# Section7Ubiquitous 8¶ permalink

So, yes, something deeper and perhaps more profound than randomness dictates the frequency with which \(8\) appears in my classes. But no wonder! And this pheonomenon is not confined to the classroom. The other day my son, who is \(8\) more or less, was flossing his teeth, and I said, “You know, son, the eighth tooth in each quadrant of an adult's mouth is called a *wisdom* tooth. \(8\) is very wise.” He looked at me with what can only be described as a mixture of love and awe. “Gee, thanks, Dad,” he replied. After a thoughtful pause he asked, “Dad? What is the smallest integer of the form \(a^b\) where \(a\) and \(b\) are distinct primes?” I tousled his hair paternally as I replied, “Take a wild guess.”^{ 1 }

Once you notice \(8\text{,}\) it is everywhere. My son has discovered this phenomenon, and he recently captured one profound “\(8\) moment” in graphic art form, reproduced here with his permission.

We close with a random number of fun facts about \(8\text{.}\)

- Do you follow the sport of number tipping? In the summer of 1969, in a much-hyped but very short match, \(8\) wrested the world championship away from \(e\text{,}\) a title that \(8\) holds to this day. The official record (reproduced below) makes it clear: as the combatants were tipped, \(e\) began to take on the aspect of a tired flower while \(8\) approached the infinite. It was a blowout.
- The heart of mathematics, namely the polar curve \(r = 1 - \sin(\theta)\text{,}\) has arclength equal to \(8\) units.
- Sometimes people ask me, “Does it bother you that 7.99999... = 8?” To these people I gently point out that this suggests it takes an infinite number of 9s and a 7 to make an 8. Meanwhile, 7.888... doesn't equal 9 or even 6. In fact, it equals \(\frac{71}{9}\text{,}\) and I need hardly mention that 7+1 = \(8\text{.}\)
- Blaise Pascal and Pierre de Fermat, fathers of probability theory, had a view of democracy ahead of their time. On one fictitious occasion they asked 50 citizens of Clemont-Ferrand to name their favorite number on a 6-sided die. Fifteen of them replied '4', and the remaining 35 were split evenly among the remaining five options. They had two weighted dice cast to match the vote: on each die, the probability of rolling a 4 was 15/50, the probability of rolling each of the other numbers was 7/50. The eager reader can check that with these dice, the most likely sum when rolling them both is \(8\text{.}\) The people have spoken!
- Consider a seven-segment display for numbers (as on a scoreboard). Which of the digits 0 through 9 requires the use of all seven bulbs, thereby proving it to be the brightest and most powerful of the connected digits? You may check for yourself:
- Terry Pratchett, knighted in 2009 by Queen Elizabeth II for his service to literature and \(8\text{,}\) famously explores the power of \(8\) in his Discworld series, where the eighth son of the eighth son of an eighth son is a sourcerer.
- Brook Taylor loved his polynomials, and his tennis. As this story goes, Taylor preferred a springy tennis ball, one that bounced to 60 percent of its previous height on any given bounce. One other fact about Taylor (which he liked to trot out at social gatherings) was that the palm of his right hand, when his arms rested normally at his sides, was precisely 2 feet above the ground. In Taylor's own words: “Notice that, though a lampshade be upon my head, if I release my lucky tennis ball from my right hand which lay relaxed by my side, I can be assured that the total vertical distance travelled by said ball before it stops bouncing will be precisely \(8\) feet.”
- As a student this author wore \(8\) on his soccer jersey for Swarthmore College.