geometry of the parabola

8/12/2019 Geometry of the Parabola

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GEOMETRY OF THE PARABOLA ACCORDING TO

THE GOLDEN NUMBER

-FROM THE HARMONY OFNATURE TO THAT OF

ARCHITECTURE-

CARLOS CALVIMONTES ROJAS

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To cover spaces is the main architectural probl

faces man. He, in their best achievements for solve

finds solutions that join conditions of beauconstructive easiness, saving of materials and go

structural quality, repeating perfect forms of natu

This has occurred with the parabolic and poin

arches, whose geometry is present in the section o

body existing in the nature that has a system of gr

stability due to the harmony between its parts.

The author found the parabola in the elongated part

the longitudinal section of the hen's egg.

considered that this should have its form configurby the Golden Number,whosepresence is over all

all that has life or relation with life. He checked t

ruling manifestation that transcends the knowledge

the egg. The result, in addition to benefiting

design and construction of the parabolic and poin

arches, contributes to the better knowledge of

parabola.

THE GOLDEN NUMBER IN THE HARMONY OF WHAT IS CREATE

The Golden Number (F =1.6180339...) is the measure of the perfect proportion between two unequal pa

Known since a very remote antiquity, in the plane geometry Vitruvio proposed that "so that a space divid

into unequal parts results pleasant and aesthetic, the relation between the smallest and the largest part must

the same as between the largest and the whole". Regarding linear systems Euclides defined that su

proportion is the "division of one length in medium and extreme ratio" or Golden Section.

As ex lained b Gh ka, that code of nature rather than bein full described it exhibits in the unsta
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concourse of all the parts of the living beings and on the matter with some form of dynamic structures, with

expression of the summarized numeric pattern that is F, with the basis of the number 5. Rather, in the form

the matter not organized for life, in the exponents of stable symmetries and in the structures of crystall

balance its numeric scheme resorts in general to the number 6.

THE PROPORTIONS IN ARCHITECTUR

In the architectural creation the best harmony of the composing parts of a work incorporate Fconnatura

man due to being in its same proportions. The human being has applied criteria developed on that harmonyspontaneous or voluntary form in the best of its creation since the antiquity, in the cultures of Sumer, Eg

and Tiwanaku; and, in Occident, starting with the studies of Policleto, Euclides and Vitruvio, those of Albe

Leonardo da Vinci, Durero, Miguel Angel, Zeising and Le Corbusier, among many others.

The architect expresses by intuition the concept of the desired design and, according to Le Corbus

"automatically makes the necessary optic corrections", in addition to what was addressed by Leibniz regard

the application of the pre-existing harmony, as "we own much knowledge of what we do not have cl

conscience even when we apply it "assuming that "all the arithmetic and all the geometry exist in an innate

virtual in our soul", although "the innate principles only appear when the attention is fixed on them".

FIN THE CONFIGURATION OF THE HEN'S EG


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NON-PARABOLIC GEOMETRY IN THE OVAL SECTIO

The drawing with arcs of four circles is the one that better configure the oval inscribed in the vesica pis

Though in this drawing there is no parabola, it has with exactness the proportions of its chord and sagitta. T

tiny difference between the parabola and the combination of circular arcs in non significant parts (see grap

of the parabola) makes that the product of the analysis of the oval figure serves for the fast design of

parabolic and pointed arcs and for a higher knowledge of the parabola.


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GEOMETRY OF THE POINTED AND PARABOLIC ARCHE


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GEOMETRY OF THE PARABOLA ACCORDING TO

All parabolas are similar: while the size varies, the constants of their configuration are the same for all the

Consequently, having demonstrated that the parabola is on the oval section configured by F, the relat

proportion of the main dimensions of every parabola are established: parameter, sagitta and chord, with

subsequent implications. Also the harmonic coherence of the joint assembly that associates the oval figure wthe parabola permits to confirm the location of the focus of it.


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geometry of the parabola

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