Collision of the essentials of the conical sections // The Circumference

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The book the Ist of the Conical ones begins with an exhibition of the motives for writing the work, this way we know that while Apolonio was in Alexandria it was visited by a geometer called Naucrate, and it was by the last one that Apolonio wrote a hurried draft of Conical in eight books. More evenings, already in Pérgamo, Apolonio took the necessary time to polish carefully these books, one for one, which explains the fact of the books the IV and VIIth begins with dedications and gratitude Tie the king of Pérgamo.

Information consulted in conical Sections. A look from the implied derivation, 2008. >

Since the purpose of this post is to enrich and to share the knowledge on: Collision of the essentials of the conical sections // The Circumference, good now well partners or reading friends a circumference can be a geometric place where two equidistant points of another interior so-called center O, also it is possible to be considered that it is a curved line in the plane, where it is being closed and flat where all his equidistant points in a point of interior form named I centre. Apara this case to measure the length of the circumference which is measured of his outline and is calculated by means of the equation: L = 2πr.

At level of sections conical it appears of the following way where P (x, y), where the distance of P to O, this one goes to be equal to r, which is a radio, also P (x, y)/d (P, O) =r, If the plane is perpendicular to the above mentioned axis produces a circumference where this axis forms with the 90th plane = β for the case of geometry. Thank you this representation demonstrates that the points for P (x, y) where the points of the variable combine the circumference with of h and k according to the radio in r, considering r2 <0 we have the equation left: R%2 = (x-h) %2 + (and - k) %2, since for center in O is (0,0).

A representation by means of the use of the following conical equation, where the following equation is had: (X-4) + (y+3) = 16, it is solved in an analytical and geometric way, since it is considered to be the canonical equation for the circumference we have any point of the circumference P (x, y) it is distant to the center of the same one, the distance r, also friends or reading partners considering r2 <0, also as the radio is the distance of the center to a point of the circumference and making use of the values of coordinated we can write the following equation: R%2 = (x-h) %2 + (and - k) %2, therefore what is wanted is to chart the circumference, to describe his elements I centre and I remove, from the general conic equation, since the process of understanding this mathematical model, treats also the geometric place for the point O (h, k), then we have left O (4,-3) and for r = 4.

I would like to share the following contribution:

Models of conical sections. For being of soft curvature, the curves of big radius of curvature are particularly the most difficult, to realize the fusilados. Using the method of the conical tracing all the curves appear as conical sections, which provides major graphic precision or more mathematical determination.

Information consulted in descriptive Geometry: compendium of descriptive geometry for technicians for B. Leighton Wellman, 1976.

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[1] - Analytical Geometry. An Introduction to the Geometry for Ann Irene Ramírez Galarza, 2004.

[2] - practical Mathematics for Claude Irwin Palmer, Samuel Fletcher, 2003.

[3] - calculation: several variables for George Brinton Thomas, 2006.

[4] - descriptive geometry: compendium of descriptive geometry for technicians Por B. Leighton Wellman, 1976.

[5]-Secciones cónicas. Una mirada desde la derivación implícita, 2008.