Belated Pi 3/15/22

Mathematics with Richard Bleil

It happened again.  Can you believe it?  I missed pi day! 

Watching a new show (very clever and fun show) where professional builders make things dreamed up by kids, they were trying to get the volume of a box.  Measuring it out, he said “36…20…okay, what is 36…times 20…times…5?”  At this point, his partner said, “I give up, let’s eyeball it.”  Those are not exact quotes, but the numbers are exactly what they said.  I solved the problem immediately; it’s 3600. 

Knowing a little bit of math can go a long way.  I solved the problem in my head as soon as he gave the last number.  Multiplication is commutative, meaning the order of multiplication doesn’t matter.  You get the same answer regardless of order, and immediately I realized that twenty times five is one hundred.  So, the easy solution is thirty-six times one hundred, or just take thirty-six and slide the decimal point two places to the right.

If I had one complaint about this show is how anti-mathematical it is.  One of the men on the show they call the “engineer” because he knows math, but every time he tries to explain something the other four men give him a hard time, cut his thoughts off and make fun of him.  What lesson is this teaching our children?  They were building a boat in one episode, and he said there is no doubt it will float because even with the passengers it is nowhere near 5,000 pounds.  How did he get this?  By knowing the volume of the boat and the density of water.  The boat and all of the passengers will basically displace water, and as long as the water displaced is less than what it would take to sink the boat (volume times density) it’ll float.  He estimated the math (we used to call it a back of the envelope calculation, meaning very simple requiring almost no scratch paper at all) and although I’m sure it was not exactly two and a half tons, any error he made in his estimate was still small enough that I also knew it would float. 

The reality is that mathematics is very cool, and excessively powerful.  When I taught chemistry, I would put together equations with multiplication and division stretching across the chalkboard (because chalkboards are so much cooler than white boards), and I would ask my students to figure out the answer.  As they furiously pushed buttons on their calculator, I would look at it and estimate it in my head.  “It’ll be around five hundred” I would say (for example).  As they continued the calculation, I would say “probably closer to four hundred and sixty.”  A student would finally chime in, “four hundred sixty-seven.”  It always astounded them, but the trick was easy.  I didn’t do the exact calculation in my head.  As above, I would estimate the numerator, and the denominator, and the final answer.  As they took time finishing up, I refined it. 

Here’s the truth; it is just not cool to insult somebody for liking or being good at math.  It should be celebrated.  It’s a gift that not everybody has, and we all benefit from it.  You should have seen these idiots and how tenuously they entered that boat, afraid of sinking it, but if they had actually listened to their friend, they would have been very comfortable bringing a barbell set with them.  If we are comfortable making fun of people who can do math, why don’t we make fun of people who lift?  Ooh, boy, you can pick up a weight…oh what a great ability.  Very useful in everyday life to be able to bench press weight.  Nope, it’s only those talented at math that we make fun of. 

Pi is actually a simple concept to understand.  If you have a (perfect) circle, and measure its diameter, then the circumference (distance around the edge) will be pi times larger.  In other words, if a circle is one inch across, its circumference will be pi.  In practice, pi is an “irrational number”, meaning that it has an infinite number of digits with no repeating pattern.  Today, the value of pi is known to 62.8 trillion digits.  Some mathematicians are trying to brute-force find a repetition in pi to prove that it is not irrational, but to no avail.  When I say no repeating pattern, what I mean, for example, is that 22/7, the closest fraction to the value of pi, is 3.142857142857142857 and so on.  The pattern “142857” repeats forever, so it’s an infinite series, but it has repetition.  Pi is 3.1415926535897932384626338327950288…  There is nothing in it that repeats forever, making it irrational.  It’s such a simple concept (ratio of circumference to diameter), but with such a complicated answer.  This, to me, is very cool.

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