AP's 240th published book of science with stunning proof that 3 arbitrary points not only determines unique circle but unique ellipse.

New True Geometry starting with cycloid correction and Geometry-of-Motion // math research

by Archimedes Plutonium

Preface: Motion Geometry such as producing the Cycloid curve in Old Math was in error. Looking at the Limacon we see this error in Motion Geometry at its worst. And the fix of the error has to come from physics of Electromagnetic theory where magnetic field is always perpendicular to electric field. The mistake made in Old Math Geometry is that they had two motions in a cycloid and limacon construction. They had the motion of a circle, but had arbitrary motion for the Pointer-Marker. This book addresses the Old Math Geometry mistakes and opens up the entire field of new math of Motion Geometry.. In the midst of that correction several major conjectures were discovered and proven in this book which has created a complete overhaul of Old Math's conic sections. For the parabola and hyperbola are not open curves but closed loop circuits of ellipse, oval, circle. The nasty mistake of Old Math to think cones are apex to apex is ridiculous to the nth degree, for true conics are base to base <>, not apex to apex ><. And I finish this book with a stunning proof that 3 arbitrary non-collinear points in the plane not only produces a unique circle, but produces a unique ellipse, yet Old Math claimed it requires 5 points to produce a unique ellipse. I suspect Old Math's 5 point requirement is based on the square or rectangle, whereas my 3 point requirement is a parallelogram that is not square and not a rectangle. If I can find a unique ellipse inside a unique circle produced by 3 arbitrary points non-collinear, then I can say in general all 3 arbitrary non-collinear points produces a unique ellipse.

Cover Picture: My photograph of holding two cones base to base. Two cones base to base forms the foundation of Conic Sections, and not the silly apex to apex.

Product details
• ASIN ‏ : ‎ B0C5VL38ZK
• Publication date ‏ : ‎ May 20, 2023
• Language ‏ : ‎ English
• File size ‏ : ‎ 626 KB
• Text-to-Speech ‏ : ‎ Enabled
• Screen Reader ‏ : ‎ Supported
• Enhanced typesetting ‏ : ‎ Enabled
• X-Ray ‏ : ‎ Not Enabled
• Word Wise ‏ : ‎ Not Enabled
• Sticky notes ‏ : ‎ On Kindle Scribe
• Print length ‏ : ‎ 78 pages

Could I have anticipated this final result-- both the ellipse and circle require just 3 arbitrary points non-collinear to be a unique ellipse and unique circle?

No, not unless I knew beforehand that the Parallelogram is unique from 3 arbitrary points and a unique parallelogram provides a unique ellipse.

AP