# math

Happy Fibonacci Day, everybody! It won’t happen again for 3019 days!

FourierToy

Inspired by Matt Henderson’s post, I created this interactive visualization of the Fourier series in terms of epicycles.

Below, you see 8 components corresponding to the integer frequencies from 1 to 8. The blue circle represents the amplitude and phase of each component. You can change these by clicking and dragging around each box. You can also set the amplitude manually by typing in a value from 0 to 1.

Holding shift will lock the phase in 45° multiples, and holding control will lock the amplitude in place.

The right-click context menu has a few wave presets.

Keyboard shortcuts

Space bar: reset everything to zero

Up / down: speed up and slow down the animation

Left / right: rotate the phases of all components at once

Ctrl + 1-8: set the associated component to zero

T: toggle the blue trace

Ctrl+backspace: clear graph

taylor series expansion of sin (x)

Some time ago a paper containing new periodic solutions to the three-body problem was circulating around tumblr. Since it kindly included the initial conditions, I took that as an excuse to make some simulations.

check that! It’s pretty interesting!

(via javert)

I am sorry I am not meant to be a math blogger

If you need help, don’t be afraid to ask. There are tons of math knowledgeable people here who can explain trig and integration in a way that’s not zomgkillmewhyareyoudoingthistome way.

In fact, there’s even a Tumblr blog just for answering math questions http://maths-help.tumblr.com/

Also http://tutorial.math.lamar.edu/ , Paul has some pretty neat notes.

We’re all gonna gang up on you and force you to get a B or better because that’s how we be rollin’ .

And when you work at NASA, I want to one day take a tour and get a discount (by that I mean free) trip into outer space and yeah

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Albany Society of Physics Students

faustprouvaire replied to your post: hey can someone give me some calc help for a…

What’s the problem?

ugh I’m just working through all the problems on this study sheet and there are a lot of ‘tricks’ that you need to know and I don’t know them and I keep getting stuck/getting the wrong answers

We should try this problem because reasons:                                         Express the indefinite integral

in terms of elementary functions. Use the symbol C to denote an arbitrary constant.

I stared at this and then it hit me like a brick (basically getting hit by 1000+ book about awesome french people really hurts).

Your U is cosx. The derivative of cosx is -sinx. So you get:

The 2 goes in front of the integral because it’s a constant and it is negative because of -sinx.

Remember the integration power rule is:

so we get:

[there should be a negative in front of the 2 but I’m too tired to mess with latex.]

Now after integrating we get:

If we put cosx back in for U, we get:

don’t forget the C because it’s an indefinite. This answer is in agreement with RPI’s answer

The rest of the problems can be pretty much solved in a similar way. For definite integral, it’ll be helpful to know the cos of pi/2 is 0, pi is 1 and the cos and sin of pi/4 is

wait isn’t the unit circle made up of just two trangles.

what

(probably yes)

(my main problem with the unit circle is I just never remember if say cos (pi/3) is 1/2 or sqrt3/2)

cos of pi/3 is 1/2. I remember this because the closer cos gets to the y axis, the smaller it is until it reaches (pi/2) or (3pi/2) both are zero for cos but 1 for sin. Which is easy to see because the unit circle has a radius of 1.

cos is the x axis and sin is the y.

but why would you graffiti the quadratic formula

some thugs just want to watch the world learn

Math, bitch!

(via driveshaftgroupie)

challenge accepted