Tag Archives: fun with numbers

November 22, 2020

Math Fail

And the total is…?

Oh the irony of it all. Two days ago I post about two math books, at least one of which (if not both) I think everyone should read. This morning, reading my newsfeed, I see one of those “People Are Confused By This Math Problem” articles that pop up from time to time.

Often those are expressions without parentheses, so they require knowledge of operator precedence. (I think such “problems” are dumb. Precedence isn’t set in stone; always use parentheses.)

Some math problems do have a legitimately confusing aspect, but my mind is bit blown that anyone gets this one wrong.

10 Comments | tags: fun with numbers, math phobia, mathematics | posted in Math, Rant, Society

November 20, 2020

Math Books

By Wyrd Smythe

There are many science-minded authors and working physicists who write popular science books. While there aren’t as many math-minded authors or working mathematicians writing popular math books, it’s not a null set. I’ve explored two such authors recently: mathematician Steven Strogatz and author David Berlinski.

Strogatz wrote The Joy of X (2012), which was based on his New York Times columns popularizing mathematics. I would call that a must-read for anyone with a general interest in mathematics. I just finished his most recent, Infinite Powers (2019), and liked it even more.

Berlinski, on the other hand, I wouldn’t grant space on my bookshelf.

11 Comments | tags: calculus, David Berlinski, derivatives, fun with numbers, integrals, numbers, Steven Strogatz, The Joy of X | posted in Books, Math

March 26, 2020

The Heart of the Mandelbrot

By Wyrd Smythe

In recent posts I’ve presented the complex numbers and the complex plane. Those were just stepping stones to this post, which involves a basic fact about the Mandelbrot set. It’s something that I stumbled over recently (after tip-toeing around it many times, because math).

This is one of those places where something that seems complicated turns out to have a fairly simple (and kinda cool) way to see it when approached the right way. In this case, it’s the way multiplication rotates points on the complex plane. This allow us to actually visualize certain equations.

With that, we’re ready to move on to the “heart” of the matter…

18 Comments | tags: cartioid, complex numbers, fun with numbers, Mandelbrot, Mandelbrot fractal, real numbers | posted in Math

March 25, 2020

The Complex Plane

By Wyrd Smythe

In the first post I explained why the mathematical “imaginary” number i is “real” (in more than one sense of the word). That weird number is just a stepping stone to the complex numbers, which are themselves stepping stones to the complex plane.

Which, in turn, is a big stepping stone to a fun fact about the Mandelbrot I want to write about. (But we all have to get there, first.) I think it’s a worthwhile journey — understanding the complex plane opens the door to more than just the Mandelbrot. (For instance, Euler’s beautiful “sonnet” also lives on the complex plane.)

As it turns out, the complex numbers cause this plane to “fly” a little bit differently than the regular X-Y plane does.

4 Comments | tags: complex numbers, complex plane, fun with numbers, imaginary unit, numbers, real numbers | posted in Math

March 24, 2020

“Imaginary” Parabola

By Wyrd Smythe

Graph of ax² for diff a values.
(green < 1; blue = 1; red > 1)

This is a little detour before the main event. The first post of this series, which explained why the imaginary unit, i, is important to math, was long enough; I didn’t want to make it longer. However there is a simple visual way of illustrating exactly why it seems, at least initially, that the original premise isn’t right.

There is also a visual way to illustrate the solution, but it requires four dimensions to display. Three dimensions can get us there if we use some creative color shading, but we’re still stuck displaying it on a two-dimensional screen, so it’ll take a little imagination on our part.

And while the solution might not be super obvious, the problem sure is.

5 Comments | tags: complex numbers, fun with numbers, imaginary unit, numbers, parabola, real numbers, x-squared | posted in Math

March 23, 2020

“Imaginary” Numbers

By Wyrd Smythe

Yes, this is a math post, but don’t run off too quickly. I’ll keep it as simple as possible (but no simpler), and I’ll do all the actual math so you can just ride along and watch. What I’m about here is laying the groundwork to explain a fun fact about the Mandelbrot.

This post is kind of an origin story. It seeks to explain why something rather mind-bending — the so-called “imaginary numbers” — are actually vital members of the mathematical family despite being based on what seems an impossibility.

The truth is, math would be a bit stuck without them.

17 Comments | tags: complex numbers, complex plane, fun with numbers, imaginary unit, integers, Leopold Kronecker, natural numbers, numbers, rational numbers, real numbers | posted in Math