Notes from the studio, not always about architecture.

Architects fall for the romantic image of vernacular architecture — but transferring a solution between climates demands rigour. Which of Fathy's cooling devices work in Ibiza, which don't, and why — a critical study with diagrams.

The Egyptian “architect of the poor” built in extreme heat and rarely reached for a machine to cool a room. The malqaf, the courtyard and the dome as a house that is its own climate — and why he is one of our references.

A body of vanishing volume and infinite surface — what surface, mass and shade mean for building in Mediterranean heat, and a rammed-earth fractal in the Ibiza landscape.

On 12 August a total solar eclipse will be visible from Ibiza — a true syzygy of Sun, Moon and Earth: the geometry of the alignment, the 400×/400× coincidence, and a note for observing.

Five resisted the compass — and hid the golden section, φ, inside the five-pointed star: the one proportion that contains itself, and the proportion of growth.

Halve a string and it sings the octave; the first four numbers hold every consonance the ear accepts — the tetraktys, and the Pythagorean music of the spheres.

From an infinite nothingness, a single point; from a point and a string, the One; and from the One the numbers up to five — drawn by hand, in the spirit of the Theology of Arithmetic.

Two circles and a few straight lines give √3, √2, √5 and the golden section — no numbers written down. From Pythagoras and the Egyptian remen to Pacioli's divine proportion, with a step-by-step construction you can watch unfold.