1

Geometrics

Train station, Ireland

Richard Zakia

			Rule of Thirds
			Centering
			Off Center
			Lead Line
			S-Curve
			C-Shape Curve
			Reverse C-Shape
			L-shape
			V-Shape
			Triangles
			Horizon Line
			Diagonals
			Symmetry
			Repetition
			Exercises

Rule of Thirds: Imagine the photograph you are about to take as having superimposed upon it four imaginary lines spaced equally apart. Two are horizontal and two are vertical. If you are photographing only one subject and place it at any one of the four intersecting lines, you will, in most cases, have a balanced photograph. If the subjects are sitting or are small children standing, the lower intersecting points could be used. When considering where to place a horizon line, the top or bottom horizon line would work well, depending upon the subject matter. The rule of thirds is a popular and practical compositional consideration device. Rules such as this were in use by painters in the nineteenth century.

Blue Angels

Vicki H. Wilson

The Navy planes performing their air show in Louisville, Kentucky, presented an interesting compositional challenge. Normally, one would want to have more distance in front of the planes than behind. Here, it was decided to include the smoke trails to suggest speed. The puffs of clouds just below the planes provide interest and balance. All of these quick visual decisions were made as the Blue Angles zipped by at over 200 mph. The dark blue color of the airplanes with a yellow trim helps them stand out against the lighter blue sky. The diagonal formation of the planes provides a dynamic arrangement that plays well against the horizontal smoke trails. Their first exhibition flight was in June 1946 at their home base, Naval Air Station, in Jacksonville, Florida.

Composite Photo-Illustration

David A. Page

Many of today’s digital cameras come with a rule of thirds pattern that displays on the viewing screen on the back of the camera. This can be helpful in framing your photographs. Here, the capture of the subject is well placed in a position at the upper-left intersection of the grid. It could have also been placed at the upper-right intersection, but this would not have given room for the boat to move speedily within the frame of the photograph. Consider how the speeding boat might have looked at the lower intersecting points. A fast shutter speed and panning the camera with the boat was necessary to avoid blur and capture a sharp image.

Lydia

Richard D. Zakia

A typical teenager with a cell phone is crouched in a soft, comfortable chair and is unaware that she is being photographed. Her head is nicely positioned so that it falls in the upper-left intersection of the rule of thirds. The color of her green blouse is given emphasis by the dark reddish chair in which she sits. The diamond-shaped patterns in the chair work well against the plain grayish background of the wall. Had there been a plant or some other object in the background, it might have drawn attention away from the main subject.

Target Area

Think of the intersecting points of the rule of thirds grid, not as a point but rather as a target area. Although Lauren and Molly are not positioned at the exact grid intersection, they are on target, providing a well-balanced photograph. Being overly concerned with placing your subjects at the exact intersection or vertical lines can impede your photographic efforts and take the fun out of photography. Insisting on a perfect positioning could cause the girls to get anxious and a bit frustrated, which could destroy some of the spontaneity of the pose.

Lauren and Molly

Susanne Conway

The twin sisters sit quietly and attentively for this Halloween photograph taken by their mother. The two girls are at ease and seem to enjoy having their picture taken. They each chose their own costume, which reflects two distinct personalities.

Liam and Lydia

Richard D. Zakia

This scene is a typical one: a food court in a mall and two teenagers at lunch, playfully using their cell phones to chat. Their two faces follow the rule of thirds in the horizontal direction but not in the vertical direction. The distance between them seems to be one with which they are both comfortable. Had they been asked to move so that their heads would fall along the vertical intersection of the grid, the photograph would be less intimate and the spontaneity of the moment lost. From the looks on their faces, they are not just posing but are actually carrying on a conversation. The photo can be read as a parody of our over-dependence on cell phones.

Hawaiian Light House

Vicki H. Wilson

Centering: Sometimes centering an object, such as this lighthouse, is the right thing to do. Its strongly centered vertical lines are counterbalanced by horizontal lines of grass and sea and a beautiful blue sky.

Penguins

Rick Sammon

Centering a photograph can be quite acceptable, depending upon the subject matter. If the penguins were a bit off to the right or to the left, the photo would appear unbalanced.

Peacock

Fatima NeJame

Off Center: The blue-feathered body of the peacock is not centered and is off to one side, close to the left vertical line of the rule of thirds. This is more interesting than having the bird placed dead center. Fan-like feathers of the bird completely fill the frame, providing an uninterrupted colorful background. The iridescent blue and green colors are a result of optical interference similar to what we see in an oil slick on water. It is the male peacock that displays such brilliantly colored tail feathers. The female has a mixture of dull green, brown, and gray. The yellow feathers that surround his blue body provide a strong color contrast.

Denali

Bill Stanko

Lead Line: The serpentine lead line meandering through the brownish foreground brings the eye to the snow-capped peaks of Mount McKinley, the highest mountain in North America, with a height of approximately 20,320 feet (nearly 4 miles). Its Indian name is Denali (The Great One) and it is the centerpiece of Denali National Park in Alaska. The narrowing lead line provides a dimension of depth, as do the black mountain peaks in the foreground that contrast against the white peaks in the distance. The warm, dark colors in the foreground complement the blue sky and white snow peaks at the end of the trail, which is central to the photograph. Had the photographer chosen a longer focal length lens, the white-capped mountain peaks in the distance would appear larger, but at the expense of a loss in the lovely meandering lead line.

Vancouver, B.C.

S-Curve: The curved lead line directs the viewer’s attention from the bottom right of the photograph to the tall buildings of downtown Vancouver. The diminishing width of the line as it curves its way downtown creates a sense of depth. The straight bicycle path at the far left side of the photograph balances the dominant S-shape curve. It is important to the composition that when a photographer incorporates a lead line; it serves a purpose, in this case inviting someone to visually “travel down the path” and be rewarded by an interesting subject at the end of the path. In this photograph, the reward is the majestic buildings and skyline of a great city. To the far left, one notices a building under construction and a very tall crane against a blue powdery sky—a sign of a growth.

S-Shape Curve

David A. Page

A 600mm lens was used to capture the colorful racecars on turns five and six at the Virginia International Raceway. This increased the shape of the S-curve by compressing the field of view, which is a useful attribute of a long focal length lens. The colorful arrangement of the racecars provides added interest to the sinuous S-shaped track. The time of the exposure was based on capturing the orange car as the first car, which required considerable planning and patience.

Joseph

Giovanni Pietro da Cemmo (1474–1507)

“By reviewing the old we learn the new”: we see here the use of the S-curve in this 500-year-old decorated painting. Joseph is being sold by his brothers and is the center of interest as the elders discuss the exchange. Illuminated manuscripts are the most common specimen of medieval painting to survive.

Richmond Raceway

Richard D. Zakia

C-Shape Curve: This photograph, taken at the Richmond Virginia racetrack, reflects the use of a compositional C-shape curve, which plays well against the straight seat arrangement in the stadium. The action is caught just at the turn when one of the cars begins to spin out, leaving a cloud of white smoke. Additional interest is generated by the dark blue color of the evening sky in the background and the normal colors of the brightly illuminated track.

Blue Ridge Parkway

David A. Page

Reverse C-Shape: The reverse C-shape curve of the wooden split-rail fence in this snow-covered field on the Blue Ridge Parkway near Floyd, Virginia, leads the viewer’s eyes into the muted background. As the fence diminishes in size, it provides an added sense of depth. The curved shape of the fence can be seen as both concave and convex. The concave side embraces the field of snow at the left while the convex side pushes against the snow on the right—much as a sail on a sailboat gathers wind and pushes the boat forward. The bare trees to the left and the grouping of snow-muted trees in the distance add to the feeling of a cold, wintry day.

Feeding Time

Bill Scanlon

L-shape: A little girl in a white dress and yellow hat is seen feeding four young ducks at the edge of a pond. Her vertical position is slightly off to the left and her hand is outstretched. It is an interesting composition and photograph. The position of the girl and four ducks suggests an L-shape. The lone mother duck standing protective guard at the edge of the blue pond extends the L. The diagonal shoreline of the pond is greatly preferable over a static horizontal shoreline.

English Lake District

V-Shape: In creating this classic view of the mountains in the English Lake District, the photographer framed his photograph so that the mountain in the background occupied the center position. On either side, there are two sloping mountains. The line that forms the left slope together with the one that forms the right slope make the letter V. A feeling of depth is provided by the formation of rocks in the foreground, the lake in the middle ground, the two mountains in the far middle ground, and the Great Gable mountain in the background.

Triangles: Thayer’s arrangement of the three figures, the tall goddess in the middle with two small girls on either side, forms a strong triangle. The goddess’s outstretched hanging arms form a narrower triangle that gives added strength to the composition. Behind, and on either side of her, is a cloud formation that takes on the appearance of a pair of wings.

A Virgin

Abbot H. Thayer

Abbot Thayer was an American artist who at the age of 18 moved to Brooklyn, New York. The central figure in his painting of 1892/3 originally was meant to represent Flora, the Greek goddessof flowers. As she is shown here, however, she represents the heroic Greek goddess Victory.

A triangle is a common and useful geometric shape that suggests strength and stability. The pyramids in Egypt are three-dimensional triangles, and in fact can be seen as such if photographed from just one side. Arranging subjects in such a way that they fit into an imaginary triangle is a very useful compositional tool. Triangular composition is basic to many images, not just photographs. One can identify them in paintings, graphic design, and architecture.

Three Photographers

Minor White

This photograph was taken in 1974 in the backyard of Minor White’s home in Cambridge, Massachusetts. The tree photographers are positioned around a large egg-shaped stone, which was the centerpiece of his Zen garden. At the time, Minor was teaching photography at MIT. He arranged the subjects as we see them here, and then set his Polaroid camera on a tripod for a delayed time exposure. From left to right are Peter Lorenz, Richard Zakia, and Minor White. The photograph was used on the back cover of their book, The New Zone System Manual (Morgan & Morgan, 1976). The original Polaroid print resides in the RIT archives.

This photograph was taken by a professional wedding photographer. She arranged the group so that their heads all fall into a tilted triangle. There is nothing more boring than a group all lined up with their heads in a horizontal line. She selected a pleasant, out-of-focus background of greens as a backdrop and used a soft fill flash to soften the shadows in the faces.

Summer Wedding

Lee Thompson

The best man, groom, bride, and bridesmaid celebrate a start of a new blended family. The body language captured by the photographer conveys the affection between the daughter and her new stepmother. The groom and his son show a warm relationship.

Lincoln at Antietam

Alexander Gardner

President Lincoln, with his tall stovepipe hat, stands erect with two shorter men at either side. His security guard, Allan Pinkerton, is to the left and Major General John McClernand is to the right. All three men look off into the distance. Behind them, the opening in the tent forms a triangle, and a flatter triangle can be seen by an imaginary connection of their heads. A long exposure time was required to make this albumen photograph. Lincoln had commented to Gardner earlier that he might not be able to hold the pose for the required time and his blurred face shows that he couldn’t.

Three Young Boys

Vicki H. Wilson

Horizon Line: The horizon line here is placed close to the center of the photograph and is interrupted up by the three boys in the foreground. The breaking up of the horizon line keeps the photograph from being static. The arrangement of the boys is such that one is separated from the other two. This provides a more interesting composition than if the three were grouped as one. As you enter the photograph, you have a tendency to look out into the ocean as the boys are doing. If they were facing you, this would not be so; attention would be focused on each boy, making the background secondary.

Book Cover

John Szarkowski

Where to place the horizon line in a photograph can lead to contradicting statement, but one rule is to never place it in the center of a photograph. We see here that the photographer (a former curator of the Museum of Modern Art) chose to locate the horizon line slightly above center of his photograph “Sarah Lake 1962.”

Ireland

Richard D. Zakia

Using a high horizon line in this photograph directs the viewer’s attention to the blue car. The uncluttered background provides a serene setting with an empty bench to the left as an invitation to the driver to step out of the car and enjoy the beauty of the quiet blue sea and sky. The three different shades of blue—car, sea, and sky—harmonize well. The photograph was taken in Ireland with the Irish Sea as a background. The American driver seems proud to be able to drive a Peugeot using a steering wheel on the right side.

Low Horizon Line

The low horizon line in this ad allows a beautiful blue sky with powdery clouds to occupy nearly the entire photograph. This suggests clean air, fresh air, open optimistic sky, and the future.

Washington Crossing the Delaware

Emanuel Leutze

Diagonals: The action and drama of this historical event are captured, in part, by four of the diagonal oars pushing away the huge pieces of broken ice. The extended arms and postures of the oarsmen suggest the hardship and danger being undertaken. The American flag proudly flies at a diagonal, with a courageous George Washington proudly standing tall and confident as he looks forward to the engagement. The crossing was on Christmas night in 1776. The semidarkness of the scene accentuates the danger and the drama about to unfold. The painting catches the desperate attempt to surprise the Hessian and British soldiers at Trenton. This important painting is billboard size, measuring, 12 feet high by 21 feet long. It is twice the size as Botticelli’s “Birth of Venus.” Leutze was a German-born American; he painted this in Germany using the Danube as his river. The painting is an American icon, like the much smaller photograph of the flag raising on Iwo Jima by Joe Rosenthal.

Flag Raising

Louis R. Lowery, USMC

This photograph taken of the first flag rising on Iwo Jima on February 23, 1945, does not have the iconic impact that the more familiar one has. However, it records a memorable event with the waving American flag standing tall and being protected by the soldier poised with his rifle. It is a powerful photograph in its own right.

Raising the Flag on Iwo Jima

Joe Rosenthal

Joe Rosenthal’s photograph of the flag raising on Iwo Jima in 1945 has become an American icon. What makes it so powerful as a symbol of embattled patriotism? “The decisive moment!” The angle of the flag is perfect in its rendition of action and suggested movement upwards, as is the ascending motion of the men raising the flag.

John Lennon

David M. Spindel

Diagonals and angles play a very important role in this dramatic photograph of John Lennon. If it has been taken straight on, perpendicular to the camera, it would not have the impact it does. This is a studied photograph of a musical artist intensely involved in his work. His body is at an angle to the camera, as is the long instrument panel. His head is tilted and his arms, one resting on the panel and the other on the chair, form additional angles, providing a sense of action and thought. The coffee cup at the left, and the cigarette in his right hand provide a needed break from what appears to be a lengthy session. David Spindel took this photograph and others in October 1980, just two months before Lennon’s tragic and untimely death.

Kayla

Irving Pobboravsky

Whereas straight vertical lines tend to be static, in this case the strong dynamic diagonal lines moving upwards activate them. A second set of dark diagonals can be seen in the upper background. The photograph is a wonderful composite of verticals, diagonals, and even two triangles in the green area to the left. The hard look of the geometrics is softened by Kayla’s gracefully flowing hair and her two inquisitive cats.

Ottawa

Symmetry: With perfect bilateral symmetry, the visual elements are mirror images of each other. In a photograph, this can be static and boring. Although the Parliament building is symmetrical, the surround is not. The trees and cloud formation on either side break up the perfect symmetry of the building, increasing the interest. The partial circular base in the foreground provides a strong perspective that leads directly to the Parliament building. It is a well-composed photograph.

Turkey

Fatima NeJame

This photograph is somewhat symmetrical, with two women on one side and two on the other. It is well balanced and provides much variety with the way the women are dressed and position themselves. They wear different colorful dresses, have different expressions, and hand positions. Two in the front and on opposite sides look at the viewer, while the two behind them are engaging each other. The background, in its wide vertical stripes of muted colors, echoes some of the color the four women are wearing. It is an interesting background in itself and helps to draw attention to the women without drawing attention to itself.

Red Lanterns

Repetition: Repeated visual elements in this photograph are linear and predictable. As with music, one can imagine the red lanterns, which decrease in size, as a constant drumbeat whose sound gradually diminishes. As the sound diminishes, so does the size of the lanterns. And as the level of sound continues to decrease, so does the size of the red lanterns, which can be imagined as continuing beyond the frame. The upper curve of the roofline repeats the curves of the lanterns. As we see here, objects that are similar and close together can be seen as a unit, as a repetitive pattern having their own beat. They can also be seen individually, as they all vary in size.

Floating White Rings

Irving Pobboravsky

Unlike the predictable linear pattern of red lanterns, we see here a varied repetition of visual elements that create a more interesting pattern. This photograph was taken in early spring, just as the snow was beginning to melt. Narrow white rings cling to each tree trunk and resemble halos. The repetitive halos, which vary in their positions, do not have a constant beat but are more like a syncopated rhythm.