"Never start a speech with an apology",  but this blog post starts with an apology to anyone who checked it from June 19 through most of July 4, 2012. After posting the preview, I was asked to split the original article into three pieces. It took me a bit of work to make sure they related properly to each other. Then it took a week to publish them all, so as to maximize their impact for the main site.

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

"A Parallelogram for Parallel Lines", image by Mike DeHaan
First is a parallelogram, because it is too easy to just think "square".

"Tall Triangles and Parallel Lines", image by Mike DeHaan
Next we have triangles that grow taller until the top point splits, freeing the two green parallel lines.

"The Numbers of Euclid's Elements", image by Mike DeHaan
When I realized the article would become a trilogy, based on Euclid's whole multi-volume Elements, I decided that a spreadsheet would illustrate the size of the book.

Later I realized I needed an image of a compass. Lo, a pair of my very own compasses!

What Are These Euclidean Articles?

The introductory article is "Euclid Laid the Foundations of Geometry". It tells a bit about Euclid himself, and introduces plane geometry.

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

I always mention DeHaan Services ("Three Euclid Articles for One Low Price")  and my Xanga blog ("One Euclidean Trilogy, Please") where I also publicize my articles.

Writing Tip based on my Euclid's Axioms Article

I think this is a new writing tip, although I probably hinted at it before.

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.

Leave a Reply.

    Mike DeHaan

    Mike DeHaan began writing professionally in 2010 as the sole proprietor of DeHaan Services.To see this information with the best background image, please refer to "About.Me",  befriend me at Facebook, or circle me at Google+.


    Circle me at Google+ with: .
    Google_+1 this post or page with:

    StumbleUpon this post or page with:

    Zoom me when it's Canadian content: .

    Friend me at Facebook.

    Tweet this article via



    Business Tips
    Writing Tip
    Writing Tips
    Writing Wordpress


    November 2013
    October 2013
    September 2013
    August 2013
    July 2013
    June 2013
    May 2013
    April 2013
    March 2013
    February 2013
    January 2013
    December 2012
    November 2012
    October 2012
    September 2012
    August 2012
    July 2012
    June 2012
    May 2012
    April 2012
    March 2012
    February 2012
    January 2012
    December 2011
    November 2011
    October 2011
    September 2011
    August 2011
    July 2011
    June 2011
    May 2011
    April 2011
    March 2011
    February 2011

    Flexible Sidebar

    Weebly's "Blog Author" widget from the Blog Sidebar's Elements menu provides a lot of flexibility. You can change both the title and the text.

    It has all the capabilities for text editing that you find in most Weebly text widgets.

    At this point, I don't see a way to code any HTML in this widget.

    The "Picture" does what you expect: it displays an image of your choice. I just added my home-made picture of "Copyright DeHaan Services 2013" as the top element in this sidebar on Jan. 22, 2013.

    The "Search Box" is a "Pro" feature; if you're paying for Weebly hosting, it may be worthwhile.

    The other widgets are pre-programmed to do what they say.

Check PageRank