1. the intersection between light and symmetry
by michael, billy, danny and rosie

2. Introduction to Photography
The camera is ideal for photography.
Contains a light-tight box with a small hole at one end, the lens.
Lens, often curved, refracts light to a reflective surface, which refracts image into light path

3. More on Cameras: Shutter Speed
Camera shutter regulates amount of light allowed through lens
Amount of light that passes through measured in fractions of 1 second
1/1000, 1/500, 1/250, 1/125, 1/60, 1/30, 1/15, 1/8, 1/4, ½, 1
From 1/1000 to 1, the time light passes through lens is geometrically increased by a ratio of 2
If you’re into photography, you understand geometric sequencing!

4. More on Cameras: Aperture, Focal Length, and f-Stop
Aperture: the dynamic diameter of the lens
The larger the diameter, the more light passes through to reflecting, light-tight surface
Increased diameter increases reflective area of mirror inside light-tight box
This is called light gathering power, using formula for area of circle (Area = Π x r2)
1:4 ratio between aperture and reflective area
Double the diameter, quadruple the reflective area because we use square of the radius of the lens
f-Stop is another way to control amount of light allowed into camera, which adjusts aperture in relation to shutter speed
Large part of light gathering power is determined by focal length
Focal length is the distance between the center of the lens and an internal reflective surface
Changing focal length controls size of image formed in eyepiece
The longer the focal length, the closer an image appears, allowing for lenses to zoom
Common zoom ranges for 35mm cameras is 28mm to 80mm, 70mm to 210mm, 100mm to 300mm

6. Cameras: Wrap-up
Larger aperture = more light a camera sees; slower shutter speed = camera lets in light for more time; larger focal length = larger image
Optimum exposure for a given aperture or f-Stop deciphered by dividing focal length by f-Stop or aperture, respectively; not too dark or too bright

7. M.C. Escher: Artist and Mathematician
Born 1898 in Leeuwarden, Netherlands
Died 1972

8. Escher: The Early Years
Secondary school: Linocuts, woodblock

9. Escher: The Early Years
School for Architecture & Decorative Arts (Haarlem, Netherlands)
Enters Architecture program, leaves with Graphic Arts degree
Moves to Rome -- Continues sketches and woodblock prints
Marries Jetta Umiker

10. Escher: Encounters Tessellation
Visits Alhambra (14th C. castle in Granada, Spain)
Islamic tessellated decorations
Fascinated -- incorporates into own work

11. Escher: Impossible Constructions // Legacy
Incorporate 3D & 2D
Light // Perspective
Symmetry

12. Fibonacci sequence and the Golden Ratio in Filmography
Considered a more natural frame than “Rule of Thirds”
Underlying principle that creates depth and draws focus to the subject of the shot
Fibonacci sequence is a sequence in
the next number is the sum of the two
previous numbers eg. 0,1,1,2,3,5,8,21,34
Sequence approaches ratio of
1:1.618 giving us the golden ratio

13. Depth and Proportion Lack of perfect symmetry creates depth
Ratio of 1:1.618 offsets certain features of
main subject while maintaining balance

14. There Will be Blood (2007), Directed by Paul Thomas Anderson

15. Iron Man (2008), Directed by Jon Favreau

16. Othello-Triangles, Line of Sight, and Power

17. Dead Man’s Cell Phone-Forced Perspective