Design and Math
Nearly every thing that gets designed in some way incorporates mathematics. Nearly everything has some aspect that needs math to overcome an obstacle or opposition. From gravity to the exploitation of materials, everything has involved math in both the design of the end product, as well as the construction process. Nearly any picture of any object could be described in the math that was involved in the design process.
Stonehenge is a great early example of the math involved in design. The monument in Wiltshire, England shows how mathematics was used in the design process long ago. The creators of Stonehenge needed to not only use mathematics to determine the exact size and placement for the stones, but the long process of getting the stones to the location. Up to 43 of the 4-ton stones were transported from 250 kilometers away, which must have involved a great deal of mathematics to move across the country, which is believed to have been a series of logs to which the stones were rolled across. It is a standing monument to the use of mathematics involved in design.
The Great Pyramids of Egypt are another standing testament to mathematics involved in the building and design process. It isn't exactly known how the Egyptians moved the giant stones and constructed the pyramids, but it can be said that a great deal of advanced mathematics must have been involved in place of the lack of technology.
Modern bridges are another great example of the amount of mathematics that is involved in the design process. There are several forces of physics that bridges must be designed to overcome, and these are mathematically computed into the overall design image that the architect or engineer had for the bridge. Not only must the bridge stand against gravity, but it must also handle the load and stress of traffic, as well as the horizontal forces of sheer winds. Not to mention bridges built in disaster areas that must be able to withstand things like earthquakes and hurricanes.
Similar to bridges, dams are designed based around mathematics in order to withstand the forces that they are subject to. But dams are also unique because of their exploitation of materials. The concrete used is designed specifically to be manipulated into the structure so it can help counteract the forces that the dam is subject to.
Aviation technology is one field that is as much about mathematics as it is about design. Aviation is solely about the manipulation and control of natural forces and certain properties of physics. The lift needed to get a large airliner off of the ground had to be meticulously calculated, and the aerodynamic properties of the fuselage of aircraft had to designed based on mathematics in order to create the least amount of drag.
The Bugatti Veyron, or anything in the automotive industry, is another examples of designed following the application of mathematics. Similar to the aviation industry, automotive designer of the Veyron had to design its hull to be as aerodynamic as possible. But the designers also had to counteract the forces of lift, and had to specially designed stabilizer wings for the car to keep it planted to the road during high speed runs, in order to give the car optimal handling at great speeds.
Finally, my favorite example of mathematics involved in design is the Nike Free. The shoe had set before it a set of parameters that it had to meet, and the shoe designers then had to use math to make the design possible. The designers were given the idea of a shoe that would be as light and flexible as possible, so as to mimic the benefits of running barefoot. The designers then had to create the idea of a shoe that could bend and twist freely, and offer the least amount of resistance to the legs, and therefore be very similar to running barefoot. The design for the sole of the shoe turned out to be a rubber base that was then sliced into small block, which remained connected to, together by a thin piece of rubber. This allowed for the most flexibility while still offering durability and comfort.
So the design process is very much involved in the field of mathematics. It all goes back to the principles of oppositions, and the resolutions to them. Every resolution involves a great deal of math in order to overcome the opposition.