Группа авторов "Mathematics in the Visual Arts"

Mathematics in the Visual Arts

Table of Contents

1В  Cover (#u1b2f0521-494a-5ce4-ad49-990a0a172aac)

2В  Title page (#uf94844f3-683b-5460-81da-bd35761cb20e)

3В  Copyright (#u3bfad633-02a6-55b1-b640-2f67f7639b33)

4В  Introduction (#u1b3e6bb3-2aee-554e-86b7-f75bd874f567)

5В  1 Infinity of God and Space of Men in Painting, Conditions of Possibility for the Scientific Revolution (#ub37ca06d-d072-5f43-a94f-848bb7e0cd5c) 1.1. A brief introduction to infinity 1.2. Infinity in painting and the invention of mathematical space (#ulink_b9b12b34-23b1-54ff-8497-8647cc3679a9)1.3. Geometrical optics and the subject in projective space (#ulink_1bbeb1cd-7bff-505e-98f7-13880becc538)1.4. The limit of time, calculus and algebra (#ulink_9034773d-b025-5c9d-ac62-ee2b4b444b0e)1.5. Rational spaces: from trade to physics (#ulink_71fc561f-a8c8-5369-865d-fa336ddc6d88)1.6. Setting a priori conditions of representation and knowledge (#ulink_d66542e5-8d0f-5989-b08c-c4be8b9ab2ad)1.7. Spaces of possibilities for the evolution of life? (#ulink_c73e18d9-97e5-552b-a77d-667cc5c30e32)1.8. Conclusion and opening: heterogeneous spaces of biological evolution (#ulink_82a7d785-b408-5fc3-9ca1-6a47912e5ac6)

6В  2 Geometry and the Life of Forms (#ue91fe8bf-e43d-528e-8118-7c7cd8a32950) 2.1. Introduction 2.2. Taking form (#ulink_fe8185eb-1a42-5805-8848-5d5caf91f63f)2.3. Art and geometry (#ulink_1c008b37-8444-51f1-82ee-5fb965ac15a7)2.4. Beyond geometry (#ulink_657c11f3-33b7-54c3-bf7d-6512fe64cfe2)

7В  3 Among the Trees: Iterating Geneses of Forms, in Art and Nature (#u53f8d50a-e89c-5978-8c00-106deb96f0f2)

8  4 The Passion of Flight: From Leonardo da Vinci to Jean Letourneur (#u0d4ec921-c2bd-59aa-bee5-70c61cfc2c59) 4.1. Introduction: from legend to reality 4.2. Leonardo da Vinci and the basis of the theory of flight (#ulink_9267c602-cd33-59de-bc82-6f57470a9975)4.3. Pioneers of the air and the first fluid movement visualizations (#ulink_35ab321e-8408-50a5-8b9c-fe0e638d0382)4.4. From Henri Werlé to Jean Letourneur, the sculptor of fluid movement (#ulink_053b1818-6962-59ac-88d8-9e0ab317e1b5)4.5. Conclusion (#ulink_c1e111ea-7c21-5992-a214-4055a92aca03)4.6. Appendix: additions to the chapter entitled “Why Can’t Man Fly?”, which refers to the article by Marielle Vergès and Kamil Fadel (see footnote 15) (#ulink_b47185d4-97ea-5f63-8cce-e7a6e2c2d6f5)

9В  5 Sculptor of Fluid Movement (#ud0be7fbc-3f0c-5b46-a415-a038538e1418)5.1. References (#ulink_1b4f1448-c27f-5754-afcd-4e93bd283b47)

10  6 Internal Geometry of “Salvator Mundi” (The “Cook Version”, Attributed to Leonardo da Vinci) (#u9e1bab48-7f77-58e7-a573-4ae76c3f0f58) 6.1. Introduction 6.2. Distinctive features of the works of Leonardo da Vinci (#ulink_09fbf688-27cd-5178-898d-767cf33a4424)6.3. Presentation of the Salvator Mundi, Cook version (#ulink_d5f6869f-78f4-5cfc-a4a7-ab437947fe1d)6.4. Investigating the compositional mesh (#ulink_7255c9e8-01b2-5a76-ab09-422604c7d313)6.5. Compositional format (#ulink_ae8fdae6-16f9-5129-b2b4-6d0e764792e7)6.6. Elements of the internal geometry of the Salvator Mundi, Cook version (#ulink_83bc1f7e-c541-57ad-8ed4-c7998bb0515c)6.7. A detailed look at the ellipses of the head of the Salvator Mundi (#ulink_743f3c9b-30ec-506c-a6d4-e22d6582dfc8)6.8. Visual consonance (#ulink_b853ef5f-2009-507e-9c8b-b32b0aba242c)6.9. Properties of the type 1 ellipse (#ulink_caeaf357-1799-51b8-96c7-d73f8cfe6094)6.10. Other applications of the type 1 ellipse (#ulink_0773aa79-66fc-5767-9e17-2e6638983c5e)6.11. The decoration of two intersecting bands of the stole (#ulink_db02a3d0-f0c7-5e28-83ee-9058d77aed39)6.12. The internal geometry of the Salvator Mundi (Ganay version) (#ulink_48f0a0d5-24b4-5eac-afce-096c48e1fed6)6.13. Conclusion (#ulink_113a89de-be81-5eba-959c-5d99253cc2f9)6.14. References (#ulink_5da1d409-5b1e-5724-bc9a-2e637c34c050)

11  7 Internal Geometry of a Night Scene by Georges de La Tour: “The Apparition of the Angel to St. Joseph” (#u016d90bb-5b10-550c-8c5b-21e0ccf65e33) 7.1. Introduction 7.2. Methodology (#ulink_ccd1892f-c7b3-511e-af92-1d0641d6c0ee)7.3. Distinctive features of the work of Georges de La Tour (#ulink_03944f51-62c5-5934-b1a7-f2dd814daea0)7.4. Internal geometry of The Appearance of the Angel to St. Joseph (#ulink_fc7055bf-86de-5421-92ae-56bec0baf323)7.5. The search for the compositional mesh (#ulink_0340b0fe-171d-594d-a504-05a81b5b9626)7.6. Compositional format (#ulink_3d759865-1130-5291-8ea0-2ad2eca53b92)7.7. The compositional architecture (#ulink_0db8f400-35be-55aa-9389-19fdf492fff3)7.8. The ellipse of light (#ulink_d0aa1a03-6e74-5bf0-8c9d-c8af52e6447a)7.9. Curved or elliptical forms (#ulink_0fcbe99b-6cba-5906-853e-3011805c5097)7.10. Internal geometry of the two protagonists’ heads (#ulink_18204653-ed20-5055-9b1e-f48316bed124)7.11. Discussion (#ulink_0314893f-f7dc-5439-9798-71fe4c9b81c7)7.12. Compositional construction (#ulink_68ff3817-3a21-5c44-96cf-c13892b21b33)7.13. Conclusion (#ulink_1f8a680f-eee5-59fe-a8aa-743a4413242f)7.14. References (#ulink_15031791-1426-5846-8307-a92dc9eeeabe)

12В  8 Emergilience, an Art Research Project (#ue9fa5f47-6315-5d6d-ae58-f39f0585a78b) 8.1. Background of the project Emergilience8.2. Description of the Emergilience project (#ulink_c031d1e4-9e28-5fae-b906-4c3257bdd57c)8.3. Let us finish with a conclusion that looks to the future (#ulink_ab0ed37b-3129-5a15-98d8-cc1aceda8335)8.4. References (#ulink_00a63773-83ad-5f3e-a6d7-2925127ea6e5)

13В  List of Authors (#ua76bcd55-3bb2-5df8-a702-eef24abe7928)

14В  Index (#uaa52e1d3-c3f8-5459-b1bc-54297237301f)

15В  End User License Agreement (#u80aa4f30-c97d-5917-8628-c5fe974adfb5)

List of Illustrations

1 Chapter 1Figure 1.1. Giotto di Bondone, Life of St. Francis, fresco, around 1290. Assisi,...Figure 1.2. Ambrogio Lorenzetti, Annunciation, tempera on wood, Siena, Pinacotec...Figure 1.3. Antonello da Messina, St. Sebastian, tempera on wood transposed onto...Figure 1.4. Brunelleschi’s experiment with linear perspective, looking through t...Figure 1.5. Andrea Mantegna, Study for the Dead Christ, pen and brown wash on pa...Figure 1.6. Paolo Uccello, Battle of San Romano, detail, 1456, tempera on wood. ...Figure 1.7. Andrea Mantegna, The Dead Christ, tempera on canvas, Milan, Pinacote...Figure 1.8. Piero della Francesca, Polyptych of Perugia, 1470, Perugia, National...Figure 1.9. Polyptych of Perugia, upper register (see Figure 1.8)Figure 1.10. De Martone, art. cit.Figure 1.11. Paolo Uccello, Battle of San Romano, 1456, tempera on wood. London,...

2В Chapter 2Figure 2.1. Reuven Berman Kadim, Hovering Object #1. Digital image, 1997

Figure 2.2. Reuven Berman Kadim, Paving B, Digital Image, 1996

Figure 2.3. Emmanuel Van der Meulen, Quadrum, 2017, acrylic on canvas, 130 Г— 130...Figure 2.4. Emmanuel Van der Meulen, Bethel, 2017, acrylic on canvas, 130 Г— 130 ...Figure 2.5. Esther Stocker, Untitled, 2010, acrylic on canvas, 200 Г— 300 cm. Cou...Figure 2.6. Esther Stocker, Unlimited Space, 2013, Roudnice, Czech Republic. Cou...

3 Chapter 3Figure 3.1. Examples of Luca Caciagli’s Komorebi project, showing fractals in na...Figure 3.2. Examples of simple mathematical fractals, from left to right: the Ko...Figure 3.3. Examples of Luca Caciagli’s Komorebi project, showing contradictions...Figure 3.4. René Magritte, Le blanc-seing (The Blank Signature in English), oil ...Figure 3.5. Simon Hantaï, Étude, oil on canvas, 275 × 238 cm, 1969. National Gal...Figure 3.6. An example of where fractals can be found in the stock market

4 Chapter 4Figure 4.1. Drawing by Leonardo da Vinci. Courtesy of the Library of the Institu...Figure 4.2. Remanta microdrone. Courtesy of ONERAFigure 4.3. Drawing by Leonardo da Vinci of bat wings and Clément Ader's Eole in...Figure 4.4. Marey’s Smoke wind tunnelFigure 4.5. Visualizations created by Marey.Courtesy of Cinémathèque françaiseFigure 4.6. ONERA’s water tunnel at Châtillon (Hauts-de-Seine)Figure 4.7. Visualizations of vortex windings on Concorde. Courtesy of ONERAFigure 4.8. Visualization from the water tunnel of a Citroën DS. Courtesy of ONE...Figure 4.9. The Mirror 1994. Marble, 100 × 49 × 49 cm visualization of an ellips...Figure 4.10. Interférences de chocs, 2005, Stuc, 61 × 7 cm, International Year o...Figure 4.11. Schlieren visualizations carried out at ONERA’s R3Ch wind tunnel in...

5 Chapter 5Figure 5.1. Ink, around 1510/1513, Windsor, 15 × 17 cmFigure 5.2. Leda, black stone and ink, around 1505/1510, Windsor, 20 × 16.2 cmFigure 5.3. Ink, around 1515, Venice, Accademia Gallery, 9.6 × 14.9 cmFigure 5.4. Ink and bistre wash, around 1514, Windsor, 15.7 × 20.3 cmFigure 5.5. Katabase, stone-effect polychrome plaster, 300 × 75 × 78 cm, 1991Figure 5.6. Marches au hasard, plaster, 10,300 × 150 × 10 cm, 2012Figure 5.7. Citadelle, plaster, 89 × 57 × 37 cm, 2010Figure 5.8. Bifurcations (detail) – bronze, 75 × 34.5 × 30 cm, 1995Figure 5.9. Mosaic, pool in the Place de l’Église, Fontenay-aux-Roses (destroyed...Figure 5.10. Discobolus – bronze, 70 × 50 × 50 cm, 1983–2005Figure 5.11a. Air – bronze, 40 × 20 × 2.5 cm, 1992Figure 5.11b. Water – bronze, 40 × 20 × 2.5 cm, 1992Figure 5.12. Fontaine Werlé – plaster and wood, 240 × 120 × 120 cm, 1994Figure 5.13a. Nuages – charcoal, 150 × 150 cm, 2011Figure 5.13b. Nébuleuse – charcoal, 150 × 150 cm, 2011Figure 5.14. Table basse – marble, 130 × 80 × 40 cm, 2001Figure 5.15. Bistre ink, – around 1508/1509, Paris Institute, 14.6 × 10.6 cmFigure 5.16. Saint-Exupéry Medal – recto/verso, diameter 8.4 cm – Monnaie de Par...Figure 5.17. The Saint-Exupéry Stele – bronze, 202 × 75 × 75 cm, 2000

6В Chapter 6Figure 6.1. Leonardo da Vinci: Salvator Mundi

(so-called Cook version) (Louvre...Figure 6.2. Study for the Salvator MundiFigure 6.3. The outline of the skull has the form of an elliptical arc (Royal Co...Figure 6.4. The semi-axes (a and b) of the ellipse form a harmonic rectangleFigure 6.5. The subdivision (3 x 3) of this rectangle determines a vertical harm...Figure 6.6. Vertical harmonic mesh (16 x 16) used as the compositional mediumFigure 6.7. Vertical harmonic mesh (16 x 16) used as the compositional mediumFigure 6.8. Internal geometry of the Salvator Mundi, Cook versionFigure 6.9. Internal geometry of the head of ChristFigure 6.10. Internal geometry of the head of the Mona LisaFigure 6.11. Properties of the type 1 ellipse modeling the head of the Salvator....Figure 6.12. Lady with an Ermine (detail) a band of interlacing runs down the ri...Figure 6.13. Study of interlacing (Leonardo da Vinci)Figure 6.14. The stole’s two bands and the patterns formed by the filigree, mode...Figure 6.15. Representation of the path taken by the filigree on the stole’s int...Figure 6.16. The various modules of the filigree’s journey. The first three are ...Figure 6.17. The internal geometry of the Salvator Mundi, Cook Version and of th...Figure 6.18. Details of the interlacing on the intersecting bands on the Salvato...

7 Chapter 7Figure 7.1. Georges de La Tour: The Apparition of the Angel to St. Joseph, oil o...Figure 7.2. Modeling the heads of the angel and JosephFigure 7.3. Determining the mesh size and the composition’s original formatFigure 7.4. Position of the protagonists’ headsFigure 7.5. Compositional architectureFigure 7.6. The ellipse of lightFigure 7.7. The elliptical formsFigure 7.8. Internal geometry of the heads of the angel and JosephFigure 7.9. Compositional construction

8 Chapter 8Figure 8.1. Tableau scénique no. 1 by Sophie Lavaud – modeling of elements of th...Figure 8.2. Tableau scénique 2.0 by Sophie Lavaud – modeling of elements of the ...Figure 8.3. Tableau scénique 2.0 by Sophie Lavaud – a viewer interacting with th...Figure 8.4. GAMA software (version 1.6.1) interface – simulation view – screensh...Figure 8.5. Agents initially placed randomly (t = 0) create a circular form over...Figure 8.6. Emergence of a spiral within a group of 64 agents. Three snapshots t...Figure 8.7. Emergence of the flashing effect in three states. Snapshots of the t...Figure 8.8a. Aerial view of tiger bush in AfricaFigure 8.8b. Emergence of irregular bands, in a group of 2,500 oriented agents, ...Figure 8.9. Representation of the predator–prey model in GAMA. Left: the initial...Figure 8.10a. Representation of the predator–prey model in GAMA. Emergence of pa...Figure 8.10b. Same representation of the predator–prey model as in Figure 8.10a,...Figure 8.11. Representation of the predator–prey model in a color space with a g...Figure 8.12. Illustration of the predator–prey model in a colors space with a gr...Figure 8.13. Representation of the predator–prey model with five agents in secti...Figure 8.14. Representation of the predator–prey model with five agents by overl...

Guide

1В  Cover (#u1b2f0521-494a-5ce4-ad49-990a0a172aac)

2В Table of Contents

3В  Title page (#uf94844f3-683b-5460-81da-bd35761cb20e)

4В  Copyright (#u3bfad633-02a6-55b1-b640-2f67f7639b33)

5В  Introduction (#u1b3e6bb3-2aee-554e-86b7-f75bd874f567)

6В  Begin Reading (#u1b3e6bb3-2aee-554e-86b7-f75bd874f567)

7В  List of Authors (#ua76bcd55-3bb2-5df8-a702-eef24abe7928)

8В  Index (#uaa52e1d3-c3f8-5459-b1bc-54297237301f)

9В  End User License Agreement (#u80aa4f30-c97d-5917-8628-c5fe974adfb5)

Pages

1В  v (#ulink_1af9db09-ac54-55bf-a58d-ed86d1307421)

2В  iii (#ulink_a1736d01-9d24-56df-8507-b8880ee91e48)

3В  iv (#ulink_3339e19c-4b22-5b26-98db-cbaff0cdc46c)

4В  ix (#ulink_cb8dd688-a98d-5354-a5bf-9a7a68982c62)

5В  x (#ulink_ceee21ec-2e3c-599e-a558-f40eaa86e7a5)

6В  xi (#ulink_f175a1ca-8c8f-52d3-a833-4e3a0dc19ab4)

7В  xii (#ulink_aa910ae3-bd82-535b-a6cd-1d89e8ea6348)

8В  1 (#ulink_33c04fe1-c372-5090-b981-0ee46dd0d56c)

9В  2 (#ulink_96b446f6-d26d-5eb7-b36c-a13bada4f571)

10В  3 (#ulink_78a67535-a662-53df-af03-ec90008ab89a)

11В  4 (#ulink_4dd03a25-8474-55ed-90bc-12ae45fd282f)

12В  5 (#ulink_bf7078d9-34cc-5445-9ba0-c1758bfe2bb7)

13В  6 (#ulink_8eb8c79e-1a52-52b5-bad0-11de93c3940b)

14В  7 (#ulink_dd4bfa1e-a181-5675-ae14-e61e90d4405f)

15В  8 (#ulink_9caf4bca-bfe6-5bb9-b337-b7a0e9a02e05)

16В  9 (#ulink_fa5d6b8c-e062-519f-9a85-c5a71254a360)

17В  10 (#ulink_e8e77a92-1373-5b2a-aab1-7769125158be)

18В  11 (#ulink_19b73c8d-29a4-5898-9ce5-9f24beb35dff)

19В  12 (#ulink_b2aa2ed2-6c63-5d9c-b5d9-52a5cb87ae01)

20В  13 (#ulink_ad41e379-f5bd-5d38-9e08-aad8058720e4)

21В  14 (#ulink_2fe428ce-e233-5d3e-ba3b-f232b498dd8c)

22В  15 (#ulink_18aa6d75-00ff-57d7-bdcc-bbdbed990b8a)

23В  16 (#ulink_99662028-d225-5036-9b2c-57f2535782d2)

24В  17 (#ulink_209a263f-6ee4-5d8d-8d6a-c5b707f8be91)

25В  18 (#ulink_e8a95b69-e4b3-548e-8e82-d5e9de759b19)

26В  19 (#ulink_1de5b4a6-0c92-5127-8918-03c6cf902c14)

27В  20 (#ulink_7d37b534-9a01-5411-8b49-a61e2cf60b04)

28В  21 (#ulink_f5209211-6af0-5e83-bc8e-bffe4e507540)

29В  22 (#ulink_aa8d2921-82d3-50b0-b799-5826b4904458)

30В  23 (#ulink_76b84dc6-5320-573e-97c9-da8d1f22395c)

31В  24 (#ulink_cd159d3f-55d0-5736-acce-b9d18cd315c3)