I use inexpensive Computer Assisted Design (CAD) software for these geometry explorations, keeping in mind that true solutions require the same drawings by hand with pencil, paper, straightedge, and compass using basic geometry rules. So, the majority of the designs are those that can be created by hand (this exploration to date would have taken decades with many errors to correct along the way and with little feedback on geometry precision (line lengths, angles, etc.)).In addition to drawing automation, the greatest benefit of the software has been the coloring of lines
, without which it would have been difficult to distinguish geometric objects within the more complex designs. Even then, I often have to declare a plateau for a study that refuses to keep advancing. Typically, that study (if significant from a design perspective) is transformed from CAD drawing to artwork; the artwork becomes my "mini-reward" and evidence of having struggled with the exploration. 
The goal for the past few years has been to show the natural geometry of squared circles (or close enough for reasonably accurate visualization). Prior to this, the goal was to "square the circle" (discover the geometry that could do this ... despite mathematicians' belief that it cannot be done). This challenge is twofold: square the circle by the Greek rules and prove geometrically that it's squared. The recent "Sublime Correlation" design is closest yet to suggesting that geometry exists to prove the square of a circle. At least, it appears close to proving that only one circle (diameter) complements a square composed of sides having length equal to half the square root of Pi.I learned several years ago that software cannot display all of the decimal digits necessary (a problem related to the number of digits in Pi
) to verify geometric accuracy, but I've gained a sense of proportion for lines, angles, and objects that keeps the studies moving forward; three decimal digits have been sufficient to create and maintain confidence but experiential intuition may be the real guide 
. 
Ultimately, it matters not whether a line length, for example, has a million decimal digits as long as that same length can be proven by geometry to exist in another part of the drawing. But the consistent focus of these many studies has been the magical 62.403.. degree radius (a 27.597.. degree angle in a right triangle created by a point at which the circle meets the square; the circle's radius is the hypotenuse and the opposite side the Y axis in an X-Y plane).From my perspective, I'm rarely trying to "square the circle" - just searching for interesting geometric patterns that have potential for proving that which has been declared to be impossible: I've known for years that it was impossible to square the circle, but I didn't know that it would be so difficult.
Rod
Goji Berry Ménage (new design)
Celebrating the start of an early Spring Break with a 2-for-1 special:
... 
If the violet diagonal is the side of a square inscribed in the cynosure circle
"Anatomy of Cynosure – Respiration"
Good symbolism (and maybe intriguing prescience) for closure of the portfolio. 
. If this angle does not exist in a "squared circle", the circle ain't squared ... period! 
As fast as possible, repeat this comment about the Say What geometry: 
