One use for matrix math is in programming 3D engines for video games. A single point on the screen can be defined as a vector. The TV or computer screen is two-dimensional only, so to create the look of depth, objects must change size as they come closer to the viewer or go farther back into the scene. An image is made up of hundreds or thousands of vectors. By multiplying this set or matrix, you can change its size. You can also multiply the vector array by another array, which allows you to rotate the image. In rotation, parts of the image become ...

The Four Color Theorem is a famous mathematical theorem that states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet. Unlike other proofs before its discovery, computers were used to resolve this long-standing mathematical conjecture that was first proposed in 1850 by Francis Guthrie. After more than a century later, mathematicians, Kenneth Appel and Wolfgang Haken, finally derived its proof in 1976, and determined that it is practicality impossible for humans to verify it without the use of a computer. According to the four color theorem, a ...

1)  Roman Numeral IV

Although the Roman numeral for the number 4 has always been taught to have been "IV," according to historians, the ancient Romans probably used "IIII" most of the time. This is partially backed up by the fact that early grandfather clocks displayed IIII for the number 4 instead of IV. Early clockmakers apparently thought that the IIII balanced out the VIII (used for the number 8) on the clock face and that it just looked better.

2)  Base 60

The Babylonians wrote numbers in a system that used 60 as the base value rather than the number 10. They did not have a symbol for "zero."

3)  Fraction Bar

The Romans did not use numerals to indicate fractions but instead used words to indicate parts of a whole. It wasn't until later in h ...

A Turing machine is a hypothetical machine thought of by the mathematician Alan Turing in 1936. Despite its simplicity, the machine can simulate ANY computer algorithm, no matter how complicated it is.

Put simply, the Turing machine isn't a physical machine, but you can imagine it as an never-ending line of tape, broken down into squares. On each of those squares is a 1, a 0, or nothing at all. The machine reads one square at a time, and depending on what it reads, it performs an action - it either erases the number and writes a new one before moving on, or simply moves on to a different square.

Each of those actions, which mathematicians call a 'state', are determined by the mathematical algorithm or problem the Turing machine has been desi ...