Here we introduce and interact with a mysterious machine that sets the scene for the entire Exploding Dots story and a transformational mindset for mathematics.

Here we figure out what the mysterious machines are doing and discover the notion of place value. We now have a powerful visual understanding of this subtle concept that profoundly helps us understand so much grade-school, middle-school, and high-school mathematics in brand new light.

Here we make profound sense of the standard algorithms.

See subtraction as the addition of the opposite. This insight, coupled with the Exploding Dots machinery, provides natural and deep insight into long subtraction.

Long division is made exceptionally clear.

Here we discover that K-6 school arithmetic is high-school mathematics in disguise.

Here we play with “infinitely long polynomials,” discover the geometric series formula, and more!

Another infinite produces more boxes in the machine. We discover decimal numbers.

Now we are just playing. We discover fractional bases, negative bases, and more. Each discovery often comes with unsolved research questions.

Is 0.9999…. equal to one or is it not? We explore this question and an even wilder one than that!

Making Exploding Dos two dimensional allows you do conduct algebra with polynomials of two variables x and y. Scottish mathematician John Napier of the 1600s did essentially this with his multiplication checkerboard.

Here is a collection of puzzles—some classic, some not so classic—that can be explained with Exploding Dots. Puzzles of all levels for all ages can be found here.