Tuesday, February 14, 2017

Mental Arithmetic


1 + 2 + 3 = 6 = 1 x 2 x 3

For such reasons, 6 is said to be a perfect number, by mathematicians. Calculations are easier if they involve amounts like 60 and 12 (a dozen). But it is 10 that is basic to our number system (because of course, we have five digits on each of our two hands), which is why that number is the first two digit number (one ten and no units).

Here are two arrangements of the ten digits, and some arithmetic:

       1 2  3  4
       5 6  7  8              0  1 2  3  4
       9 0                      5  6 7  8  9


     12 = 3 x 4
     56 = 7 x 8
     90                        0 + 12 = 3 x 4
                                  5 + 67 = 8 x 9 = 72

There are 360 degrees in a circle. A square has four sides, so the angles at its corners have 360/4 = 90 degrees. And a pentagon has five sides, so the angles at its corners have 360/5 = 72 degrees.

And 360/6 = 60. There are 60 seconds in a minute, and 60 minutes in an hour. And 60 + 12 = 72. There are 12 hours on a clock-face, and 12 months in a year. And 60 x 12 = 720 = 1 x 2 x 3 x 4 x 5 x 6.

Sixties are useful for calculations, because fifths, quarters, thirds and halves of sixties are all whole numbers. Similarly, dozens are useful, because quarters, thirds and halves of dozens are all whole numbers. But we originally counted in fives and tens.

The Roman for five was V, which is like the Vulcan greeting; and ten was X, which is two of them stuck together. And following the fall of the Roman empire, there was an obsession with the number 666. Surprisingly, here is some more arithmetic:

                     1 + 2 + 3 + 4 = 10 = 5 + 5
             1 + 2 + 3 + ... + 8 = 36 = 6 x 6

           1 + 2 + 3 + ... + 10 = 55
           1 + 2 + 3 + ... + 36 = 666

The Roman for 55 was LV, incidentally.

LoVe

The Bible ends with there no longer being any sea, in a new world; and there is indeed no sea on Mars. Will the wealthiest of us end up relocating to Mars? The Bible seems to think so...