Once again I will use this blog to publish some of my own creations: images to be added to an

upcoming article in

Decoded Science.

[ Edited June 13, 2011: "The Proof and Practice of Thales' Theorem for Circled Triangles" was published today. It explains how to prove the theorem that angle(AOC) in the first diagram is always 90 degrees, no matter where point C is placed on the circumference. Well, anywhere but points A or B, obviously. As always, I also promoted the Dec.Sci. article in my main site, in the blog entry "

Decoded Science Reveals How to Prove Thales’ Theorem". ]

"Thales Triangle with Notes" by Mike DeHaan

This is the basic diagram for Thales' Theorem.

It is so clear, simple and obvious, it is a wonder there is any need for an article at all.

"Triangle in a Circle" by Mike DeHaan

Surprisingly, this is the initial diagram for the article. Clearly the previous diagram is built from it.

"Starting to Seek the Centre of a Circle" by Mike DeHaan

Completely different circles and triangles are used for the second pair of images in my article about Thales' Theorem.

"Having Found the Centre of a Circle" by Mike DeHaan

Finishing the group of diagrams is the completion of the previous image. Hopefully this will be crystal clear to the readers of Decoded Science.