Pi

Tom Kando 

My previous post began a discussion of some interesting mathematical problems which I want to share with you. I am fully aware that I am a novice in this field. Last time, I wrote about prime numbers. Today, I want to talk about another fascinating topic, namely Pi (π). 

You have heard of the expression “squaring the circle,” right? It means doing (or trying to do) the impossible. 

In order to construct a square with the same area as a given circle, you must first determine the area of the circle, using the following steps: 

1. measure the circle’s circumference. 

2. measure the diameter, that is the distance across the circle between the two halfway points of the circumference. 

3. determine the radius, which is half the diameter. 

4. Square the radius and multiply this number by 3.14 (π). 

In other words A (Area) = π x r 2 (r is radius) 

Then, you simply compute the square root of the circle’s area. This gives you the length of the square’s side. 

Example. You want to square a circle which has a circumference of 1,000 meters. 

Using the π approximation of 3.14, The circle’s diameter is therefore about 318.5 meters, and the radius is half of that - 159.25 meters. The circle’s area is therefore 3.14 x 159.25 2 = 79,582 square meters. The square’s side is the square root of this (√79,582) i.e. approximately 282.1 meters. 

For practical purposes, this procedure will do. However, the problem is that π is a transcendental number. 

Transcendental numbers are non-algebraic and irrational: They are NOT the solution of an algebraic equation. They cannot be expressed as the ratio of two numbers. They have a non-terminating decimal.

22/7 is often used as an approximation of π. It is about 3.14. Since it is a fraction, it is a rational number. Like π,, it has an infinite, non-terminating number of decimals. 

However,UNLIKE π,, the decimals consist of a six-digit repetend. . For example, if you divide 22 by 7 to 24 decimals, you get 3,142857 142857 142857 142857. “142857" is called a “repetend,” and it repeats ad infinitum. Read more...

SOME INTERESTING MATHEMATICAL TOPICS

Tom Kando

Most of my recent posts have been negative. There are so many wrong things these days. The third year of Covid, 5th month of war in Ukraine, the Supreme Court abolishing our constitutional rights, the proliferation of weapons and therefore of mass murder, no progress on the environmental front, the rightward political drift toward fascism in many countries, etc. 

So how about something not depressing, for once? 

A field which has long piqued my curiosity is mathematics, if only because I am not well versed in that area. Incidentally, some of my ancestors were eminent mathematicians and scientists. They include my great-grandfather Beke Mano, who was a pioneer in differential equations and my grand-uncle 

Kalman Kando who invented the phase converter. 

My secondary school education was stellar on the humanities side, but mediocre on the quantitative side: At the gymnasium, we had six years of six languages - Dutch, English, French, German, Latin and Greek! However, our quantitative training did not go beyond algebra, trigonometry, analytic geometry and stereometry. Later, obtaining my PhD at the University of Minnesota required a strong quantitative component in the form of advanced statistics. However, most of my quantitative skills, limited to begin with, have atrophied. I remain fascinated by fields about which I know little, wondering sometimes if I might chose the direction of the exact sciences if I were to do things all over again. 

Take prime numbers, for instance. You can check out a previous post of mine about this: 

Prime Numbers, Large Numbers 

A prime number is a whole number that can only be divided by 1 and by itself. Or put differently, prime numbers cannot be divided by any other whole number without leaving a fraction. The smallest twenty-five prime numbers (those under 100) are: 

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by Madeleine Kando

 

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Thank God for the Vaccine (From my Coronavirus Diary)

By Madeleine Kando

Day 1

What a wonderful time we had in San Francisco. Aside from the joy of being with my 10 year old grandson, there was the city with its parks, its architecture and its museums. Even without any of that, it would have felt like a get out of jail free card after so much time being cooped up in our own universe, back in Boston. For almost two years, we steered clear of the claws of this ruthless monster called Covid. We didn’t go to restaurants, we had friends over one at a time, no parties, no movies, no nothing. 

Now, it is time to fly back home. Squeezed in the window seat, my glasses fogging up above a n95 mask, I am ready to zone out and pretend I am somewhere else for the next 6 hours. Long gone are the days when I fully enjoyed flying cross-country. The window shade is partially open, symbolic of my ambivalence about an experience that I used to find absolutely thrilling. Most of us think nothing of propelling ourselves at 500 miles an hour, at an altitude that only two bird species on earth are known to reach, but I was born two years before the first transatlantic commercial flights began, and there is still this sense of wonder in me. I open the window shade and endure the dirty looks from my co-passengers who are trying to sleep. I cannot get myself to be completely indifferent to this wonder of aviation.

That evening I collapse on my king-size bed and realize how exhausted I am. My throat doesn’t feel good, but I don’t give it a second thought. Home sweet home…

Day 2

The next day, my throat is painful. I can barely swallow. I have intense body aches and a great desire to stay in bed. I test myself for Covid, but I am negative. I go outside to inspect the vegetable garden and notice that little bites have been taken out of all the seedlings. Cukes, beans, peas, all rendered inedible. ‘Oh I forgot to tell you about the groundhogs, mom’, my daughter says. 

We install chicken wire around everything that we assume would go on a groundhog menu: Marigolds, nasturtiums, pansies.. I sprinkle ‘deer repellant’ around the raised beds, which is a terrible mistake. Its odor is so repulsive, that even I cannot go in the garden.

I crawl back in bed. An hour later, I look through our French doors and see a fat groundhog, probably the mother, blissfully eating away at a clover patch. She stares straight at me, her jaws working a mile a minute. A smaller version has materialized and follows in her footsteps. Like two efficient lawnmowers, they quickly decimate half of the clover patch.

Day 3

My symptoms are worse. The lozenges are pretty much all I can tolerate. Having the flu is no picnic. 

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