Heavy Metal Math

fibonacci schmibonacci

The pattern of numbers shown in the picture above has been studied for over 2,000 years by people all over the world. They are invaluable in the mathematical field of combinatorics, which is a fancy way of saying counting things. They are called the binomial coefficients because they are the numbers multiplying terms of the expansion of the binomial (a+b)n, which is a cornerstone of the study of algebra. The patterns and inter-relationships among the numbers fascinated people in ancient times, and are still essential today to the study of fields as modern as computer science. 

The Preakness Stakes

The Preakness Stakes is an American Grade I stakes race 1-3/16 mile thoroughbred horse race for three-year-old horses, held on the third Saturday in May each year at Pimlico Race Course in Baltimore, Maryland. Colts and geldings carry 126 pounds; fillies 121 lbs.
The Preakness Stakes has been termed "The Run for the Black-Eyed Susans" because a horseshoe of black-eyed susans, the state flower of Maryland, is traditionally placed around the winner's neck. The Preakness is the second leg in American thoroughbred racing's Triple Crown and almost always attracts the Kentucky Derby winner, some of the other horses that ran in the Derby, and often a few horses that did not start in the Derby. The Preakness is 1 3/16 miles or about 9 furlongs, compared to the Kentucky Derby (10 furlongs) and the Belmont (12). It is followed by the third leg, the Belmont Stakes.

Images of Conic Sections

Follow the link to see a sweet Animation

You can even create a similar model at home using a portion of a cone that you probably have just lying around... a styrafoam cup!

Conic Sections History

Conic Section Application and Career link.

Apollonius of Perga (about 262-200 B.C.) was the last of the great mathematicians of the golden age of Greek mathematics. Apollonius, known as "the great geometer," arrived at the properties of the conic sections purely by geometry. His descriptions were so complete that he would have had little to learn about conic sections from our modern analytical geometry except for the improved modern notation. He did not, however, describe the properties of conic sections algebraically as we do today. 

Apollonius defined the conic sections as sections of a cone standing on a circular base. The cone did not have to be a right cone, but could be slanted, or oblique. Apollonius noticed that all sections cut through such a cone parallel to its base were circles. He then extended the properties that he observed from these circles to ellipses and the other conic sections. He even solved the difficult problem of finding the shortest and longest distances from a given point to a conic section. These distances lie on lines called normals, which cut the curve of a conic section at right angles.

It is fortunate that scientists like Johannes Kepler, who lived many centuries later, had the principles of conic sections discovered purely mathematically by Apollonius and others to aid them in their work. This enabled them to realize the connections between mathematics and the natural world. It was Isaac Newton who first fully identified the connection between conic sections and the movement of celestial bodies, such as planets and comets. He was able to show that if the gravitational attraction between the sun and the celestial bodies varies inversely as the square of the distance between them, then the shapes of the orbits will be conic sections, as had been observed by Kepler and others.

Combinations and Permutations

Kentucky Derby link

personally i am betting on 

1st   Big Truck

2nd  Z Fortune

3rd   Visonaire

How many different combinations of winners are there?

How is a permutation different from a combination?

How many different combinations are there for a mixed up Rubik's Cube?

Rubik's Games online here

Or check out this guy solving different Rubik's puzzles.

Puzzle King (Neue Massenproduktion, 2003)

Rubik's Cube is a mechanical puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the "Magic Cube" by its inventor, this puzzle was renamed "Rubik's Cube" by Ideal Toys in 1980 and also won the 1980 German Game of the Year (Spiel des Jahres) special award for Best Puzzle. It is said to be the world's best-selling toy, with over 300,000,000 Rubik's Cubes and imitations sold worldwide. In a typical Cube, each face is covered by nine stickers of one of six solid colours. When the puzzle is solved, each face of the Cube is a solid colour. The Cube celebrated its twenty-fifth anniversary in 2005, when a special edition Cube in a presentation box was released, featuring a sticker in the centre of the reflective face (which replaced the white face) with a "Rubik's Cube 1980-2005" logo.The puzzle comes in four widely available versions: the 2×2×2 (Pocket Cube, also Mini Cube, Junior Cube, or Ice Cube), the 3×3×3 standard cube, the 4×4×4 (Rubik's Revenge), and the 5×5×5 (Professor's Cube). Even larger sizes have been built and are to be launched in September of 2008.