Perfect Toast

Picture Courtesy of BBC

The equation for toast and butter temperatures cost £10000 with a total time of 3 months.

h is Thickness (Where the Butter is one-seventeenth of the Toast)
Cp is Specific Heat Capacity
p is Density
T is Initial Temperature of Toast
w is Weight
a is Toast
b is Butter

Basically, the toast needs to be at least 120 degrees centigrade and the butter needs to used straight from the fridge. The butter needs to be applied in patches 2 minutes after the toast has finished.

For more information go to http://news.bbc.co.uk/1/hi/uk/3248822.st

Fibonacci Number

It has a definition that the first 2 numbers in the sequence are 0 and 1.

F(p) = F(p-1) + F(p-2)

Here is the sequence for the first 25: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368 and 75025

It closely related to Pascal's Triangle


It also has a negative scale called the Negafibonacci Numbers.

F(-p) = (F(p))(-1)^(p+1)

It has the same scale except when p is even, F(-p) numbers are negative.

It is also involved with the Wall-Sun-Sun prime.

The equation used is F(p-(p/5)) and that p > 5, where the resulting number has to be prime and in integer form.

p = 10   F(10-(10/5)) = F(10-2) = F(8) = 21 (not prime)

It is believed that there are infinitely many Wall-Sun-Sun primes but yet there are none discovered to date.

Charles Babbage (1791-1871)

He is acknowledged as a mathematician and the inventor of the first automatic digital computer.

Here is a list of his achievements:

• Helped found the Analytical Society whose ambition was to utilise the use of analytical calculus rather than Newtonian calculus.
• Founded the Royal Astronomical and Statistical societies.
• Created a calculator which could perform certain mathematical calculations up to 8 decimal places which was then upgraded to 20 decimal places.
• Devoted himself to mechanical engineering whilst teaching mathematics at the University of Cambridge.
• Developed plans for the Analytical Engine which was the start of the modern digital computer.

The Analytical Engine was never completed however his unpublished notebooks for it's design were found in 1937.

Difference Engine was also a invention that was verging on being the first computer  was on the verge of being the first computer but funding ran out in the 1820s. In 1991 British scientists built the Difference Engine No.2 to Babbage's designs which is accurate to 31 digits.

The Difference Engine is designed to tabulate polynomial functions which can be used to approximate both logarithmic and trigonometric functions.

The Analytical Engine was the upgrade to the Difference Engine. It had a control flow, arithmetical unit and integrated memory which can be found in all modern computers.