January 2nd, 2016, 11:51 AM  #11 
Senior Member Joined: Nov 2015 From: usa Posts: 152 Thanks: 0 
I forgot to mention if you take this single picture, and make four of these pictures in a square of these four pictures. you will develop another hidden exact picture in the center. Just as if you put four particles in the solid formation of particles. The Quadraarc, will be the shape between these four particles, in solid formation. Again the Quadraarc is the difference in area between the circle and the square. I hope you find these relationships as amazing as I do. Thank you. Last edited by skipjack; January 2nd, 2016 at 12:10 PM. 
January 2nd, 2016, 12:06 PM  #12 
Senior Member Joined: Nov 2015 From: usa Posts: 152 Thanks: 0 
I do see from what you are saying, that there are different possibilities to solve this puzzle. Though this may be the simplest answer. 8 of the two shapes to make a circle and 12 of the two shapes to make the square. From the Biarc and the triangular mono arc, as the two shapes being used. I know that these shapes are important as you are now showing me from this information, in different exact ways. Thank you. 
January 2nd, 2016, 12:07 PM  #13 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra 
Again, why is this important? Also, why would it be amazing for the remains pieces after cutting an inscribed circle from a square to have an area equal to the difference between the areas of the square and the circle. Isn't that kind of obvious? 
January 2nd, 2016, 12:59 PM  #14 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  
January 3rd, 2016, 11:20 PM  #15 
Senior Member Joined: Aug 2012 Posts: 2,356 Thanks: 739  I take no position on the arcane geometrical considerations of this thread. I only wanted to mention that there was a huge lawsuit between Apple and Samsung over rounded rectangles and who has the right to use them as icons. Apple sues Samsung over Galaxy lookandfeel • The Register 
January 4th, 2016, 03:19 AM  #16 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra 
Use of a shape for a specific purpose may be copyrightable, but the shape itself is not.

January 6th, 2016, 03:05 PM  #17 
Senior Member Joined: Nov 2015 From: usa Posts: 152 Thanks: 0 
You are right, just the information, though you can get a design patent of a shape. You cannot patent a formula, but you can patent a purpose for using a new formula. The shapes are only copy written in their content, names used regarding these shapes. These shapes are nothing new, they are seen in nature, and most places on our universe. I do have a copyright on, The Shapes of Our Universe, Geometric Arc Shapes. copyright M Eaton 2012. You are correct, you can not get a copyright, or design patent on shapes that are found in nature. I should have been clearer about this. Thank you. Last edited by mark eaton24; January 6th, 2016 at 03:34 PM. 

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