I made several images to explain Euclid's "parallel postulate" for an upcoming article in Decoded Science. To establish copyright, I always pre-publish my own images in a site that I control. It's also an excuse to publicize my articles.

## DeHaan's Images for Euclidean Articles

## What Are These Euclidean Articles?

Next is "Elements of Geometry: A Brief Guide to the Euclidean Axioms". It's focus is on the axioms, which are really brief and simple.

The final article is "A Brief Guide to the Euclidean Postulates". The postulates are almost as simple as the axioms, but use a few more words. However, the final "parallel postulate" is really what I had in mind when I started writing this trilogy. Mathematicians had tried to work around this lengthy and non-trivial postulate. Finally they learned what happens if you mess with it!

## Further Publicity for my Articles about Euclid's Axioms

## Writing Tip based on my Euclid's Axioms Article

Rather than drawing everything by freehand in my Paint program, I started with an Excel spreadsheet. Then I added a few data values, and inserted a "scatter" graph to provide the points for the first image.

I was completely dissatisfied with the first graph, because I was trying to get Excel to draw the lines automatically. Rather than spending time to work out those technical details, I decided to simply use the "scatter" graph as a background. Then I could Paint the rest.

I jumped from Excel to Paint for the second graph, since the multiple triangles would be even more of a nuisance.

As a bonus writing tip, remember that you could construct good graphics in other programs too. "Visio" comes to mind; its primary purpose is flow charts, but you might find it handy to help people visualize Euclid's axioms.