The Archimedean solids are a set of thirteen convex polyhedra whose faces are regular polygons, but not all alike, and whose vertices are all symmetric to each other. The solids were named after Archimedes, although he did not claim credit for them. They belong to the class of uniform polyhedra, the polyhedra with regular faces and symmetric vertices. Some Archimedean solids were portrayed in the works of artists and mathematicians during the Renaissance.
Luca Bartolomeo de Pacioli, O.F.M. was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting. He is referred to as the father of accounting and bookkeeping and he was the first person to publish a work on the double-entry system of book-keeping on the continent. He was also called Luca di Borgo after his birthplace, Borgo Sansepolcro, Tuscany.
In geometry, the truncated icosahedron is a polyhedron that can be constructed by truncating all of the regular icosahedron's vertices. Intuitively, it may be regarded as footballs that are typically patterned with white hexagons and black pentagons. It can be found in the application of geodesic dome structures such as those whose architecture Buckminster Fuller pioneered are often based on this structure. It is an example of an Archimedean solid, as well as a Goldberg polyhedron.
Piero della Francesca was an Italian painter, mathematician and geometer of the Early Renaissance, nowadays chiefly appreciated for his art. His painting is characterized by its serene humanism, its use of geometric forms and perspective. His most famous work is the cycle of frescoes The History of the True Cross in the Basilica of San Francesco in the Tuscan town of Arezzo.
Linear or point-projection perspective is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. Perspective drawing is useful for representing a three-dimensional scene in a two-dimensional medium, like paper. It is based on the optical fact that for a person an object looks N times (linearly) smaller if it has been moved N times further from the eye than the original distance was.
The Vitruvian Man is a drawing by the Italian Renaissance artist and scientist Leonardo da Vinci, dated to c. 1490. Inspired by the writings of the ancient Roman architect Vitruvius, the drawing depicts a nude man in two superimposed positions with his arms and legs apart and inscribed in both a circle and square. It was described by the art historian Carmen C. Bambach as "justly ranked among the all-time iconic images of Western civilization". Although not the only known drawing of a man inspired by the writings of Vitruvius, the work is a unique synthesis of artistic and scientific ideals and often considered an archetypal representation of the High Renaissance.
In geometry, a tetrakis hexahedron is a Catalan solid. Its dual is the truncated octahedron, an Archimedean solid.
In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for physical models of polyhedra to be constructed from material such as thin cardboard.
Sansepolcro, formerly Borgo Santo Sepolcro, is a town and comune founded in the 11th century, located in the Italian Province of Arezzo in the eastern part of the region of Tuscany.
In geometry, the compound of three cubes is a uniform polyhedron compound formed from three cubes arranged with octahedral symmetry. It has been depicted in works by Max Brückner and M.C. Escher.
Divina proportione, later also called De divina proportione is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, completed by February 9th, 1498 in Milan and first printed in 1509. Its subject was mathematical proportions and their applications to geometry, to visual art through perspective, and to architecture. The clarity of the written material and Leonardo's excellent diagrams helped the book to achieve an impact beyond mathematical circles, popularizing contemporary geometric concepts and images.
Peter Forakis was an American artist and professor. He was known as an abstract geometric sculptor.
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.
Robert Longhurst is an American sculptor who was born in Schenectady, New York, in 1949. At an early age he was fascinated by his father's small figurative woodcarvings.
De prospectiva pingendi is the earliest and only pre-1500 Renaissance treatise solely devoted to the subject of perspective. It was written by the Italian master Piero della Francesca in the mid-1470s to 1480s, and possibly by about 1474. Despite its Latin title, the opus is written in Italian.
The Portrait of Luca Pacioli is a painting attributed to the Italian Renaissance artist Jacopo de' Barbari, dating to around 1500 and housed in the Capodimonte Museum, Naples, southern Italy. The painting portrays the Renaissance mathematician Luca Pacioli and may have been painted by his collaborator Leonardo da Vinci. The person on the right has not been identified conclusively, but could be the German painter Albrecht Dürer, whom Barbari met between 1495 and 1500.
Summa de arithmetica, geometria, proportioni et proportionalita is a book on mathematics written by Luca Pacioli and first published in 1494. It contains a comprehensive summary of Renaissance mathematics, including practical arithmetic, basic algebra, basic geometry and accounting, written for use as a textbook and reference work.
Perspectiva corporum regularium is a book of perspective drawings of polyhedra by German Renaissance goldsmith Wenzel Jamnitzer, with engravings by Jost Amman, published in 1568.
De quinque corporibus regularibus is a book on the geometry of polyhedra written in the 1480s or early 1490s by Italian painter and mathematician Piero della Francesca. It is a manuscript, in the Latin language; its title means [the little book] on the five regular solids. It is one of three books known to have been written by della Francesca.
