Leonardo da Vinci's good friend, Pacioli

Leonardo da Vinci's good friend, Pacioli

Luca Pacioli Pacioli was born in 1445 in a small Italian town called Borgo San Sebolcolo. When he was a child, his family was not rich, and he could only attend free church schools, but little Luca was talented, hard-working and loved to learn, and the teachers were very fond of this thinking and sensible child. Later, he was fortunate enough to be appreciated by Piero della Fracesca, and he studied art under him. Francesca was a well-known master of art at that time, proficient in geometry, and his "Theory of Pictorial Perspective" can be described as a milestone in the application of mathematical elements to art. Under the guidance of his teacher, Pacholi has a deep foundation in mathematical logic and artistic painting. Later, through the introduction of the teacher, he was taught by Alberti leon Battista. Alberti is also a well-known master of art, with high attainments in painting and sculpture. In his book Painting, he pointed out that to be a qualified painter, one must first master geometry. Under the influence of these masters of art, Pacioli, in addition to mastering the principles of these arts, has become a strong awareness that the beauty of all art originates from mathematics.

Guided by this awareness, Pacioli began to delve into mathematics. At the age of thirty he was employed as a principal lecturer at the University of Perugia, where he taught mathematics. During this time, he went into the church, became a devout monk, and had a close relationship with Pope Paul III. Paul III wanted Pacholy to popularize mathematical knowledge and infiltrate religion. And Pacioli knows that mathematical applications are much more than that. At that time, in the era of rapid development of the commercial economy, the establishment of scientific bookkeeping methods seemed to become very important, And Pacho used his heart to do this research, combined with practice, finally published "Arithmetic, Geometry, Ratio and Proportion Integration", referred to as "Mathematics Encyclopedia". This work ushered in a new era of modern accounting, and he was also revered by the world as the "father of modern accounting".

In addition to this, one will not forget his other masterpiece, The Divine Proportions. This tome was written in Milan around 1497 and published in Venice in 1509. Prior to writing this book, Pacioli was invited to teach mathematics at the house of L. Sforza, Duke of Milan. In the house, he happened to meet Leonardo da Vinci, and the two of them had heard each other's names, which was really a hero's pity for each other, and soon the two became good friends who talked about everything. Although a master artist, Leonardo da Vinci still prayed to pacholi, who was 7 years old, to teach mathematics, and pacholi was very attentive to explain mathematics to this "student". Deeply influenced by art since childhood, Pacioli realized the importance of proper proportions in artistic creation, and thus came up with the idea of writing "Divine Proportions". Leonardo da Vinci was very sympathetic to Pacioli's idea and took it upon himself to accompany the illustration of the book. For example, "Vitruvius" is one of them.

The Divine Proportions consists mainly of 3 volumes. Volume 1 deals with the "Outline of the Divine Ratio", i.e., the "Golden Ratio" and its properties, and contains Euclid's discussion of the "Golden Ratio". Euclid gives the proposition in The Primitives of Geometry, Volume II: "Divide a line segment into two segments, so that the whole segment and the rectangle contained in one of the segments are equal to the squares on the other segment." The points in this are the so-called golden section points. In addition, the correlation properties of regular polyhedra and semiregerahedron are discussed in Volume 1. Volume 2 deals mainly with "architecture", adding to the results of the study of mathematical proportions on the basis of ancient architecture. Volume 3 is primarily "Proportionality" and is based primarily on the teacher Francesca's discourse on proportion. From the perspective of the convergence of disciplines, the book is a model of the combination of "art and mathematics". The master artist Leonardo da Vincigan made illustrations of green leaves, which is unique in the history of human civilization.

Today, the "golden ratio" is well known, and it has been covered in our basic education textbooks from the beginning, and it has been applied to the corners of our lives. Whether in life or in the magical natural world, the beautiful shape of the conch, the number of branches and petals of the plants that grow according to the "Fibonacci sequence" distribution, even our great mathematician Hua Luogeng also promoted the 0.618 optimal method. The theologian Aquinas said, "Pleasant sensations come from the right proportions." No wonder Kepler once said that there are two treasure houses in geometry, one is the Pythagorean theorem and the other is the golden section. The former can be compared to a gold mine and the latter to a precious diamond mine.

Pacholi later published other works, and later traveled from place to place to lecture and preach, and also worked as an official until his death. But our descendants will still be immersed in the extraordinary years of the fusion of science and art, and it will be difficult to let go for a long time.