Graphing Explicit vs Implicit Equations

There has been a lot of interest in licensing meta calculator. Our company, Engaging Edu , has licensed various IP over the last few years, and, of late, our scientific/graphing calc  has been in hot demand–whether it’s from companies that want to buy it or companies that want to license it.

A recurring issue in the process of licensing the app is how to handle the graphing calculator’s server based requests, but –before going any further let ‘s make sure we’ve defined two important ‘mathy’ phrases:

  • explicit equations-these are the equations that  any graphing calculator is expected to be able to handle and they look like
    • y = x^2 (parabola)
    • y = 2x +3 (line)
    • y = log(x) + 2x + x^3
  • implicit equations -These equations are studied in high school but  are rarely supported in graphing calculators.
    • x * y = 1 (hyperbola)
    • x^2 + y ^2 = 25 (circle with radius of 5)
    • sin(x) = cos(y) (funky cool graph that has no name)

 

Why draw a distinction between these two types of equations?

Because it is much, much tricker, and computationally expensive to graph implicit equations .  On the other hand, explicit equations, are relatively straight forward to graph and do not need anywhere near the same level of CPU power.

Most graphing Calculators  only graph explicit equations!

For instance, your typical high school level Texas Instruments graphing calculator can only do explicit equations (Even the TI-89, I think , can only graph explicit equations).

What about meta-calculator?

It can graph explicit equations and implicit; however, to be able to do all the intense math that is required for graphing implicit , we cannot rely on your browser–which would probably freeze up if it tried to handle certain graphs . Instead, the app sends  a request to our server app .

However,  there is no need to use the server for explicit equations.  One of the improvements that we were planning on rolling out this fall is to graph explicit ones in your browser–an improvement which can only speed things up since the app wouldn’t need to communicate with a server  and the server would also get fewer requests so it could dedicate its number crunching to those equations that require it.

Therefore, this month we are working on moving the graphing of explicit equations to your browser! A change that will , I imagine , go unnoticed by the 1,000’s of users that graph equations daily; however, these sorts of small improvements, in combination,  start adding up to a tangibly more performant app.

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