Geometric constructions of Phi in Circles (con imágenes ...

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The All-Seeing Eye

1/10/2019

Eye within an interlocking circle and triangle

The 18th century church of Santa Maria della Maddalena (1763-90), better known simply as La Maddalena, was designed by the Venetian architect Tommaso Temanza (1705-89).

The entrance to the church is surmounted by the inscription SAPIENTIA AEDIFICAVIT SIBI DOMUM (Wisdom has built herself a home) and a curious image of an eye surrounded by an interlocking circle and triangle.

The all-seeing eye is one of the symbols of freemasonry and both the architect and the patron (a member of the Baffo family) of the church were freemasons.

Temanza's ashes are interred in La Maddalena.

La Maddalena

Tomb of Tommaso Temanza

https://www.picturesfromitaly.com/venice/freemasonry-and-the-church-of-santa-maria-della-maddalena-venice

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Connect the points with lines at AF and DG (in red). At Y, the intersection of DG and EF, create perpendicular lines from Y to AF at Z, and again from Y to ED at W. This produces a number of phi relationships, or golden sections: Numero Aureo, Aula De Química, Aurea, Fractales, Geometría Sagrada, Nombre, Conocimiento, Matemáticos, Ad Hoc

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Artículo de goldennumber.net

Geometric constructions of Phi in Circles

Phi appears in a number of geometric constructions using circles. There are a number of geometric constructions using a circle which produce phi relationships, as described below. Among mathematicians, there’s a bit of a competition to see how few lines can be used to create a phi proportion, or golden section, in the construction, or …

Numero Aureo Aula De Química Aurea Fractales Geometría Sagrada Nombre Conocimiento Matemáticos Ad Hoc

Artículo de Chris Macey

Phi, the Golden Ratio, construction with a triangle in a circlensert an equilateral triangle inside a circle, add a line at the midpoint of the two sides and extend that line to the circle. The ratio of AG to AB is Phi. Seccion Aurea, Proporcion Aurea, Sucesiones, Proporciones, Geometría Sagrada, Geometria, Mandalas, Patrones, Disenos De Unas

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Phi, the Golden Ratio and Geometry

Golden ratios appears in many geometric constructions, including triangles and squares in circles, the pentagon and also in solids such as the dodecahedron.

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Ancient Metrology - Numbers Don't Lie - World Mysteries Blog

A. Sokolowski There is an underlying order in Cosmos. Our ancestors discovered it in ancient times and expressed it in their writings and monuments. This article is an invitation to all our visitor to explore and expand this subject. Please share facts that should be mentioned here (via comments and/or e-mail) – if you are […]

Dibujo Tecnico Ejercicios Clases De Dibujo Técnicas De Dibujo Cursos De Matematicas Funciones Matematicas Dibujo Tecnico Arquitectonico Rectangulo Aureo Espiral De Fibonacci Aula De Química

Artículo de S. D.

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3 Phi and Triangles

3.1 Phi and the Equilateral Triangle

Chris and Penny at Regina University's Math Central (Canada) show how we can use any circle to construct on it a hexagon and an equilateral triangle. Joining three pairs of points then reveals a line and its golden section point as follows:

On any circle (centre O), construct the 6 equally spaced points A, B, C, D, E and F on its circumference without altering your compasses, so they are the same distance apart as the radius of the circle. ABCDEF forms a regular hexagon.
Choose every other point to make an equilateral triangle ACE.
On two of the sides of that triangle (AE and AC), mark their mid-points P and Q by joining the centre O to two of the unused points of the hexagon (F and B).
The line PQ is then extended to meet the circle at point R.
Q is the golden section point of the line PR.

Q is a gold point of PR
The proof of this is left to you because it is a nice exercise either using coordinate geometry and the equation of the circle and the line PQ to find their point of intersection or else using plane geometry to find the lengths PR and QR.

The diagram on the left has many golden sections and yet contains only equilateral triangles. Can you make your own design based on this principle?

Chris and Penny's page shows how to continue using your compasses to make a pentagon with QR as one side.