Tiny Manu #90

Grime City PD News

I've not been writing many comic strips recently. Or, indeed, any. So I've had nothing to post, but I'm pleased to say that Grime City PD has been accepted by the London Short Film Festival.

Hooray.

This may be an old joke, but...

... I've not seen it before.

Ersby's Triangle

Pascal's Triangle is a famous and fascinating piece of mathematical architecture. In its sequences are many interesting patterns that also appear in the mathematics of probability, fractals, and geometry.

One day, I decided to take a closer look at it. In particular, I wanted to find a formula to describe the numbers along each diagonal.

So far, so good. But I came a bit unstuck when I reached the fourth diagonal. At first, I thought I found something to do with the differences between the numbers...

 Eventually, after several false starts I guessed that since the first two numbers in the sequence were 1 and 4 perhaps the answer was something to do with square numbers. Before long, I came up with something else...

The fifth diagonal was also difficult, but when I went back to working only with square numbers, the answer came quite quickly.

I noticed that 1 squared was being multiplied by the following numbers: 1, 1, 2, 2, 3, 3...

This time the multiples of 1 squared were 1, 2, 4, 6, 9... But I was also interested in how the multiples seemed to "move along" the sum because now 2 squared was being multiplied by 1, 1, 2, 2, 3... I wondered if something was going on so, for clarity's sake, I wrote these multiples on a copy of Pascal's triangle, beside the number that each sum belonged to.

This is not a photo blog #5

I went into Badock's Wood this morning, and found that the river had made some Andy Goldsworthy type shapes with fallen leaves.