By: Danielle Tebbai Jessica Dawson Amy Metger Suzi Rinker Aimee McHugh

1. Geometry in Art and Architecture By: Danielle Tebbai Jessica Dawson Amy Metger Suzi Rinker Aimee McHugh

2. Geometry in Art Geometry can be found all throughout art. In: • Fractals • tessellations • Digital & Optical art • Ethnic art forms

3. Fractals • Fractals are geometric figures, just like rectangles, circles and squares • They can be found in Art and in natural things like ferns and coastlines

4. Three Ring Circus Freidman's exploration of the dynamics of a system of three interconnected rings resulted in the visualization of a three-torus. Following a suggestion of Bill Thurston, he ray traced an object in this three-torus by allowing light rays to follow geodesics specified by the configuration space metric. This project is described in detail in the Summer Institute 1992 reports.

5. Optical Art Designs • Optical art involves the study of perception • Op artists use geometric shapes as a theme in their work • It evolved in the twentieth century

6. Digital Art Plants on a Island in Water These plants were created with L-systems, which also simulate the impact of outside forces on the plant such as gravity, wind, and sunlight.

7. Tesselation • This image, produced by postdoc John Sullivan of the Geometry Center, represents tessellation of the 3-sphere by 120 regular dodecahedra. This image is entitled “120 Soap bubbles.”

8. Islamic Art • Geometric motifs were popular with Islamic artist in decorating everything • Islamic art is a representation of their religion

9. The Mandala • The word Mandala arises from the Sanskrit and means sacred circle. The shapes that are formed from these divisions are symbols that embody the mathematical principles found throughout creation.

10. Icosahedron Roads Untaken by George W. Hart. Let your eye meander along the light roads which run between hexagons or the dark roads which run between triangles.  The form can be called the exploded propellorized truncated icosahedron.

11. The Topkapi Scroll • In this scroll there is a rich repertory of geometric drawings for wall surfaces and vaults • This important document belongs to the Islamic tradition

12. Ancient American Art and Geometry • This piece demonstrates geometry via the use of triangular shapes, of a face or a square.

13. Cultural Art As you can see, geometric art is a unique way to express one’s culture.

14. Geometry in Architecture

15. Ancient Greek Architecture • The Parthenon is known as a geometric masterpiece. • The Parthenon at the acropolis near Athens, Greece is enclosed by a golden rectangle by design. • The Parthenon is geometrically proportional.

16. PARTHENON When the triangular pediment is restored….

17. PARTHENON • The ancient temple fits almost precisely into a golden rectangle.

18. PARTHENON Subdivisions show the rectangle align perfectly with major architectural features.

19. Hindu Architecture • The Hindu’s believe that geometry is absolute, eternal, and unchanging. • Therefore, they build temples reflecting the universe.

20. Christian Architecture • Many of the Gothic churches were built by proportions derived from the geometry inherent in the cube or the double-cube. • Many churches are still built in this form today.

21. The Middle Ages • The middle Ages were excited about ratios and geometry • The great cathedrals are a symbol of the Middle Ages

22. Gothic Geometry • Since the ‘golden section’ of ideal proportion invented by the Greeks geometric shapes in architecture have imparted a feeling of order and harmony

23. Christian Architecture • The cross is used as the major emblem for the Christian Religion.

24. Christian Architecture • The windows show geometry. • Tracery is exclusively constructed from circular arcs and straight line segments.

25. Christian Architecture • The theme of the window is geometry. • Regular n-gons are shown. • Variations of the pentagon show the pentagram and rose.

26. Ancient Egyptians Here we see a mathematical view of the Great Pyramid.

27. Ancient Egyptians Architecture • The ancient Egyptians used regular polygons in their construction. • Egyptians also used the square as a symbol of kingship.

28. Ancient Indian Architecture • From this we get a glimpse of advanced knowledge of geometry that the Vedic Hindus developed

29. Geometry in the Desert • A geodesic shape is where all the vertices lie on a sphere • Common shapes are a tetrahedron and a cube

30. Pier Six Pavilion • Located in Baltimore • Has many geometric shapes • Is home to many concerts, art galleries, and lectures

31. Geometric shapes in Structures • Six basic elements in geometry have been identified in the bridge • Point, segment, ray, triangle, line, and angle

32. The Valence School - retrofit of sheds, is an example of every day use of trianglesin one’s community.

33. The Chapel at the U.S. Air Force Academy building, is another example of triangular architecture.

34. Not only do the ceiling arches of the Shelly Ridge Girl Scout Centerdemonstrate symmetry, geometry, and the structural support of triangles, but it also demonstrates tessellations in the walls of the building.

35. The front of the Berkshire building.

36. Both the visible side of Brick Street Café, as well as the upper part of Hawkins Hall demonstrate Geometry in architecture.

37. This structure, in and of itself, is a geometric figure. Not only does it demonstrate symmetry, but it’s windows and openings are almost formed of tessellations of squares.

38. This photo demonstrates symmetry in each of the sub sections, as well as the use of many different polyhedrons and other geometric figures.

39. This picture shows the usage of several different geometric shapes in one architectural construction.

40. THE END