## Archive for **August 4th, 2020**

## Low wild petunia

From Vaught Ranch Road on June 13th come two views of a native wildflower

I’d never photographed before: *Ruellia humilis*, known as low wild petunia.

Here’s an unrelated little mathematical diversion: the four numbers 1, 1.2, 2, and 3 have the interesting property that whether you add all of them or multiply all of them you get the same result (in this case 7.2). Are they the only foursome like that? Hardly. For example, whether you add -2, -1, 0, and 3 or multiply -2, -1, 0, and 3, you get the same result (in this case 0). Would you believe that *infinitely many* sets of four numbers exist that also have the property that adding the four numbers gives the same result as multiplying them? That turns out to be the truth of the matter. Are you surprised?

The second example suggests a template for generating as many more sets of numbers as you like that have the desired property. Let the first of the four numbers be 0. Now pick any two different negative numbers you like (say for example –4 and –6). Finally, add the two negative numbers and make the sum positive (in this case 10). You’ll now have four numbers with the desired property (–4, –6, 0, 10). This works because 0 times any other number is 0, and you’ve rigged the addition in such a way that the positive number cancels out the two negative numbers. In fact you can extend the pattern to as many numbers as you like. For instance, here are six numbers such that adding them gives the same result as multiplying them: 0, -3, -7, -10, -15, 35.

As a quotation for today, let me quote myself: Zero may be nothing, but not for nothing is zero special.

© 2020 Steven Schwartzman