SAN DIEGO
CALIFORNIA; JANUARY 2013: It has been two years since Lexington and I have evolved ever so slowly the mechanical meter of central force curves and lines. Lexington is about my early methods to understand and construct with Euclidean Geometry gravity curves; San Diego is about source primitive of my main tool to do so, the dependent curve UNIT PARABOLA. I provide code for plane geometry parametric computer construction of 3-space Apollonian section parabola, discover the dependent conic UNIT PARABOLA curve following changing surface curvature of our ancient heritage, the solid geometry cone, and demonstrate independent curve UNIT CIRCLE right cone diameter propensity to acquire physical properties of energy curve propagation, using time for their meter, through the space surrounding human conics. Alexander
ORIGINAL COPYRIGHT GEOMETRY BY THE SANDBOX
CALIFORNIA; JANUARY 2013: It has been two years since Lexington and I have evolved ever so slowly the mechanical meter of central force curves and lines. Lexington is about my early methods to understand and construct with Euclidean Geometry gravity curves; San Diego is about source primitive of my main tool to do so, the dependent curve UNIT PARABOLA. I provide code for plane geometry parametric computer construction of 3-space Apollonian section parabola, discover the dependent conic UNIT PARABOLA curve following changing surface curvature of our ancient heritage, the solid geometry cone, and demonstrate independent curve UNIT CIRCLE right cone diameter propensity to acquire physical properties of energy curve propagation, using time for their meter, through the space surrounding human conics. Alexander
ORIGINAL COPYRIGHT GEOMETRY BY THE SANDBOX
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Wednesday January 9, 2013, 8:30 a.m.-10:55 a.m.
MAA General Contributed Paper Session: Teaching Introductory Mathematics Room 7A, Upper Level, San Diego Convention Center Alexander L. Garron; Jr.*, CEO Sand Box Geometry LLC (1086-VP-1320) ON CONSTRUCTING AN APOLLONIAN SECTION PARABOLA FOCUS USING PARAMETRIC GRAPHING UTILITY OF MATHEMATICA.. Apollonius never mentioned or used the parabola focus. Since ancient Greek geometers missed little, especially something as productive as the parabola focus, I needed to construct the section using computer software, linear algebra of two space and three space, to find the Apollonian section focus and satisfy my curiosity as to why? I will explore the dual nature a parabola focus and locus seems to possess both on and off the surface of a cone using Mathematica enabled parametric geometry. By mapping Cartesian location for profile cone construction of required parabola loci, the vertex and principal axis on the (pi/2) generator , the focal axis constructed normal with the (3pi/2) generator, cone diameter holding the section vertex, cone diameter holding the section latus rectum, I find specific identities using cone slope and altitude needed to construct the solid geometry of Apollonius’ parabola section. When the Apollonian parabola section is finally computer generated on to the 3-space cone surface, a view along the (Z) axis will reveal the dual interpretation a parabola curve can present. We will see one vertex, two latus rectum, two foci, all from one Apollonian parabola section locus. I will show that the Apollonian 3-space section curve is actually the source primitive of our two space plane geometry curve providing the focal utility we use today. Alexander CEO Sand Box Geometry LLC alexander@sandboxgeometry.com |
Texas Instrument n-spire demonstration of Apollonin section parabola 3-space skeleton with Latus Rectum, principal and focal axis.
I MIGHT send this PDF document from San Diego if requested via email @ SBG>COM
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