# The Geometry of Antoni Gaudi

** Under construction **

## Magic Square

Jesus and Judas with the Magic Square.

The passion facade of the Sagrada Familia was also worked on by the Catalan sculptor Josep Maria Subirachs (1927 -).

Close up of the magic square

Subirachs created a magic square where the rows and columns add up to 33, the age of Jesus at the time of his death. Two numbers are repeated: 10 and 14. If we add these numbers we get 48. The number 48 is the same number one obtains if the letter of INRI (Iesus Nazarenus Rex Iudeourum) are assigned a number according to their order in the Latin Alphabet.

 A B C D E F G H I K L M N O P Q R S T V X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

So that 9 + 13 + 17 + 9 = 48

## Catenary Arches and Catenoids

A catenary arch is the shape one gets when we suspend a rope or chain from its endpoints. Gaudi used catenary arches in many of his projects. The advantage of the catenary arch is that it can be constructed from relatively light materials while still being able to support great weights.

## Hyperbolic Surfaces

### Hyperbolas

Sketch of a cross section showing hyperbolas.

The hyperbola is a curve created when we slice a double cone vertically. This type of curve is used in the interior of the Sagrada Familia. The curves create fairly high vaults, and in the main church Gaudi used this to create pillars that resemble the structure of of tree complete with branched tree trunks.

A hyperbola is created (in cross section) when we slice a double cone vertically.

### Hyperboloids of One Sheet

A hyperboloid can be created if a column of strings is twisted about its central axis. Gaudi used this type of curved surface in the construction of some of the windows in the Sagrada Família in Barcelona.