You messed with me~

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Math Thread

Talk about Math and shit like that

312 posts and 187 image replies omitted. Click reply to view.Talk about Math and shit like that

>>3683504

This is one of the subtle points of relativity. You can also shine the point of a laser across a distant object faster than the speed of light - has nothing to do with light vs dark. Special relativity says all observers in inertial reference frames measure the same speed for light. This means that*massive objects* cannot travel faster than the speed of light. It also means *information* cannot be transmitted faster than the speed of light.

This is one of the subtle points of relativity. You can also shine the point of a laser across a distant object faster than the speed of light - has nothing to do with light vs dark. Special relativity says all observers in inertial reference frames measure the same speed for light. This means that

>>3685130

I was feeding my fat bologna into your mom last night.

I was feeding my fat bologna into your mom last night.

>>3685130

I agree it seems to be missing some key parts that were seemingly left out on purpose.

I agree it seems to be missing some key parts that were seemingly left out on purpose.

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https://youtu.be/068rdc75mHM

Top tier NOVA documentary released on youtube yesterday about quantum entanglement. Description:

*Einstein called it “spooky action at a distance,” but today quantum entanglement is poised to revolutionize technology from computers to cryptography. Physicists have gradually become convinced that the phenomenon—two subatomic particles that mirror changes in each other instantaneously over any distance—is real. But a few doubts remain. NOVA follows a ground-breaking experiment in the Canary Islands to use quasars at opposite ends of the universe to once and for all settle remaining questions.*

Top tier NOVA documentary released on youtube yesterday about quantum entanglement. Description:

I just read that if you could accumulate something like 10 stellar masses of Toejam, or Smegma, or aborted babies or whatever, it would collapse into a black hole that would be indistinguishable in the way it formed from any other black hole.

Is this true?

Is this true?

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>>3685694

General relativity implies that's the case. Called the no-hair theorem:

*The no-hair theorem states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent externally observable classical parameters: mass, electric charge, and angular momentum. Other characteristics (such as geometry and magnetic moment) are uniquely determined by these three parameters, and all other information (for which "hair" is a metaphor) about the matter that formed a black hole or is falling into it "disappears" behind the black-hole event horizon and is therefore permanently inaccessible to external observers after the black hole "settles down" (by emitting gravitational and electromagnetic waves). Physicist John Archibald Wheeler expressed this idea with the phrase "black holes have no hair", which was the origin of the name.*

https://en.wikipedia.org/wiki/No-hair_theorem

However, quantum mechanics says information cannot be destroyed. But if black holes radiate away their mass over time, and this radiation is random black-body radiation, then the information of what fell into the black hole (or what collapsed to form it) is erased. This contradiction is known as the black hole information paradox:

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

General relativity implies that's the case. Called the no-hair theorem:

https://en.wikipedia.org/wiki/No-hair_theorem

However, quantum mechanics says information cannot be destroyed. But if black holes radiate away their mass over time, and this radiation is random black-body radiation, then the information of what fell into the black hole (or what collapsed to form it) is erased. This contradiction is known as the black hole information paradox:

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

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Elon Musk has speculated that we might be living in a simulation. If we are, then what is real and outside of this simulation?

There is no way to know what’s outside of the simulation. This isn’t just unknown, in the way that the existence of life after death, or parallel universes, is unknown; it is an unanswerable question. Let’s suppose that we are in a computer simulation, either created by a higher intelligence or humans in the future.

Now imagine that through some bug left in the code, we are accidentally able to step beyond the constraints of our programming and ‘see’ the simulation’s raw scaffolding, like Neo in The Matrix. How would you be able to decide whether this lay outside the simulation, or was still part of it – as a joke or an Easter egg, put there by programmers?

Could you even definitively say that the columns of ones and zeros scrolling past your eyes proved that reality was a simulation at all? Maybe that’s just what the Universe is made of, once you zoom all the way in past the atoms and quarks.

And even if you were able to unplug yourself and emerge blinking into the higher reality, how do you know this is what it is? Perhaps there is another reality around that, and so on. If none of these realities are reachable except in our imaginations, are they real? Reality comprises the things we can measure; everything else is fantasy or speculation.

Asking what lies beyond this reality is like asking who we were before being born. Shakespeare’s Hamlet tells Horatio that there are more things in Heaven and Earth than are dreamt of in his philosophy. But it may be the other way round. Humans are good at dreaming up things that do not exist, so you can’t use your ability to imagine something as evidence for it, one way or another.

There is no way to know what’s outside of the simulation. This isn’t just unknown, in the way that the existence of life after death, or parallel universes, is unknown; it is an unanswerable question. Let’s suppose that we are in a computer simulation, either created by a higher intelligence or humans in the future.

Now imagine that through some bug left in the code, we are accidentally able to step beyond the constraints of our programming and ‘see’ the simulation’s raw scaffolding, like Neo in The Matrix. How would you be able to decide whether this lay outside the simulation, or was still part of it – as a joke or an Easter egg, put there by programmers?

Could you even definitively say that the columns of ones and zeros scrolling past your eyes proved that reality was a simulation at all? Maybe that’s just what the Universe is made of, once you zoom all the way in past the atoms and quarks.

And even if you were able to unplug yourself and emerge blinking into the higher reality, how do you know this is what it is? Perhaps there is another reality around that, and so on. If none of these realities are reachable except in our imaginations, are they real? Reality comprises the things we can measure; everything else is fantasy or speculation.

Asking what lies beyond this reality is like asking who we were before being born. Shakespeare’s Hamlet tells Horatio that there are more things in Heaven and Earth than are dreamt of in his philosophy. But it may be the other way round. Humans are good at dreaming up things that do not exist, so you can’t use your ability to imagine something as evidence for it, one way or another.

>>3685341

The universe is likely based on a fringe of realities that act as staples of themselves. These mirroring particles are an advanced reflection from hypergeometries (expanded memories) that have reach their extents before the information is dropped off/unobservable from any source (itself or any other range of effective interaction) This can occur right in front of you because the particles have been sleighted into "entanglement" or a incongruency which can also explain residual stuff just happening. Particles are actually able to glitch other particles too creating a chain reaction but generally is filtered naturally in atomic processes and not by direct result. A random particle can become entangled and exhibit unknown states for no real reason. "HyperGeometry" is a corrective process in which information is "adjusted" or stressed/sleighted and can cause glitchy/unsafe particle behavoir, but over a large range of other factors having to do with polar observability. (A quantum flux particle that has "experienced" a change in half-life exhibits retroactivity in simultaneity with other particles in a particle cloud/zerospace much like the diffraction experiment, but they follow the same pattern with other molecules so closely they are likely of the same "source"-of-observation/information. (This can occur from a very pronounced A to B)

Probably has alot to do with how particles turn into alloy'd molecules and how they require electron sharing/defractionation in ionisations. (They share their orientations in which to transcode electrons in a cloud/superfluid timespace)-but due to other factors have been displaced from other forces at work)–particle telemetry and is somewhat advanced but easier explained that there is interdimensional-quantum-entanglement occuring and not the beginnings of a wyrmhole (ironically that could not exist under these conditions even though they exhibit qualifiers for those conditions-due to acceleration of hyperspace also being a pre-requisite)

The universe is likely based on a fringe of realities that act as staples of themselves. These mirroring particles are an advanced reflection from hypergeometries (expanded memories) that have reach their extents before the information is dropped off/unobservable from any source (itself or any other range of effective interaction) This can occur right in front of you because the particles have been sleighted into "entanglement" or a incongruency which can also explain residual stuff just happening. Particles are actually able to glitch other particles too creating a chain reaction but generally is filtered naturally in atomic processes and not by direct result. A random particle can become entangled and exhibit unknown states for no real reason. "HyperGeometry" is a corrective process in which information is "adjusted" or stressed/sleighted and can cause glitchy/unsafe particle behavoir, but over a large range of other factors having to do with polar observability. (A quantum flux particle that has "experienced" a change in half-life exhibits retroactivity in simultaneity with other particles in a particle cloud/zerospace much like the diffraction experiment, but they follow the same pattern with other molecules so closely they are likely of the same "source"-of-observation/information. (This can occur from a very pronounced A to B)

Probably has alot to do with how particles turn into alloy'd molecules and how they require electron sharing/defractionation in ionisations. (They share their orientations in which to transcode electrons in a cloud/superfluid timespace)-but due to other factors have been displaced from other forces at work)–particle telemetry and is somewhat advanced but easier explained that there is interdimensional-quantum-entanglement occuring and not the beginnings of a wyrmhole (ironically that could not exist under these conditions even though they exhibit qualifiers for those conditions-due to acceleration of hyperspace also being a pre-requisite)

>>3685710

Imo quantum welling (power routing) and cation/anion particles are a direct example of this effect in entagled-states but also denote there is higher-level of science in quantum mechanics creating a universal glue for data over long distances between any imprinted particle having a "butterfly effect" from its own "source". The half life in an entanglement is shared as a tensor in hyper-space that gives applies the memory/data for which the information is observed.

These are directly translated through a cation/anion that "glues" the particle/data together and effects its superfluid/sharedClouds through hyperspace(accelerations in quantum space/vectors). The now imprinted partcle colloborates with other particles or effectively reaches a halflife in which the relationship of its memory/data is effected through polarized settings (causing self-telemetry of the cation/anion as well). Electrons shared or Fallouts Made in this way also effect the superfluid/cloudGroup of particles which can create shortlived worm-holing as well as the particles develop entangled states(timespace).

It is advanced because data/observability is transferred where there would be no case otherwise (telemetry) and the "superglue" gets handled in unpredictable ways in simultaneity/retroactivity as a plasma between data/particle (matter/energy) in a semi-state of matter/energy. This can exhibit itself as spontaneous plasma that is depedent on other active plasmas in a seperate location.

Imo quantum welling (power routing) and cation/anion particles are a direct example of this effect in entagled-states but also denote there is higher-level of science in quantum mechanics creating a universal glue for data over long distances between any imprinted particle having a "butterfly effect" from its own "source". The half life in an entanglement is shared as a tensor in hyper-space that gives applies the memory/data for which the information is observed.

These are directly translated through a cation/anion that "glues" the particle/data together and effects its superfluid/sharedClouds through hyperspace(accelerations in quantum space/vectors). The now imprinted partcle colloborates with other particles or effectively reaches a halflife in which the relationship of its memory/data is effected through polarized settings (causing self-telemetry of the cation/anion as well). Electrons shared or Fallouts Made in this way also effect the superfluid/cloudGroup of particles which can create shortlived worm-holing as well as the particles develop entangled states(timespace).

It is advanced because data/observability is transferred where there would be no case otherwise (telemetry) and the "superglue" gets handled in unpredictable ways in simultaneity/retroactivity as a plasma between data/particle (matter/energy) in a semi-state of matter/energy. This can exhibit itself as spontaneous plasma that is depedent on other active plasmas in a seperate location.

>>3685712

Seperate polarization of those locations may also have some involvement in developing timespace connectivity and tether themselves into hyperspace under a plasma-state of matter/energy. Their data is transferred in this quantum bridge that particles form a wormhole or are broadcast to form a tunnel that yields to any outlet redirect of its superfluid/field evidenced as a light-trail.

The imprinted particles or impact site of an activated plasma causes Further entanglement of folded space into a warpportal/Simultaneity becomes a Source as to share data/particles through remote telemetry. And makes the superglue(subatomic-forces) of cation/anions susceptible to hyperspace/polarized-geometries otherwise inaccessible from their timespace(simultaneity/retroactivity).

These information states can then likely swap upon observability and the tethered particle therefore follows the shared path…teleporting through the cloud/fields/space/fluids(plasma) into shared-locations. The cation/anion then normalizes or is entangled in that way.

Seperate polarization of those locations may also have some involvement in developing timespace connectivity and tether themselves into hyperspace under a plasma-state of matter/energy. Their data is transferred in this quantum bridge that particles form a wormhole or are broadcast to form a tunnel that yields to any outlet redirect of its superfluid/field evidenced as a light-trail.

The imprinted particles or impact site of an activated plasma causes Further entanglement of folded space into a warpportal/Simultaneity becomes a Source as to share data/particles through remote telemetry. And makes the superglue(subatomic-forces) of cation/anions susceptible to hyperspace/polarized-geometries otherwise inaccessible from their timespace(simultaneity/retroactivity).

These information states can then likely swap upon observability and the tethered particle therefore follows the shared path…teleporting through the cloud/fields/space/fluids(plasma) into shared-locations. The cation/anion then normalizes or is entangled in that way.

>>3685694

true. and outside this smegma-baby Black hole there would be another Universe filled with only Jews (the ones with the large hats) talking, plotting and pushing buttons on their money-making machines all day long.

true. and outside this smegma-baby Black hole there would be another Universe filled with only Jews (the ones with the large hats) talking, plotting and pushing buttons on their money-making machines all day long.

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Did i just invent a new fractal?

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Seems like it…

>>3687901

that always happens in that context what is weird how it tricks you in the core expression of what values are flipped or not

that always happens in that context what is weird how it tricks you in the core expression of what values are flipped or not

>>3687901

i would have at least tried to show some reciprocation

i would have at least tried to show some reciprocation

>>3687908

So it's not supposed to look like that? What woulda correct rendering look like then?

So it's not supposed to look like that? What woulda correct rendering look like then?

File: 1675122661742-0.gif (1.71 MB, 374x250, mandelbrot-zoom-fractal.gif)

>>3687900

>Did i just invent a new fractal?

Doesn't seem like it. You'd have to prove it's self-similar or has a fractal dimension. For instance, the boundary of the Mandelbrot set is quasi self-similar, because when you zoom in, you can find smaller, distorted versions of the whole. Also, the Mandelbrot set's boundary has a fractal dimension of 2; whereas, the boundaries of non fractal 2D shapes are 1D.

>Did i just invent a new fractal?

Doesn't seem like it. You'd have to prove it's self-similar or has a fractal dimension. For instance, the boundary of the Mandelbrot set is quasi self-similar, because when you zoom in, you can find smaller, distorted versions of the whole. Also, the Mandelbrot set's boundary has a fractal dimension of 2; whereas, the boundaries of non fractal 2D shapes are 1D.

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Math Monday

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journey to the center of a triangle

https://www.youtube.com/watch?v=v_oZ9Pe0yRg

https://www.youtube.com/watch?v=v_oZ9Pe0yRg

Mathematics is a vast and rapidly evolving field that has far-reaching implications for a wide range of disciplines, including science, engineering, economics, and even the arts. In recent decades, modern mathematical theory has made tremendous advances, leading to new insights and a deeper understanding of mathematical concepts and their applications.

One area of modern mathematics that has seen significant growth is number theory. Number theory is a branch of mathematics that studies the properties of numbers and the relationships between them. One of the most important developments in number theory in recent years has been the theory of elliptic curves. Elliptic curves are a type of mathematical object that can be used to solve problems in cryptography, coding theory, and number theory. Researchers have made significant advances in our understanding of elliptic curves, including finding new algorithms for solving problems related to elliptic curves, and discovering new applications for these objects.

Another area of modern mathematics that has seen significant growth is algebraic geometry. Algebraic geometry is a branch of mathematics that studies the relationships between algebraic equations and geometric objects. In recent years, researchers have made tremendous advances in our understanding of algebraic geometry, including the discovery of new geometric objects, the development of new techniques for solving problems in algebraic geometry, and the discovery of new applications of algebraic geometry.

One area of modern mathematics that has seen significant growth is number theory. Number theory is a branch of mathematics that studies the properties of numbers and the relationships between them. One of the most important developments in number theory in recent years has been the theory of elliptic curves. Elliptic curves are a type of mathematical object that can be used to solve problems in cryptography, coding theory, and number theory. Researchers have made significant advances in our understanding of elliptic curves, including finding new algorithms for solving problems related to elliptic curves, and discovering new applications for these objects.

Another area of modern mathematics that has seen significant growth is algebraic geometry. Algebraic geometry is a branch of mathematics that studies the relationships between algebraic equations and geometric objects. In recent years, researchers have made tremendous advances in our understanding of algebraic geometry, including the discovery of new geometric objects, the development of new techniques for solving problems in algebraic geometry, and the discovery of new applications of algebraic geometry.

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Why the metric system matters - Matt Anticole

https://www.youtube.com/watch?v=7bUVjJWA6Vw

https://www.youtube.com/watch?v=7bUVjJWA6Vw

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>>3690210

You can see these lines in soap bubbles.

You can see these lines in soap bubbles.

>>3690213

all shapes can be reduced to a point and all formulas can be reduced to an integer. goodoooooing.

all shapes can be reduced to a point and all formulas can be reduced to an integer. goodoooooing.

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Guys, my math homework is sooo hard!

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>>3690215

The USA put a dozen men on the moon and brought them safely back using the INCH-FOOT-POUND SYSTEM…. over 50 YEARS AGO.

NONE of the rest of the world has done it YET.

Not even ONCE.

So shut the fuck up.

Why should we follow the rest of you off a cliff?

We're not lemmings like you are.

The USA put a dozen men on the moon and brought them safely back using the INCH-FOOT-POUND SYSTEM…. over 50 YEARS AGO.

NONE of the rest of the world has done it YET.

Not even ONCE.

So shut the fuck up.

Why should we follow the rest of you off a cliff?

We're not lemmings like you are.

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>>3692297

How'd you get that?

How'd you get that?

you forgot the cover and the back so technically its 50

>>3692348

Don't you fucking Professor Layton me.

Don't you fucking Professor Layton me.

>>3692359

you have a book its

3/8 unknown and 5/8 known

x(30)….solve.

3/8 is less than half and 5/8 is more then half.

if 30 more than half one way what is les than half other way.

Pro tip halfway mark is 24 and difference is 6.

24-6 =18

30+18=48

how you find halfway mark now?

you have a book its

3/8 unknown and 5/8 known

x(30)….solve.

3/8 is less than half and 5/8 is more then half.

if 30 more than half one way what is les than half other way.

Pro tip halfway mark is 24 and difference is 6.

24-6 =18

30+18=48

how you find halfway mark now?

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>>3692342

Yep. I did it in my head. I added the fractions together to get 3/8. Then I deduced that the 30 pages made up 5/8 of the whole. Scaling the 30 pages by the reciprocal of that fraction gives the whole: 30 pages * 8/5 = 6 pages * 8 = 48 pages. So he read 30 pages on Monday, 6 pages on Tuesday, and 12 pages on Wednesday.

Yep. I did it in my head. I added the fractions together to get 3/8. Then I deduced that the 30 pages made up 5/8 of the whole. Scaling the 30 pages by the reciprocal of that fraction gives the whole: 30 pages * 8/5 = 6 pages * 8 = 48 pages. So he read 30 pages on Monday, 6 pages on Tuesday, and 12 pages on Wednesday.

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This one's a bit trickier.

If x and y are positive integers (counting numbers) such that x+xy+y=54, what is x+y?

Bonus: If you plot x+xy+y=54, you get pic related. What kinds of curves are these?

If x and y are positive integers (counting numbers) such that x+xy+y=54, what is x+y?

Bonus: If you plot x+xy+y=54, you get pic related. What kinds of curves are these?

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>>3692410

There's the trick to solving this.

x+xy+y=54

x(1+y)+y=54

x(1+y)+1+y=55

(1+x)(1+y)=55

So you know 1+x and 1+y are factors of 55. Neither factor can be 1, because in that case one of the variables would have to be 0, which is not a positive integer as specified in the problem. So the factors must be 5 and 11, which means the variables are 4 and 10.

x+y = 4+10 = 14

There's the trick to solving this.

x+xy+y=54

x(1+y)+y=54

x(1+y)+1+y=55

(1+x)(1+y)=55

So you know 1+x and 1+y are factors of 55. Neither factor can be 1, because in that case one of the variables would have to be 0, which is not a positive integer as specified in the problem. So the factors must be 5 and 11, which means the variables are 4 and 10.

x+y = 4+10 = 14

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>>3692410

Oh, I forgot the bonus question. Those red curves form a hyperbola. Just like the curves in the first attached pic - the ones that aren't circles or straight lines. Hyperbolas are conic sections.

Here's the equations I put into Desmos to get the attached plot: https://www.desmos.com/calculator/aknbdu4iiw

Oh, I forgot the bonus question. Those red curves form a hyperbola. Just like the curves in the first attached pic - the ones that aren't circles or straight lines. Hyperbolas are conic sections.

Here's the equations I put into Desmos to get the attached plot: https://www.desmos.com/calculator/aknbdu4iiw

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>>3623885

This is the most advanced question I posed itt. Again, I got this problem from the following video:

https://youtu.be/NiDbbPKrs-0

Pic related is how I solved it. There may be a better way, but this works. So I started by substituting the Taylor series for the exponential function in the integrand. Then I distributed the x^t term. Then split up the definite integral, evaluating each at the endpoints. So the definite integral becomes a series. Use this series and its derivative in Newton's method of approximation. Here's a python script I wrote to do this:

import math

t = 0

for i in range(100):

nsum = -3/2

dsum = 0

for j in range(100):

nsum = nsum + 1 / (math.factorial(j) * (t+1+j))

dsum = dsum + 1 / (math.factorial(j) * (t+1+j) ** 2)

t = t + nsum / dsum

print(t)

I know some of you are learning to code, so you might find this useful in that regard. Running this script returns a value for t = 0.1931547055, rounded to ten decimal places.

This is the most advanced question I posed itt. Again, I got this problem from the following video:

https://youtu.be/NiDbbPKrs-0

Pic related is how I solved it. There may be a better way, but this works. So I started by substituting the Taylor series for the exponential function in the integrand. Then I distributed the x^t term. Then split up the definite integral, evaluating each at the endpoints. So the definite integral becomes a series. Use this series and its derivative in Newton's method of approximation. Here's a python script I wrote to do this:

import math

t = 0

for i in range(100):

nsum = -3/2

dsum = 0

for j in range(100):

nsum = nsum + 1 / (math.factorial(j) * (t+1+j))

dsum = dsum + 1 / (math.factorial(j) * (t+1+j) ** 2)

t = t + nsum / dsum

print(t)

I know some of you are learning to code, so you might find this useful in that regard. Running this script returns a value for t = 0.1931547055, rounded to ten decimal places.

>>3694710

Meh, shoulda known the indentation in my code would get fucked. Here:

https://pastebin.com/7g30F7N7

Meh, shoulda known the indentation in my code would get fucked. Here:

https://pastebin.com/7g30F7N7

>>3694710

So just factor it into pie and it works with every other ratio to form pi lol unrelated pi though is a definite issue if you are running scripts with password protections welcome to the new age

So just factor it into pie and it works with every other ratio to form pi lol unrelated pi though is a definite issue if you are running scripts with password protections welcome to the new age

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>>3694704

Needed more circles and hyperbolae. And no grid lines.

https://www.desmos.com/calculator/itywmhszw1

Needed more circles and hyperbolae. And no grid lines.

https://www.desmos.com/calculator/itywmhszw1

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Happy Pi Day!

Pi Day fun fact: the probability that two randomly selected integers are coprime is 6/π^2, or about 60.8%. Coprime means the two integers share no common divisors except 1.

Pi Day fun fact: the probability that two randomly selected integers are coprime is 6/π^2, or about 60.8%. Coprime means the two integers share no common divisors except 1.

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World's Strongest Magnet!

https://www.youtube.com/watch?v=g0amdIcZt5I

https://www.youtube.com/watch?v=g0amdIcZt5I

File: 1678819100340-0.png (832.07 KB, 1200x635, missile defelctors.png)

File: 1678819100340-1.jpg (12.24 KB, 230x219, download.jpg)

File: 1678819100340-2.png (1.85 MB, 1920x816, Gungan_Shield.png)

>>3695184

Could be used in brakes for maglevs or even projectile deflectors to reduce damage from buildings, tanks, etc.

Could be used in brakes for maglevs or even projectile deflectors to reduce damage from buildings, tanks, etc.

File: 1678842066069-0.png (335.04 KB, 1024x1024, Penrose_Tiling_(Rhombi).sv….png)

File: 1678842066069-1.jpg (2.61 MB, 4032x3024, minor_correction.jpg)

https://youtu.be/-eqdj63nEr4

https://aatishb.com/patterncollider/

Penrose tiles and minor correction to >>3694710. Penrose tiles are an example of aperiodic tiling.

https://aatishb.com/patterncollider/

Penrose tiles and minor correction to >>3694710. Penrose tiles are an example of aperiodic tiling.

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