (surface contact of a nucleus will result in a nuclear heat death) it recognizes any impulse as a reason to cause retroactive half life.

and its the same reason why we have trouble touching nucleus without breaking the electron cloud. (surface contact of a nucleus will result in a nuclear heat death) it recognizes any impulse as a reason to cause retroactive half life.

>>3649454

and also can help trace quantum activity residually in order to predict where heatdeath occurs if you chart it right you will be able to automate causation and probability in quantum mechanics but im just some random dood lol.

and also can help trace quantum activity residually in order to predict where heatdeath occurs if you chart it right you will be able to automate causation and probability in quantum mechanics but im just some random dood lol.

>>3649455

After some deliberation of a real world application you might find it better just to settle for a 3d-Screen system that employs Sonar, maybe interactively, as a vector state imaging might be too advanced for even this type of mathematic, but would be more or less the same use. (VectorState Mapping Involves the unobservable universe)

After some deliberation of a real world application you might find it better just to settle for a 3d-Screen system that employs Sonar, maybe interactively, as a vector state imaging might be too advanced for even this type of mathematic, but would be more or less the same use. (VectorState Mapping Involves the unobservable universe)

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>>3638762

Planet Inception?

Planet Inception?

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>>3649895

What happens if you pick up yourself up like a voodoo doll?

What happens if you pick up yourself up like a voodoo doll?

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>still pi day in murica

Happy Pi Day!

Happy Pi Day!

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Pi day Challenge:

Imagine you have a floor made from floorboards, each of which runs the full length of the room and each with the same width. If you drop a toothpick with the same length as the width of a floorboard randomly, what is the probability the toothpick will lie across a crack in the floorboards?

Imagine you have a floor made from floorboards, each of which runs the full length of the room and each with the same width. If you drop a toothpick with the same length as the width of a floorboard randomly, what is the probability the toothpick will lie across a crack in the floorboards?

>>3650682

This is interesting because at first you might think this is a constant, but it's grossly changed by the dimensions of the room and how many floor boards you use.

Using three extremes for examples:

1 floor board = 0% chance for the toothpick to land on a crack.

Floor is 1 mile long, and you have two boards (1 line), about 50% chance it crosses the singular crack (only configuration it does not is damn near perfectly parallel anywhere or exactly as far as possibly from the line perpendicular to the line. The odds change at a 1/1 ratio as you rotate the stick. Upwards the room (Y axis) is basically irrelevant with a floor this long.

Now we have another room that's an inch long and two miles wide. Each toothpick is one mile long, and has to fit in an inch. There is one crack. We are now at basically 100% chance it falls on a crack. There are two points (really small vectors in reality) where you can drop the toothpick and not have it cross the line, each at the furthest point possible from the line. The minimal rotation available to the toothpick is basically meaningless.

The trick is to model these extremes in your answer, which I do not have the brain to do, but these three examples illustrate how the answer changes based on your input (board number, X and Y dimensions), which means the answer is an equation and not a definite number. Somebody smarter than me can take it from there.

This is interesting because at first you might think this is a constant, but it's grossly changed by the dimensions of the room and how many floor boards you use.

Using three extremes for examples:

1 floor board = 0% chance for the toothpick to land on a crack.

Floor is 1 mile long, and you have two boards (1 line), about 50% chance it crosses the singular crack (only configuration it does not is damn near perfectly parallel anywhere or exactly as far as possibly from the line perpendicular to the line. The odds change at a 1/1 ratio as you rotate the stick. Upwards the room (Y axis) is basically irrelevant with a floor this long.

Now we have another room that's an inch long and two miles wide. Each toothpick is one mile long, and has to fit in an inch. There is one crack. We are now at basically 100% chance it falls on a crack. There are two points (really small vectors in reality) where you can drop the toothpick and not have it cross the line, each at the furthest point possible from the line. The minimal rotation available to the toothpick is basically meaningless.

The trick is to model these extremes in your answer, which I do not have the brain to do, but these three examples illustrate how the answer changes based on your input (board number, X and Y dimensions), which means the answer is an equation and not a definite number. Somebody smarter than me can take it from there.

>>3650682

the probable chance is 1:100 if you think of a floor board as 99% board and 1% crack.

the probable chance is 1:100 if you think of a floor board as 99% board and 1% crack.

>>3649898

you will magically levitate much to the surprise of the scientific community. Thus end up on the Fire as a Heretic.

Stuff you bum with Marshmallows, think of the children

you will magically levitate much to the surprise of the scientific community. Thus end up on the Fire as a Heretic.

Stuff you bum with Marshmallows, think of the children

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>>3650848

Ignore boundary influence - assume the room is infinite if you want. But all that's required to assume is that there are multiple floorboards of equal width to the toothpick length (which was specified), and that the floorboards are at least as long as the toothpick (which wasn't specified). These two conditions imply a single probability that's independent of the dimensions of the room. Do you know how to calculate this probability?

Pi Day video:

https://youtu.be/GToqKcd-yA4

Ignore boundary influence - assume the room is infinite if you want. But all that's required to assume is that there are multiple floorboards of equal width to the toothpick length (which was specified), and that the floorboards are at least as long as the toothpick (which wasn't specified). These two conditions imply a single probability that's independent of the dimensions of the room. Do you know how to calculate this probability?

Pi Day video:

https://youtu.be/GToqKcd-yA4

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>>3651206

actually its not 1:100 its .01% because of probable inclusions it simply does not define the answer, in the case for all answers there is always this .01% "oversight".

actually its not 1:100 its .01% because of probable inclusions it simply does not define the answer, in the case for all answers there is always this .01% "oversight".

>>3651206

This is such a dumb thing to mention because you arleady know the quotients are represented that..pi=pi. There are many formats of it included extensions of pi in a pattern.

But no one is saying the oversight. It is an unknown (even if its pi). Or written in some other value. Or variable. 1-2-3…and then just listed as an extension of what it already is. 4. And then 5 which isn't even necessary unless you are going for'Throughput Quantum Symphonium'm a full theory of that PI(1)=PI(2).

To explain we know it is probably that the answer is there. For the case that it occurs under the expression or paradigm. Numbers=Solved or Proof.

But to say we how figure it out iis completely dependent on the end result as well.

Now we have that the oversight occurs. So we say, the standard, or the variable, or the unknown, or the offset-way of saying its known, and then eventually a full quantum theory explaining the parameters and location of a black hole in quantum hyperspace, is basically a token of Pi.

This is such a dumb thing to mention because you arleady know the quotients are represented that..pi=pi. There are many formats of it included extensions of pi in a pattern.

But no one is saying the oversight. It is an unknown (even if its pi). Or written in some other value. Or variable. 1-2-3…and then just listed as an extension of what it already is. 4. And then 5 which isn't even necessary unless you are going for'Throughput Quantum Symphonium'm a full theory of that PI(1)=PI(2).

To explain we know it is probably that the answer is there. For the case that it occurs under the expression or paradigm. Numbers=Solved or Proof.

But to say we how figure it out iis completely dependent on the end result as well.

Now we have that the oversight occurs. So we say, the standard, or the variable, or the unknown, or the offset-way of saying its known, and then eventually a full quantum theory explaining the parameters and location of a black hole in quantum hyperspace, is basically a token of Pi.

>>3651282

There is the preface of the full pi plot, by my own reasoning, we can include substitions and eliminations of its conversions (in any quadratic) (sometimes quartic which is borderline insanity imo and quintic which boils down to what type of caliber do you prefer to take before bed)

That once you have plotted these (and a vector of that being the next iteration) You can then finally begin to convert the correct "undisturbed by the enviroment" measure of what that proof is really by 'term or zero-energy' Because being exact is not enough if you are also "defining it in a space-time" you need to balance that with every step in the pattern…then its still .01% chance it lands at all.

There is the preface of the full pi plot, by my own reasoning, we can include substitions and eliminations of its conversions (in any quadratic) (sometimes quartic which is borderline insanity imo and quintic which boils down to what type of caliber do you prefer to take before bed)

That once you have plotted these (and a vector of that being the next iteration) You can then finally begin to convert the correct "undisturbed by the enviroment" measure of what that proof is really by 'term or zero-energy' Because being exact is not enough if you are also "defining it in a space-time" you need to balance that with every step in the pattern…then its still .01% chance it lands at all.

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>>3651285

I don't feel like explaining this again but this is pretty much how i would try to teach a complete noob about 'certainty'

I don't feel like explaining this again but this is pretty much how i would try to teach a complete noob about 'certainty'

>>3651206

if pi is consider 100% a whole of 1 its 1:100 chance if pi is then considered as a formfactor of quantum casaulty (itself in casuality so therefore 2=2/sqrt2) it is considered more in terms of .01% because there is more inclusion of probability.

if pi is consider 100% a whole of 1 its 1:100 chance if pi is then considered as a formfactor of quantum casaulty (itself in casuality so therefore 2=2/sqrt2) it is considered more in terms of .01% because there is more inclusion of probability.

>>3651294

literally its because you choose to call salt instead salt peter, but there is no real difference until you are trying to redefine something because of a .01% change in observation of when it was ever to begin with.

literally its because you choose to call salt instead salt peter, but there is no real difference until you are trying to redefine something because of a .01% change in observation of when it was ever to begin with.

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>>3650848

>>3651206

>These two conditions imply a single probability that's independent of the dimensions of the room.

Whoops, this part is wrong. I concluded that the boundary influences would always cancel out, based on absolutely nothing! Well, based on the fact that none of the explanations of this problem I've read mention boundary influences.

That said, the boundary effects*can* cancel out. The probability that a toothpick crosses a crack drops to 0 when the center of the toothpick lands within 1/2 the toothpicks length to a boundary (wall) parallel to the floorboards. But if my calculations are correct, the probability that a toothpick, the center of which lands within 1/2 its length to a wall running *perpendicular* to the floorboards, crosses a crack is approx 0.9259685260. So a rectangular room with parallel walls (wrt the floorboards) which are 0.4540795935 times the length of the perpendicular walls should have boundary effects that cancel out, leaving you with a total probability of a toothpick crossing a crack equal to the probability if there were no walls (infinite room). I'm not accounting for the corners, because I've already complicated the problem enough.

Anyway, the point is you want to ignore boundary influences. Unless you*really* want to overcomplicate things. And you don't need an infinite room, just one with sufficiently large dimensions. **The probability of a toothpick crossing a crack in the large room will be the same as for an infinite room ***if* you discount the instances when a toothpick lands such that its center is within 1/2 the toothpick's length to a wall. This is the probability I was inquiring about in >>3650682 - the probability for a toothpick landing in the bulk of the room, free from the angle-constraining effect of the walls.

>>3651206

>These two conditions imply a single probability that's independent of the dimensions of the room.

Whoops, this part is wrong. I concluded that the boundary influences would always cancel out, based on absolutely nothing! Well, based on the fact that none of the explanations of this problem I've read mention boundary influences.

That said, the boundary effects

Anyway, the point is you want to ignore boundary influences. Unless you

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Fuck it. The answer is 2/pi, which is approx 0.6366197724. This is a problem in geometric probability from the 1700's, known as Buffon's needle. **This result means you can approximate pi by simply dumping a box of toothpicks on a wooden floor, counting, and then dividing the total number of toothpicks by the number that lie across cracks.** If the floorboards are twice as wide as the toothpicks are long, then your calculation will approximate pi. If the floorboard width and toothpick length are the same as I posed the problem, then you'd need to multiply your result by 2 to get a value approximating pi.

Here's a video showing how to solve Buffon's needle problem two ways - one explanation using calculus and another using just basic probability theory and geometric arguments:

https://youtu.be/szUH1rzwbAw

Here's a video showing how to solve Buffon's needle problem two ways - one explanation using calculus and another using just basic probability theory and geometric arguments:

https://youtu.be/szUH1rzwbAw

>>3651454

I can overcomplicate things by boundary influences being used marginally to the values involved also being used marginal saying that even with 100% chance there is a 0% chance that the toothpick is even there and that the floor lands on itself.

I can overcomplicate things by boundary influences being used marginally to the values involved also being used marginal saying that even with 100% chance there is a 0% chance that the toothpick is even there and that the floor lands on itself.

>>3651464

for instance the toothpick lands perfectly on a zero point…now we have a perfect and undetected polarized non-angle artifact in an immaculate cube…Schroedinger would have a seizure.

for instance the toothpick lands perfectly on a zero point…now we have a perfect and undetected polarized non-angle artifact in an immaculate cube…Schroedinger would have a seizure.

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Anyways the "anamolous toothpick" reminds me of something happening like this. Where the idea of it disentegrates or "is moved out of sight" and just keeps phasing away everytime it is "defined". Like if you wired a ruperts drop to a trigger and shot it off, it would just be unpredictable. It's pure confetti.

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I found this amusing. Recently Youtube recommended me these two videos:

https://youtu.be/BbX44YSsQ2I

https://youtu.be/5ddF5e-2SfM

The first shows a*Who Wants to Be a Millionaire* contestant (and the audience too) failing to get a question about which square number is the sum of two smaller square numbers. He consequently loses $15,000. The second video is about how ancient Babylonians understood Pythagorean triples 3,800 years ago.

>>3651454

>0.4540795935

Should be 0.4545079594. No use calculating all those digits if I miscopy them. The exact value I got is pi*Si(pi)/4 - 1, where Si() is the sine integral function. The exact value I got for the probability that, a toothpick which lands with its center within half its length to a wall running perpendicular to the length of the floorboards, also lies across a crack is Si(pi)/2. I'll explain how I got these results if anyone's interested.

>>3651497

That's pretty cool. Sounds trippy. I wonder what the webs in pic related would sound like.

https://youtu.be/BbX44YSsQ2I

https://youtu.be/5ddF5e-2SfM

The first shows a

>>3651454

>0.4540795935

Should be 0.4545079594. No use calculating all those digits if I miscopy them. The exact value I got is pi*Si(pi)/4 - 1, where Si() is the sine integral function. The exact value I got for the probability that, a toothpick which lands with its center within half its length to a wall running perpendicular to the length of the floorboards, also lies across a crack is Si(pi)/2. I'll explain how I got these results if anyone's interested.

>>3651497

That's pretty cool. Sounds trippy. I wonder what the webs in pic related would sound like.

>>3651604

til spider thoughts

weed looks like spider weed version

benzedrine shows vertigo

caffeine webs showing absolute beamer math

salt showing the 9 layers of hell

meth websalso a good study of a brain being hacked.

til spider thoughts

weed looks like spider weed version

benzedrine shows vertigo

caffeine webs showing absolute beamer math

salt showing the 9 layers of hell

meth websalso a good study of a brain being hacked.

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>>3655464

I'm pretty sure that inmate posts in this thread regularly.

I'm pretty sure that inmate posts in this thread regularly.

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W = Width

H = height

B = What?

What does B mean? Google got nothing.

H = height

B = What?

What does B mean? Google got nothing.

>>3657709

https://en.wikipedia.org/wiki/Bust/waist/hip_measurements#:~:text=Bust%2Fwaist%2Fhip%20measurements%20(,of%20the%20female%20body%20shape.

Bust/waist/hip measurements (informally called 'body measurements' or ′vital statistics′) are a common method of specifying clothing sizes. They match the three inflection points of the female body shape.

https://en.wikipedia.org/wiki/Bust/waist/hip_measurements#:~:text=Bust%2Fwaist%2Fhip%20measurements%20(,of%20the%20female%20body%20shape.

Bust/waist/hip measurements (informally called 'body measurements' or ′vital statistics′) are a common method of specifying clothing sizes. They match the three inflection points of the female body shape.

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