Mathematics and art

mathematical artmathematics in artmathematics of art
Leonardo da Vinci (1452–1519) illustrated the text with woodcuts of regular solids while he studied under Pacioli in the 1490s. Leonardo's drawings are probably the first illustrations of skeletonic solids. These, such as the rhombicuboctahedron, were among the first to be drawn to demonstrate perspective by being overlaid on top of each other. The work discusses perspective in the works of Piero della Francesca, Melozzo da Forlì, and Marco Palmezzano. Da Vinci studied Pacioli's Summa, from which he copied tables of proportions. In Mona Lisa and The Last Supper, Da Vinci's work incorporated linear perspective with a vanishing point to provide apparent depth.

Piero della Francesca

della Francescadella Francesca, PieroFrescoes
Piero's work on solid geometry was translated in Pacioli's Divina proportione, a work illustrated by Leonardo da Vinci. Biographers of his patron Federico da Montefeltro of Urbino record that he was encouraged to pursue the interest in perspective which was shared by the Duke. In the late 1450s, Piero copied and illustrated the following works of Archimedes: On the Sphere and Cylinder, Measurement of a Circle, On Conoids and Spheroids, On Spirals, On the Equilibrium of Planes, The Quadrature of the Parabola, and The Sand Reckoner.

Florence Baptistery

Florence BaptistryBaptisteryBattistero di San Giovanni
Leonardo da Vinci is said to have given him technical advice; the pose of John the Baptist resembles that of Leonardo's depiction of the prophet. Ghiberti was now widely recognized as a celebrity and the top artist in this field. He was showered with commissions, even from the pope. In 1425 he got a second commission, this time for the east doors of the baptistery, on which he and his workshop (including Michelozzo and Benozzo Gozzoli) toiled for 27 years, excelling themselves. These had ten panels depicting scenes from the Old Testament, and were in turn installed on the east side.


FlorentineFlorence, ItalyFirenze
Medieval art was abstract, formulaic, and largely produced by monks whereas Renaissance art was rational, mathematical, individualistic, consisted of linear perspective and shading (Chiaroscuro) and produced by specialists (Leonardo da Vinci, Donatello, Michelangelo, and Raphael). Religion was important, but with this new age came the humanization of religious figures in art, such as Expulsion from the Garden of Eden, Ecce Homo (Bosch, 1470s), and Madonna Della Seggiola; People of this age began to understand themselves as human beings, which reflected in art.

Italian Renaissance

Renaissance ItalyRenaissanceFlorentine Renaissance
Italian Renaissance art exercised a dominant influence on subsequent European painting and sculpture for centuries afterwards, with artists such as Leonardo da Vinci, Michelangelo, Raphael, Donatello, Giotto di Bondone, Masaccio, Fra Angelico, Piero della Francesca, Domenico Ghirlandaio, Perugino, Botticelli, and Titian. The same is true for architecture, as practiced by Brunelleschi, Leon Battista Alberti, Andrea Palladio, and Bramante. Their works include, to name only a few, the Florence Cathedral, St. Peter's Basilica in Rome, and the Tempio Malatestiano in Rimini, as well as several private residences.


the RenaissanceEarly RenaissanceEuropean Renaissance
One of the distinguishing features of Renaissance art was its development of highly realistic linear perspective. Giotto di Bondone (1267–1337) is credited with first treating a painting as a window into space, but it was not until the demonstrations of architect Filippo Brunelleschi (1377–1446) and the subsequent writings of Leon Battista Alberti (1404–1472) that perspective was formalized as an artistic technique. The development of perspective was part of a wider trend towards realism in the arts. Painters developed other techniques, studying light, shadow, and, famously in the case of Leonardo da Vinci, human anatomy.

Filippo Brunelleschi

The results were drawings with accurate perspective. The original panels were lost. To compare the accuracy of his image with the real object, he placed his drawing next to a mirror reflecting the building. The observer saw the striking similarity between the drawing and the mirror image. Both panels have since been lost. Brunelleschi's studies on perspective were amplified by further studies of the topic by Leon Battista Alberti, Piero della Francesca and Leonardo Da Vinci. Following the rules of perspective studied by Brunelleschi and the others, artists could paint imaginary landscapes and scenes with perfectly accurate three-dimensional perspective and realism.

Albrecht Dürer

DürerDurerAlbrecht Durer
He was also familiar with the 'abbreviated construction' as described by Alberti and the geometrical construction of shadows, a technique of Leonardo da Vinci. Although Dürer made no innovations in these areas, he is notable as the first Northern European to treat matters of visual representation in a scientific way, and with understanding of Euclidean principles. In addition to these geometrical constructions, Dürer discusses in this last book of Underweysung der Messung an assortment of mechanisms for drawing in perspective from models and provides woodcut illustrations of these methods that are often reproduced in discussions of perspective.

De pictura

Della pittura
Alberti was the first post-classical writer to produce a work of art theory, as opposed to works about the function of religious art or art techniques, and reflected the developing Italian Renaissance art of his day. Artist, architect, poet and philosopher, Leon Battista Alberti revolutionized the history of art with his theories of perspective in On Painting (1435).

Giorgio Vasari

VasariVasari, GiorgioVasari, G
He was the first to use the term "Renaissance" (rinascita) in print, though an awareness of the ongoing "rebirth" in the arts had been in the air since the time of Alberti, and he was responsible for our use of the term Gothic Art, though he only used the word Goth which he associated with the "barbaric" German style. The Lives also included a novel treatise on the technical methods employed in the arts. The book was partly rewritten and enlarged in 1568, with the addition of woodcut portraits of artists (some conjectural).

Lorenzo Ghiberti

Rustici may have been aided in his design by Leonardo da Vinci, who assisted him in the choice of his tools. After the completion of these doors, Ghiberti was widely recognized as a celebrity and the top artist in this field. He was given many commissions, including some from the pope. In 1425 he got a second commission for the Florence Baptistery, this time for the east doors, on which he and his workshop (including Michelozzo and Benozzo Gozzoli) toiled for 27 years, excelling themselves. The subjects of the designs for the doors were chosen by Leonardo Bruni d'Arezzo, then chancellor of the Republic of Florence.

Andrea Mantegna

MantegnaA. MantegnaMantegna, Andrea
Leonardo da Vinci took from Mantegna the use of decorations with festoons and fruit. Mantegna's main legacy in considered the introduction of spatial illusionism, both in frescoes and in sacra conversazione paintings: his tradition of ceiling decoration was followed for almost three centuries. Starting from the faint cupola of the Camera degli Sposi, Correggio built on the research of his master and collaborator into perspective constructions, producing eventually a masterwork like the dome of Cathedral of Parma. Mantegna's only known sculpture is a "Sant'Eufemia" in the Cathedral of Irsina, Basilicata. * Berger, John and Katya, Lying Down to Sleep. Corraini Edizioni. 2010.

Paolo dal Pozzo Toscanelli

Paolo ToscanelliToscanelliPaul Toscanelli
He knew the mathematician, writer and architect Leon Battista Alberti, and his closest friend was Cardinal Nicholas of Cusa—himself a wide-ranging intellect and early humanist, who dedicated two short mathematical works in 1445 to Toscanelli, and made himself and Toscanelli the interlocutors in a 1458 dialogue titled On Squaring the Circle (De quadratura circuli). Toscanelli along with Nicholas of Cusa appears to have belonged to a network of Florentine and Roman intellectuals who searched for and studied Greek mathematical works, along with Filelfo, George of Trebizond, and the humanist Pope Nicholas V, in company with Alberti and Brunelleschi.

Science and inventions of Leonardo da Vinci

conceptda Vinci BridgeDa Vinci Helicopter
Da Vinci – The Genius: A comprehensive traveling exhibition about Leonardo da Vinci. The technical drawings of Leonardo da Vinci – a high resolution gallery. Leonardo da Vinci: anatomical drawings from the Royal Library, Windsor Castle, exhibition catalog fully online as PDF from The Metropolitan Museum of Art. Leonardo da Vinci, Master Draftsman, exhibition catalog fully online as PDF from The Metropolitan Museum of Art.


Italian Renaissance exercised a dominant influence on subsequent European painting and sculpture for centuries afterwards, with artists such as Leonardo da Vinci, Brunelleschi, Botticelli, Michelangelo, Raphael, Giotto, Donatello, and Titian, and architects such as Filippo Brunelleschi, Leon Battista Alberti, Andrea Palladio, and Donato Bramante. Following the conclusion of the western schism in favor of Rome at the Council of Constance (1415–1417), the new Pope Martin V returned to the Papal States after a three years-long journey that touched many Italian cities and restored Italy as the sole centre of Western Christianity.

Renaissance art

RenaissanceRenaissance paintingEarly Renaissance painting
The publication of two treatises by Leone Battista Alberti, De pictura (On Painting), 1435, and De re aedificatoria (Ten Books on Architecture), 1452. The use of proportion – The first major treatment of the painting as a window into space appeared in the work of Giotto di Bondone, at the beginning of the 14th century. True linear perspective was formalized later, by Filippo Brunelleschi and Leon Battista Alberti. In addition to giving a more realistic presentation of art, it moved Renaissance painters into composing more paintings. Foreshortening – The term foreshortening refers to the artistic effect of shortening lines in a drawing so as to create an illusion of depth.

M. C. Escher

M.C. EscherEscherMaurits Cornelis Escher
Escher's interest in curvilinear perspective was encouraged by his friend and "kindred spirit", the art historian and artist Albert Flocon, in another example of constructive mutual influence. Flocon identified Escher as a "thinking artist" alongside Piero della Francesca, Leonardo da Vinci, Albrecht Dürer, Wenzel Jamnitzer, Abraham Bosse, Girard Desargues, and Père Nicon. Flocon was delighted by Escher's Grafiek en tekeningen ("Graphics in Drawing"), which he read in 1959. This stimulated Flocon and André Barre to correspond with Escher and to write the book La Perspective curviligne ("Curvilinear perspective").

Italian Renaissance painting

Italian RenaissanceItalian Renaissance artItalian primitives
Masaccio's work became a source of inspiration to many later painters, including Leonardo da Vinci and Michelangelo. During the first half of the 15th century, the achieving of the effect of realistic space in a painting by the employment of linear perspective was a major preoccupation of many painters, as well as the architects Brunelleschi and Alberti who both theorised about the subject. Brunelleschi is known to have done a number of careful studies of the piazza and octagonal baptistery outside Florence Cathedral and it is thought he aided Masaccio in the creation of his famous trompe l'oeil niche around the Holy Trinity he painted at Santa Maria Novella.

Ibn al-Haytham

This translation was read by and greatly influenced a number of scholars in Christian Europe including: Roger Bacon, Robert Grosseteste, Witelo, Giambattista della Porta, Leonardo Da Vinci, Galileo Galilei, Christiaan Huygens, René Descartes, and Johannes Kepler. His research in catoptrics (the study of optical systems using mirrors) centred on spherical and parabolic mirrors and spherical aberration. He made the observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens. His work on catoptrics also contains the problem known as "Alhazen's problem".

Fra Angelico

Beato AngelicoAngelicoBlessed Fra Angelico
Rinascita delle arti e Umanesimo cristiano nell'Urbe di Niccolò V e Leon Battista Alberti, Firenze, Olschki, 2017 (Fondazione Carlo Marchi, Studi, vol. 34). Cyril Gerbron, Fra Angelico. Liturgie et mémoire (= Études Renaissantes, 18), Turnhout: Brepols Publishers, 2016. ISBN: 978-2-503-56769-3. Gerardo de Simone, La bottega di un frate pittore: il Beato Angelico tra Fiesole, FIrenze e Roma, in " Revista Diálogos Mediterrânicos" (Curitiba, Brasil), n. 8, 2015, ISSN 2237-6585, pp. 48-85 – Gerardo de Simone, Fra Angelico : perspectives de recherche, passées et futures, in "Perspective, la revue de l'INHA.

Perspective projection distortion

distortion of perspectiveperspective distortion
One of the first uses of perspective was in Giotto's Jesus Before the Caïf, more than 100 years before Filippo Brunelleschi’s perspectival demonstrations galvanized the proper widespread use of convergent perspective of the Renaissance. "Artificial perspective projection" was the name given by Leonardo da Vinci to what today is called "classical perspective projection" and, as noted above, is the result of a geometric protocol. 'Artificial perspective projection' is used here rather than 'classical perspective projection' in order to recognize Leonardo's priority in developing the concept.


ManneristMannerist styleLate Renaissance
It drove artists to look for new approaches and dramatically illuminated scenes, elaborate clothes and compositions, elongated proportions, highly stylized poses, and a lack of clear perspective. Leonardo da Vinci and Michelangelo were each given a commission by Gonfaloniere Piero Soderini to decorate a wall in the Hall of Five Hundred in Florence. These two artists were set to paint side by side and compete against each other, fueling the incentive to be as innovative as possible.

Donato Bramante

Leon Battista Alberti. Giorgio Vasari. Donato Bramante Source Information, Pictures & Documentaries about Donato.

List of Italian inventions and discoveries

List of Italian inventions
Perspective: linear perspective was invented by the Renaissance architect Filippo Brunelleschi, whose system depicts how objects shrink in size according to their distance from the eye. Perspective was later reported in "Della pittura" (1435) by Leon Battista Alberti. Piano, an acoustic, stringed musical instrument played using a keyboard, with hammers striking the strings, invented by Bartolomeo Cristofori in 1709. Pistol: first handheld guns were probably created in the city of Pistoia around 1540. Anyway, the etymology of the word is still debated. Pizzeria: established in 1738 as a stand for peddlers, Antica Pizzeria Port'Alba was opened in 1830 in Naples. Polypropylene:.

Culture of Italy

Italian cultureItalianculture
To him we also owe a scientific discovery of the first importance in the history of art: the rules of perspective. In painting, Leonardo da Vinci and other Italian painters used a technique called sfumato that created softness in their portraits. At the same time, Italy witnessed the revival of the fresco. In music, both the small-scale madrigal and the large-scale opera were inventions of the period with a long future. Italian cities invented the modern conservatory to train professional musicians, as they invented the art academy as a place to master the techniques and the theory of painting, sculpture, and architecture.