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Mathematics Thread
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CheesecakeCuber
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I'm sorry?
ben1996123
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number+"".zfill(howmutchzerós)
number+"0000000"
number+"0000000"
CheesecakeCuber
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Ahh, I see. Thanks ben
ben1996123
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hearce a question that i'm trying to do but cantdooeet yet because ittuce wery hard (or maby i'm being stoopd)
that is a squaer. find α
that is a squaer. find α
5BLD
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hearce a question that i'm trying to do but cantdooeet yet because ittuce wery hard (or maby i'm being stoopd)
that is a squaer. find α
Okso did you get arccosA+arccosB+arccosC=2pi and get stuck there
ben1996123
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noterly, go on skype or fekbuk
5BLD
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Okso f*** this problem is hard
I might make a program to guess the answer
Also I can't solve equations of the form Sigma arccos fx but maybe you can
edit: sidelength is:
x = sqrt(5+2 sqrt(2))
3pi/4 rad or 135 deg
Last edited:
ben1996123
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5BLD
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no its not
ben1996123
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ok ittuce not
arek found d anser but wasnt sure if correct because used a guessing program but i prufed it now anywae
ittuce 3pi/4rad or 135deg
let the side length of the square be k and the point where the 3 lines cross be (x,y), then:
\( x^2+y^2=4 \)
\( x^2+(y-k)^2=1 \)
\( (x-k)^2+y^2=9 \)
\( (x-k)^2+(y-k)^2=6 \)
\( x^2-2kx+k^2+y^2-2ky+k^2=6 \)
\( -2kx+2k^2-2ky=2 \)
\( -kx+k^2-ky=1 \)
\( k^2=1+kx+ky \)
\( x^2+(y-k)^2=1 \)
\( x^2+y^2-2ky+k^2=1 \)
\( 4-2ky+k^2=1 \)
\( k^2-2ky+3=0 \)
\( k=y+\sqrt{y^2-3} \)
\( (x-k)^2+y^2=9 \)
\( x^2-2kx+k^2+y^2=9 \)
\( 4-2kx+k^2=9 \)
\( k^2-2kx-5=0 \)
\( k=x+\sqrt{x^2+5} \)
\( k^2=2ky-3=1+kx+ky \)
\( ky-3=1+kx \)
\( y-x=\frac{4}{k} \)
\( x+\sqrt{x^2+5}=y+\sqrt{y^2-3} \)
\( y^2=4-x^2 \)
\( x+\sqrt{x^2+5}=y+\sqrt{1-x^2} \)
\( y-x=\sqrt{x^2+5}-\sqrt{1-x^2} \)
\( \frac{4}{k}=\sqrt{x^2+5}-\sqrt{1-x^2} \)
\( \frac{4}{x+\sqrt{x^2+5}}=\sqrt{x^2+5}-\sqrt{1-x^2} \)
\( \text{insert boring algebra here} \)
\( x=\sqrt{\frac{2}{17}(5-\sqrt{8})} \)
\( k=\sqrt{5+\sqrt{8}} \)
\( \text{use cosine rule on the triangle with }\alpha\text{ in it} \)
\( k^2=5-4cos(\alpha) \)
\( 5+\sqrt{8}=5-4cos(\alpha) \)
\( cos(\alpha)=-\frac{\sqrt{2}}{2} \)
\( \alpha=\frac{3\pi}{4} \)
\( x^2+y^2=4 \)
\( x^2+(y-k)^2=1 \)
\( (x-k)^2+y^2=9 \)
\( (x-k)^2+(y-k)^2=6 \)
\( x^2-2kx+k^2+y^2-2ky+k^2=6 \)
\( -2kx+2k^2-2ky=2 \)
\( -kx+k^2-ky=1 \)
\( k^2=1+kx+ky \)
\( x^2+(y-k)^2=1 \)
\( x^2+y^2-2ky+k^2=1 \)
\( 4-2ky+k^2=1 \)
\( k^2-2ky+3=0 \)
\( k=y+\sqrt{y^2-3} \)
\( (x-k)^2+y^2=9 \)
\( x^2-2kx+k^2+y^2=9 \)
\( 4-2kx+k^2=9 \)
\( k^2-2kx-5=0 \)
\( k=x+\sqrt{x^2+5} \)
\( k^2=2ky-3=1+kx+ky \)
\( ky-3=1+kx \)
\( y-x=\frac{4}{k} \)
\( x+\sqrt{x^2+5}=y+\sqrt{y^2-3} \)
\( y^2=4-x^2 \)
\( x+\sqrt{x^2+5}=y+\sqrt{1-x^2} \)
\( y-x=\sqrt{x^2+5}-\sqrt{1-x^2} \)
\( \frac{4}{k}=\sqrt{x^2+5}-\sqrt{1-x^2} \)
\( \frac{4}{x+\sqrt{x^2+5}}=\sqrt{x^2+5}-\sqrt{1-x^2} \)
\( \text{insert boring algebra here} \)
\( x=\sqrt{\frac{2}{17}(5-\sqrt{8})} \)
\( k=\sqrt{5+\sqrt{8}} \)
\( \text{use cosine rule on the triangle with }\alpha\text{ in it} \)
\( k^2=5-4cos(\alpha) \)
\( 5+\sqrt{8}=5-4cos(\alpha) \)
\( cos(\alpha)=-\frac{\sqrt{2}}{2} \)
\( \alpha=\frac{3\pi}{4} \)
brandbest1
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Good math research topics for a 10th grader that pretty much has basic knowledge of calculus? I have to write a research paper about something and I came up with these ideas:
-Mandelbrot set/Fractals
-Diophantine Equations
-Fibonacci Numbers and Related Sequences
-Graph Theory
-Algorithms (i saw the above posts and became quite interested in them, but not sure where to start)
Any other ideas would be appreciated.
-Mandelbrot set/Fractals
-Diophantine Equations
-Fibonacci Numbers and Related Sequences
-Graph Theory
-Algorithms (i saw the above posts and became quite interested in them, but not sure where to start)
Any other ideas would be appreciated.
CheesecakeCuber
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Algos as in fast multiplication? Would your paper need to have some kind of relation to Calc? If so, not sure if algos would be the best topic. (Basic algorithms)
brandbest1
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The paper doesn't have to be related to Calculus, I mean I am only in an Algebra 2/Trigonometry class but I do know Calculus. And currently I don't have much knowledge about Algorithms (other than cubing lol) but I would assume so, as well as wherever algorithms are used in math. Could you give me some sources for it?
And sources for other topics? I'm a bit worried that I won't be able to pick up Algorithms that well.
CheesecakeCuber
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O how cool. Someone also like maff algorithms
What I would do with the paper (if you settle on algs), is first propose the concept of improving the time to carry out multiplication, go into time complexity of the naive alg (what we learned in school :3), then go on to speak about some of the more basic algs: Karatsuba, Toom-3, discuss their time complexities, and maybe do a small bit about Schonhage-Strassen with FFT just to show that there are more advanced methods.
For karatsuba:
Well, after Alex helped me with my Karatsuba project, I made a thread in the Off Topic Forum here, explaining as simply as I could, to the best of my knowledge, the Karatsuba algorithm.
Linky: http://www.speedsolving.com/forum/showthread.php?43850-Karatsuba-Algorithm-Example
For Toom-Cook use wikipedia and the net
If you have any questions, just post it here and I'm sure someone will rep
brandbest1
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O how cool. Someone also like maff algorithms
What I would do with the paper (if you settle on algs), is first propose the concept of improving the time to carry out multiplication, go into time complexity of the naive alg (what we learned in school :3), then go on to speak about some of the more basic algs: Karatsuba, Toom-3, discuss their time complexities, and maybe do a small bit about Schonhage-Strassen with FFT just to show that there are more advanced methods.
For karatsuba:
Well, after Alex helped me with my Karatsuba project, I made a thread in the Off Topic Forum here, explaining as simply as I could, to the best of my knowledge, the Karatsuba algorithm.
Linky: http://www.speedsolving.com/forum/showthread.php?43850-Karatsuba-Algorithm-Example
For Toom-Cook use wikipedia and the net
If you have any questions, just post it here and I'm sure someone will rep
Wow, thanks for all the info! Although there definitely should be a section which introduces the concept of the general algorithm.
Do you have any other ideas or comments about the other ideas?
CheesecakeCuber
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Oh, np! Also, don't forget to discuss recursion! And you could also, if you know any coding languages (like python, perl, C), include some sample code, just don't completely copy mine if you don't understand tho. Pseudo Code could also be a good alt. if you don't know any languages.
Now, on the other ideas, Fractals and Fibonacci are cool, but a lot of people seem to gravitate towards them. tWould help if you listed some criteria for the paper. Like a rubric?
Also, project euler: pronounced oiler (just google it) is good for finding interesting math subjects, like pascal triangles, stuff on factorial properties, etc
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Cheesecake cuber have you done toom cook now? Also project euler will keep you up for dozens of hours
CheesecakeCuber
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No cuz school :'(. l still don't have enough knowledge of the alg, which is the mistake I made when taking on Karatsuba. I basically just went in blind other than some light reading.
I may have to implore your majestic math skillz once more '
And yes, Project Euler....o my is it interesting.
brandbest1
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Yep, I know python so I will try and make some code for them if I use Algorithms for the paper.
I currently don't have a rubric because this wasn't assigned yet, but our teacher already said we have to do this, so I'm currently just brainstorming.
