The First Program I Ever Wrote

When people ask how I got into programming, I usually tell them “mostly for maths stuff”. And they look at me, kind of confused. I think people forget (or don’t know) that my degree was in Theoretical Physics. Originally, I was a maths nerd, and programming was just a tool for making doing maths easier.

Pythagoras

Back in secondary school (high school), we’d just been taught about Pythagoras’s theorem

$a^2 + b^2 = c^2$

And we were doing exercises, which was pretty dull - once you get the concept, the exercises are just putting numbers in to the equation.

But an interesting thing was that a lot of the exercises used ‘pythagorean triplet’ - sets of three integers which fit the equations. I guess the textbooks use them because the numbers work out nicely, no rounding and all that.

• $3^2 + 4^2 = 5^2$
• $5^2 + 7^2 = 12^2$

After doing a few of these exercises, I noticed a pattern in some of the triplets - that the two largest values were one different from each other - 4 and 5, 12 and 13

With a little algebra, you can work out

So for example if x = 3, y = (3^2 - 1) / 2 = 4; y + 1 = 5

You’ll notice that because of that divide-by-two, this only works if x is odd. But it works for all odd numbers

• 3, 4, 5
• 5, 12, 13
• 7, 24, 25
• 111, 6160, 6161

The Calculator

To test my theory, I was working through all the odd numbers, putting numbers into my calculator, seeing if my equations worked. After a handful, I was thinking - there’s got to be an easier way of generating these triplets.

And it just so happened that my calculator was a graphing calculation (Casio fx-9750 PLUS)

Now I’ve never been one for reading the whole instructions start to end. I’m pretty lazy, I just skim until I find the bits that are relevant to what I’m trying to do.

(And to be fair, the instruction book for that calculator was pretty chunky)

Which brings us to the first program I ever wrote

?->N:(N^2-1)/2
Ans+1

On the first line ?->N asks for input and assigns it to variable N

It then calculates (N^2 - 1) / 2 and outputs it to screen

Then when you press EXE (enter) again, it calculates Ans+1 - the previous result + 1 - and outputs that to screen

In python this would be roughly

while True:
	N = int(input("?"))
	Ans = (N**2 - 1)/2
	print(Ans)
	input()
	print(Ans+1)

So now I could generate all the triplets I wanted!

Branching Out

I later decided I wanted a version of this program that would run on my Windows 98 PC. I didn’t know anything about programming languages, so I initially went with one that happened to be on a CD ROM stuck to the front of a computer magazine. The language was a variation on BASIC.

Then I later did a google search for something like “best programming language”, which lead me to python. I read the ‘getting started’ thing on the python website, and the rest is history…

Chris.

[I need to figure how to make Jekyll do LaTeX]