all nostalgia aside, arras.io is so much better
Hint:
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Try out the following tasks before going for the big one
a.a, let that be your rotational speed.x axis) at your rotational speed.You should now have an idea on how to draw a hypocycloid.
Draw a hypocycloid using a graphical calculator (such as Desmos or Geogebra).
Your hypocycloid should include
t increases the point on the inner circle should trace out the pattern, you can animate the graph using t.Below is the link to a Desmos graph:
Hint
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If you are studying the algorithm, you are doing it wrong
Solution: https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-08-04_extended-euclid.html
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n and m are coprime, show that there exist integer n' such that nn' mod m=1.(I'm too lazy to type out the algorithm again, so look at the image yourself)
Hint:
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Let x mod y = a
Solution: https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-08-01_multiple-of-modulus.html
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z(x mod y) = (zx) mod (zy)Be rigorous
(trust me bro im gonna daily post trust me bro)
EDIT: assume all variables are integers
Hint:
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The size of a set is the number of possible values that an element can take.
because I have never heard of this argument before, ever. most media's stance on politics is "their party bad our party good", but the "all the parties are pretty hypocritical" argument has never been explored properly, because its depressing and nobody likes it.
yup thats the intended solution, im not really familiar with taylor series yet, but maybe for a person who knows taylor series would be able to see it right away
Hint
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The solution I have in mind is related to the Taylor series
Hint 2
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It converges to -ln(2), but why
Solution:
Hint:
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It is not a telescoping series
Solution:
yup there u go, btw can u please spoiler it so its harder for people to accidentally see it
Me and my friend from school reinvented the product integral a while back, we tried to approximate x!, later we discovered that what we just did was already done 200 years ago, but to this day I still don't get where the root(2 pi) in Stirling's approximation comes from.
I did a bit of writeup as things happened, slowly finding out that what we're doing isn't original, followed shortly by extreme demotivation.
proprietary, btw