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Section1An Introduction to 8

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.