Celestial Mechanics is the study of celestial bodies such as planets, satellites, comets and meteors, but not the bodies themselves. Visitors can work a machine that acts as an analog computer. The surface is shaped so that when a ball is launched, it acts like a planet moving around the sun or a satellite around the earth. Johannes Kepler's three laws of planetary motion and Sir Isaac Newton's mathematical interpretation of those laws are explained.
The History Wall spans the time from the 12th century (approximately the beginning of modern mathematics) to the explosive development of mathematics today. Many of the world's greatest creative mathematicians are depicted. Each is designated by a panel made up of a portrait, personal introductory notes and significant mathematical achievements. Surrounding the portraits and biography are panels and notations that illustrate the active influence on the mathematicians and the important accomplishments of the period. A computer kiosk deployed more recently brings the analysis of mathematics up to date and allows for the expansion into future generations.
The Image Wall is made of a variety of familiar items including a snowflake, a sea shell, an egg, a photograph of a tornado. All have a relationship to various forms of mathematics, and the wall provides visitors with a sketchbook like look at the evolution of mathematical problems. Additional kiosks help weave a richer history of math in contemporary society by offering looks at the logic behind modern computer science, discussions of how Math will evolve, and even some humor through math jokes.
Mathematicians occasionally construct models to prove or disprove theories. Such models are often elegant, their shapes re-affirming the aesthetic relationship of mathematics to the arts. What would the reflection of a doughnut look like in a spherical mirror? Can a curve be made of straight lines? How many spheres do you need to fill a box? Mathematical models provide the answers, and visitors can view a series of dynamic models built to demonstrate some very hard to define concepts.
Four towns want to build the shortest possible road to connect them all. The answer to such problems of minimums can be found by dipping a model of the problem in a soap solution. Because surface tension makes the surface contract as much as possible, soap bubbles form the shape that encloses a given volume with a minimum amount of surface. The bubble machine in this exhibit demonstrates various closed curves and minimal surfaces that help solve the problem.
Visitors observe a motorized train, shaped like an arrow, that seems to travel around the Mobius Band on both sides, but the surface only has one side and one edge. On a Mobius Band, up and down have no meaning. The Mobius Band is not just a mathematical oddity, however. it has shown up in manufacturing as a method for creating longer conveyor belts in small spaces.
A cube of lights acts as a 3-dimensional matrix and creates a visually unique calculating machine. Any number from one to eight can be multiplied, squared or cubed. The result is displayed as rows and columns of lit incandescent light bulbs.
The Probability Machine demonstrates how a probability curve can be found by experiment. When the balls are dropped from the center top of the machine they invariably form a pattern. The number of possible paths to a given space in the array of pins is given by Pascal's Triangle. For the number of paths to a space is the sum of the number to the two spaces above it. The probability of a ball's dropping in any box can be found by counting the number of paths to that box and comparing it to the total number of paths. Probability theory is used in genetics, thermodynamics, traffic control, economics, and insurance.
The human eye and brain are built to order information that may other wise be cluttered or without meaning. When viewed from their projective focus, a seemingly disorganized group of shapes and colors appear as a neat and orderly pattern. Projections are used in many things we are familiar with: maps, paintings, photographs. Brunelleschi understood the power of projective geometry and used it to render some of the first paintings with linear perspective.