Don't love the network graph illustrating the spread of a virus.<p>It's deceptive and is counter to the purpose of explaining exponential growth. If the people infected are represented by relatively uniform points on a plane, and infection is shown as an ever expanding circle, the growth is geometric, not exponential. I understand that the exponential growth could be captured by the acceleration of the radius, but that is not intuitive.
Trigonometry please (specifically Sin, Cos, Tan)! I can calculate the values when I need them, but I want to understand the 'why' and the 'how' on a fundamental level.
Here's a StackExchange thread full of similar visualizations (which has been shared here a few times in the past):<p><a href="http://math.stackexchange.com/q/733754" rel="nofollow">http://math.stackexchange.com/q/733754</a>
I am jealous of the engineering students to come after me. Can you imagine when every advanced textbook is so clear and interactive? Eigenvalues, differential equations, relativity...
An example of eigenvalues: Suppose you take a polynomial of x and then you change x for -x, you obtain a new polynomial. Some polynomials doesn't change they are associated to eigenvalue 1, other change sign they are associated to eigenvalue -1, those are the only ways in which a polynomial gets transformed into a multiple of itself when changing sign. And what happens with the others polynomials? Well, you can write any of them as a sum of those with even exponents (those that doesn't change when changing the sign of x) and those with odd exponents (those are the ones that change sign), so any polynomial can be expressed as the sum of an even polynomial and an odd polynomial in a unique way. In the same way, taken the conjugate of a complex number the part that doesn't change is the real part (associate to eigenvalue 1) and the part that change sign is the imaginary part (associate to eigenvalue -1) and every complex number is written as the sum of its real and imaginary part. Take a matrix and computes its transpose, the matrix can be expressed as a sum of a symmetric matrix (corresponding to eigenvalue 1, doesn't change with the transpose operator) and an antisymmetric matrix (change the sign, associated to eigenvalue -1). Finally take for example any function of x and consider the function obtained when you change x to -x, then any function can be expressed in a unique way as the sum of a even function (corresponding to eigenvalue 1, that is doesn't change with that transformation) and an odd function (associate to eigenvalue -1, that is change sign). For example our familiar function exponential of x is the sum of the hyperbolic cosiness and the hyperbolic sinus.<p>This way you are near the Euler Formula:<p>e^x = cosh(x) + sinh(x) (real case)<p>e^it = cos(t) + i sin(t) (complex case)<p>I must add that in this example the transformation satisfies that applied two times is the identity, that is called involution A^2=1 and the only eigenvalues K are those that K^2=-1 that is 1 and -1.
This is incredible. I still remember the first time I read through Eliezer Yudkowsky's Intuitive Explanation of Bayes Theorem [1], and how it was one of those moments where the lense with which I saw the world changed forever. I still refer people to that page whenever I have a tough time explaining it myself, as well as a handful of other pages (now including this one).<p>I know Show HN is typically used for getting constructive criticism, but I don't have much to say there other than to keep it coming.<p><a href="http://yudkowsky.net/rational/bayes" rel="nofollow">http://yudkowsky.net/rational/bayes</a>
Bret Victor is doing some amazing work in this area.
<a href="http://worrydream.com/#!/InteractiveExplorationOfADynamicalSystem" rel="nofollow">http://worrydream.com/#!/InteractiveExplorationOfADynamicalS...</a>
As a visual thinker, this is great! Especially for mathematics which I was great at until secondary school began, where I struggled a lot due to impatient math teachers poorly explaining concepts.<p>Congrats to the team for shipping this, I've subscribed and hope to see more stuff like this. It would be great if you could explain basic concepts (and gradually to complex formulas) and hopefully beginners who struggle due to bad teaching can bump into your website and keep their interest alive.
This is very cool!<p>As a piece of constructive feedback, consider waiting until a visualization is scrolled into view to start animation. I'm particularly thinking of the Exponentiation page. Mike Bostock wrote about this recently: <a href="http://bost.ocks.org/mike/scroll/#4" rel="nofollow">http://bost.ocks.org/mike/scroll/#4</a>
An example of a visual explanation I would like to see:<p>Suppose the length of your thumb doubles in each step then in 33 steps it would be equal to the distance from earth to the moon.<p>I would like to see such an animation, being able to touch the moon with my finger in 33 steps is to grow really fast.
This is awesome! Thanks for sharing. Can't wait for Eigenvalues to be covered! Shameless plug: I created a similar visualization for explaining Monte Carlo simulations by computing Pi. <a href="http://montepie.herokuapp.com/" rel="nofollow">http://montepie.herokuapp.com/</a>
On your main page I'd mention Bayes theorem on the entry for conditional probability since it might get anyone curious about Bayes theorem and satisfying it with a search engine to your page for the best explanation I've ever seen.
Awesome. I've been wanting to seed a project like this for a while. You should definitely be pushing this open source and soliciting contributions.
you explained the concepts very well...I am especially impressed with the way you effectively used animation to bring the concepts to life.
I would like to know what tools you used to create the analytics (R language?) and visualization(D3.js?).