THE GOLDEN TRIANGLE

CARLOS CALVIMONTES ROJAS

The author refound the emblematic geometric figure of the qualities of the Golden Number, the Golden Triangle, he defined his properties and he discovered his manifestations in the Nature and the human creation. In the front of the castle l'Herm found the best example of the application of that polygon, that would have been known in the antiquity of diverse cultures and used in express form specially in the harmonic proportion of remarkable architectonic works (Puerta del Sol of Tiwanaku and cathedral of Milan). In others, not less important, it appears by the use of inherited criteria of general composition (temples of México), it is revealed spontaneously by the design with aesthetic and/or structural excellence (project of Norman Foster in Moscow and Eiffel tower) or it is pronounced by emulation of existing proportions in the Nature (temple of La Sagrada Familia of Antoni Gaudí with towers that imitate forms of gasteropods).

Here one exposes the configuration of the Golden Triangle, its presence  in the Nature  and its expression in the architecture as canon of design, calculated or intuitive, specially in the configuration of external forms; with the exceptions of the cathedral of Milan, where it participates in the internal design, and of the Puerta del Sol of Tiwanaku, where the Golden Triangle is a component more of its composition.

C ONFIGURATION

The Golden Triangle is the one that reunites the set of essential qualities of the Golden Number: himself, its inverse and its square; and, in addition, it is not derived from any other geometric figure.

  • It has of height F (1.618033989...) and of base  1 F (0.618033989...) .

  • The ratio between the height of the Triangle and its base is F 2 (2.618033989...).

  • If the base is equaled to 1 the height it is F 2

Therefore, one is the Golden Triangle par excellence, paradigmatic geometric figure by his harmonic proportions.

It is known as ‘golden triangle’ one isosceles ones generally whose equal sides are worth 2 F and its base F ; nevertheless, this figure is a product of the configuration of the pentagon that, as it is known, absolutely is defined by F in all its parts and derived figures. That 'golden triangle' has as equal sides to two of the diagonals of the pentagon and their base are a side of this one.

The Golden Triangle is some similar to the figure that can in the end be constructed with the Series of Fibonacci (0-1-1-2-3-5-8-13-21.......).

THE GOLDEN TRIANGLE OF CALVIMONT

Castle of l'Herm of Jean III de Calvimont (s. XV)

Of that flambloyant gothic work is known like 'treasure' the set of elements in which they stand out, like architectonic jewels, the front, the spiral stairscase and the vault with triangled rib, that are formed with the Golden Number.

Between remarkable works of architecture of different times and places with the proportions from the Golden Triangle, the beautiful composition of the front of that castle by his detailed design with the participation of the Golden Number.

PRESENCE OF THE GOLDEN TRIANGLE

As it happens with all singular manifestation of F , the Golden Triangle is present in the Nature and the human creation, specially in architecture works; as [with base is defined in its configuration or with its longitudinal half 1/(2 F )]. In the illustrations of the first case is the bilateral center line.

Leaf of Japanese Maple,

acer palmatum

Leaf of the Tree of Estoraque ,

liquidambar styraciflua

GEOMETRÍA DE HOJAS DE ÁRBOLES SEGÚN EL NÚMERO DE ORO

 

Cypress of Lawson , chamaecyparis lawsoniana

Red fir , picea abis

Sugi, cryptomeria japonica

Puya Raimondi

pourretia gigantea

C onfiguration of the egg of hen according to C. Calvimontes R.

GEOMETRÍA DE LA PARÁBOLA SEGÚN EL NÚMERO DE ORO

Gasteropods

S uperposition to graphs of the book The Curves of Life of Theodore Andrea Cook

Globigerina

S uperposition to drawing of Ernst Haeckel

GEOMETRÍA DE LOS EXAPENTA SEGÚN EL NÚMERO DE ORO

GEOMETRÍA DEL DODECAEDRO SEGÚN EL NÚMERO DE ORO

Central figure in the Puerta del Soi de Tiwanaku. Its navel stands out, common vertex of the triangles of composition with the Golden Number.

Configuration of the Puerta del Sol de Tiwanaku (circa s. V)

according to C. Calvimontes R.

PROPORCIONES ARMÓNICAS EN LA PUERTA DEL SOL DE TIWANAKU

Cathedral of Chartres (s. XIII)

Cathedral of Cologne (s. XIV)

Cathedral of Milan (s. XIV)

Harmonization of the proportions of the cathedral of Milan by Stornalocho architect in 1391 with the use of triangles and presented, with the added one of circles, by Cesare Cesariano in 1591 in its translation and commentary of the work of Vitruvio. In 1931 Ernst Moessel it used that base to propose a thesis that interprets the design of Stornalocho. Nevertheless, the work of Moessel only considers external equilateral triangles and not both inner isosceles triangles. Indeed the greater one of these is a Golden Triangle complete and the interior its half. The design spread by Cesariano appears without no intervention and in the copy of its central part with the presence of those two triangular figures.

Castle of the Bran (s. XIV), where Vlad II ( well-known like count Dracula ) lived. 

Fronts of temples in the city of México (circa s. XVI).

Superposition to drawings of Domingo García Ramos

Eiffel tower (s. XIX). S uperposition to drawing of Gustave Eiffel

Fountain of the Rabies of Gottfried Semper, Dresden (s. XIX)

Drawing of C. Calvimontes R.

Temple of the Sagrada Familia (s. XX) de Antoni Gaudí

Project of Norman Foster

Building of 600 m of height in the international center Moscow City (s. XXI)

Project of Daniel Libeskind and David Childs

Building Freedom Tower, of 541 ms, in Ground Zone of New York (s. XXI)

Project of Adrian Smith

Building Burj Dubai, of 808 ms, Dubai (s. XXI)

Libros del autor:

TO GO TO THE MAIN PAGE

http://urbtecto.es.tl

http://urbtecto.es.tl

1