![]() “Pi squared represents a three-dimensional surface that constitutes a new form – a transition between a cube and a sphere. C-L.įor an antisphere with a radius and hemisphere height equal to 1, the lateral area is remarkably similar to pi squared, an algebraic expression that involves a new dimension, says Cabeza-Lainez. With Ramanjuan’s formulas for determining the perimeter of an ellipse as a function of the two axes, Cabeza-Lainez began calculating the lateral surface of an antisphere divided into two hemispheres. One approach was to use the length of an ellipse designed by Indian mathematician Srinivasa Ramanujan, whose life inspired the movie The Man Who Knew Infinity. How to find the area of that surface formed by straight lines that run from the end of the rectangle to the points of the semicircle? But the construction of the university’s engineering building added more complexity with a design that called for a surface connecting both shapes. Cabeza-Lainez’s solution addressed efficient solar light transfer between a semicircle joined at the bottom to a rectangle. In the process, he glimpsed the solution to the problem, which he wrote about in a book about solar light transfer ( Fundamentos de transferencia radiante luminosa Netbiblo, 2010). C.-L.Ĭabeza-Lainez, determined to achieve greater efficiency of radiation and light, has designed light-pipes with better lighting capability and lower energy consumption. This is the formula for calculating psi: J. Both articles present his proposal of a number psi (Ψ), with a value of 3.140923, close to pi but which can be applied to a versatile geometric form that he calls an antisphere. After 30 years of research, Cabeza-Lainez published a paper about his discovery in ScienceDirect and issued another unreviewed report. ![]() But this ratio between the perimeter of a circle and its diameter also has limitations, such as the one discovered by Joseph Cabeza-Lainez, an architect and academic at the University of Seville (Spain).ĭuring the construction of the university’s new engineering building, Cabeza-Lainez found that calculating the area of a roof with straight lines resting on a semicircle was impossible just by using pi. This irrational number has crept into every facet of life, from engineering and architecture to statistics and quantum mechanics. The mathematical constant was first calculated about 4,000 years ago, and its approximations can be found in numerous ancient cultures, including the Egyptian Rhind Mathematical Papyrus and the Bible. The number pi (π) is celebrated internationally on March 14 because it starts with 3.14, or the 14th day of the third month. ![]() ![]() Joseph Cabeza-Lainez displays models of ‘antispheres’ in Seville, Spain March 11, 2023. ![]()
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