Skip to main content

# Section1An Introduction to 8¶ permalink

The goddess of fame has smiled upon some numbers, leaving others to a life of toil and anonymity. Take $\pi\text{.}$ So much has been written about Mr. 3.1415...8... . Much of its allure, no doubt, comes from the fact that $\pi$ “arises naturally.” School kids, some of them not yet eight, are taught that if you divde the circumference of any circle by its diameter you get $\pi\text{.}$ At some point, these same kids are asked to worship the fact that the area enclosed by a circle having radius one foot is $\pi$ square feet, on the nose. But are these kids taught that if you take two circles, each having radius $\frac{2}{\sqrt{\pi}}$ feet, and you place them one just resting on top of the other so that they form an $8\text{,}$ then the total area enclosed by both circles is $8$ square feet on the nose?

Other stars in the number world include $e, i,\phi = \frac{1+\sqrt{5}}{2}\text{,}$ and 0. Zero! Why not $8\text{?}$ Sure, celebrations of the Golden Ratio $\phi$ are fun. It's cute to see it pop up in pleasing architecture, art, and seashells, but has anyone pointed out to you that $\phi$'s building block integers, 1, 5, and 2, sum to $8\text{?}$ Is this a coincidence? I don't think so. And isn't $8$ foundational to the product of $\pi$ and $e\text{:}$ $\lfloor \pi \cdot e\rfloor=8\text{?}$ And isn't 0 just $8$ without its belt?

One hears whispers of a conspiracy to keep $8$ in the shadows. Consider the base 10 number system that has been thrust upon us, even though base $8$ has clear advantages. For instance, the diabolical number 666 would be written in base $8$ as a harmless and pleasing 1232, practically a kid's song waiting to happen. Consider Urbain Le Verrier's discovery of Neptune in 1845 (using mathematics, not a telescope) which gave us an eighth planet in our solar system. This incited a mad dash to find another planet, presumably because $8$ just wouldn't do. Of course, this led to the regrettable classification of Pluto as a planet, an error we corrected just a few years ago.

But $8$ has its champions. I recently spoke with Alan Moby, secretary of Gather Renown for $8$ (GR8), a new organization that is working to promote eight to its rightful place among the world's most famous numbers. I asked about the GR8 campaign to get eight added to the equation $e^{\pi i} + 1 = 0\text{.}$ Moby said, “GR8 has worked tirelessly to assemble the key numbers in a way that ensures equality, and we couldn't be more pleased with the result. We now have the world's greatest numbers joined in one superstar equation. Behold!”

\begin{equation*} e^{8\pi i} - 1 = 0. \end{equation*}

Is eight's inclusion in this equation deserved? What follows is a brief, objective tour of $8$ through the ages. I invite the reader to weigh the evidence before agreeing that $8$ clearly belongs in this superstar equation.