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May 22nd, 2016, 01:59 AM  #1 
Senior Member Joined: Jul 2015 From: Florida Posts: 147 Thanks: 2 Math Focus: noneuclidean geometry  π
Invariant Quantity π π/4 = blue sin = red 
May 22nd, 2016, 02:03 AM  #2 
Senior Member Joined: Jul 2015 From: Florida Posts: 147 Thanks: 2 Math Focus: noneuclidean geometry 
studiot, my friend, thank you for patiently dragging me from the 20th into the 21st century.

March 28th, 2018, 01:46 PM  #3 
Senior Member Joined: Jul 2015 From: Florida Posts: 147 Thanks: 2 Math Focus: noneuclidean geometry 
We need volunteers for peer review. The paper concerns a trigonometric relationship that exists between directions in threedimensional space that does not exist in twodimensional space. 3D identities (tridentities) in Euclidean 3space.pdf If the proof is valid, it means that direction is a scalar, in addition to being the vector that we all know and love. 
March 28th, 2018, 02:53 PM  #4 
Senior Member Joined: Jul 2015 From: Florida Posts: 147 Thanks: 2 Math Focus: noneuclidean geometry  3Didentities.pdf 