Skip to main content

Fourier Series Grapher

Here's a simple JavaScript + HTML program I wrote. It will graph a given number of terms of a Fourier series. To graph a Fourier series, type the appropriate expressions into the text fields and click "Update." The text fields support JavaScript, so you can write a whole function in there if you need to.

I also added some functions.
  1. even(x) - returns true if x is even, false otherwise.
  2. odd(x) - returns true if x is odd, false otherwise.
  3. power(x, a) - returns xa.
Some examples of input to try:
  • odd(k)?(2/k):0
  • even(k)?(4/k/PI):0
  • odd(k)?(4/(k+PI)/k):0
The default Fourier series is equal to sin(2.5x) on (-π, π).

Enjoy!




To receive updates, subscribe now!
Labels:

Comments

  1. Raheela KhanJuly 6, 2014 at 11:00 PM

    You're awesome! I'm teaching myself JavaScript along with HTML, JQuery, and CSS and your blog is very inspiring! I saw your program, "DRAW", on KhanAcademy and it was so cool! How did you learn how to make such great programs? I don't even know where to start-_-.

    Oh! And I'm a self-taught pianist as well*thanks to suzuki piano book, hehe*

    Keep up the great work!

    ReplyDelete
    Replies
    1. MathGeekJuly 7, 2014 at 6:33 PM

      Thanks for commenting! I started by learning BASIC (mostly from the documentation), and after that JavaScript came easily. I just had to learn the syntax and some object-oriented programming concepts.

      Of course, math is indispensable in programming. Looking at other programmers' source code can help with technique and structure, and practice helps a lot too.

      Usually I come up with an idea for a program first, and then I figure out how to write it. If I don't know how, I research it. It can take a while, but when I'm done I know a lot more about it than I did when I started.

      Good luck with programming!

      Delete

Post a Comment

Popular posts from this blog

Dividing Paper Puzzle

When I was young, I would fold a sheet of letter paper in half, for origami projects. It occurred to me that the two halves looked almost the same as the whole sheet of paper - except they were smaller. I could see they weren't exactly the same shape; they were off by a little bit. But the idea stuck in my head. You can use a pen, instead of scissors, to halve the paper. Those rectangles all have the same shape, but are different sizes. One night when I was 12, I thought about my idea. I wondered if it was possible to have a sheet of paper that could be cut in half, resulting in 2 smaller versions of the same paper. That would be neat, to be able to cut a paper in half and get 2 papers that had the same exact shape. If that were possible, then you could cut  those  papers, too; and the resulting papers would have the same shape as all the other papers. You could keep cutting in half forever, and each paper, no matter how small, would have the same shape as all the others. I HAD to
6 comments
Read more

Pluto No Longer on the Horizon

This morning, New Horizons became the first spacecraft to make a flyby observation of the Pluto system. During the mission, the spacecraft captured the most detailed photographs of Pluto's surface we've ever had, and possibly ever will have. It also found many new properties including size, mass, atmosphere, and surface composition. In a period of a few hours, we discovered more about Pluto than we've found in the 85 years since Clyde Tombaugh captured its first photograph. Before After  (images credit: NASA) To complete this mission, the spacecraft flew for more than 9 years through the emptiness of space. This may sound like a long time, but it's actually amazingly quick. In fact, New Horizons set the record for the fastest speed at launch, and during the flyby, the spacecraft was moving at a rate of over 30,000 mph, or roughly 50 times the speed of sound. Picture an object twice as heavy as a grand piano moving 25 times faster than a bullet from a gun. Yikes. The man
2 comments
Read more

Gravity

Imagine the universe is filled with water. Instead of empty space, every inch of it contains pure water. No planets, no stars, only water. What happens? And what would happen if an air bubble formed? The answer to this question requires a basic understanding of gravity. Gravity is very important. It helps hold matter together, bends light, and distorts space-time (which, incidentally, is how it bends light). It also makes it possible to play football, and as Americans are big football fans, they would certainly agree that we couldn't live without it. Unfortunately, many Americans don't understand how gravity works. Admittedly, scientists haven't figured out a lot of things, but we do understand it well enough to make predictions and model physical events. One of the important things about gravity is that its strength is proportional to the inverse of the square of the distance. In other words, it gets weaker as you get farther away, based on the equation: F = c/d 2 where c
6 comments
Read more