Musings
Sum of Whole Numbers
Sum of Square Numbers
Sum of Cubes
Fibonacci Numbers
1 The first 7 Fibonacci numbers are listed below
1, 1, 2, 3, 5, 8, 13, ……………
2 a) The 10th Fibonacci number is 55. The 11th Fibonacci number is 89.
What are the 12th 13th and 14th Fibonacci numbers?
b) Given that 377 and 610 are two Fibonnaci numbers, find the Fibonacci number
preceding 377
c) Given that the 20th and 21st Fibonacci numbers are 6765 and 10 946 respectively, what
are the 19th and 22nd Fibonacci numbers?
3 Consider the following list of Fibonacci numbers
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584
The sum of the of the first 7 Fibonacci numbers is 33
The sum of the of the first 10 Fibonacci numbers is 143
Find the pattern. Using the pattern calculate
a) the sum of the first 13 Fibonacci numbers
b) the sum of the first 16 Fibonacci numbers
1, 1, 2, 3, 5, 8, 13, ……………
2 a) The 10th Fibonacci number is 55. The 11th Fibonacci number is 89.
What are the 12th 13th and 14th Fibonacci numbers?
b) Given that 377 and 610 are two Fibonnaci numbers, find the Fibonacci number
preceding 377
c) Given that the 20th and 21st Fibonacci numbers are 6765 and 10 946 respectively, what
are the 19th and 22nd Fibonacci numbers?
3 Consider the following list of Fibonacci numbers
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584
The sum of the of the first 7 Fibonacci numbers is 33
The sum of the of the first 10 Fibonacci numbers is 143
Find the pattern. Using the pattern calculate
a) the sum of the first 13 Fibonacci numbers
b) the sum of the first 16 Fibonacci numbers
Morley’s theorem
Pythagoras' Theorem
Not only is the theorem of Pythagoras the best known mathematical theorem of any kind, it also has the record of having been proved in a greater number of ways than any other result in mathematics.
Bhaskara II’s proof
Platonic Solids
An infinite number of regular polygons could be inscribed in the circle but in three dimensional space they are only five polyhedra. Platonic Solids.
The Three Great Problems of the Ancient World
Squaring the Circle Duplicating the Cube Trisecting the Circle
Double the Square
Goldbach Conjecture
Goldbach conjecture, in number theory, that every even counting number greater than 2 is equal to the sum of two prime numbers. The Russian mathematician Christian Goldbach first proposed this conjecture in a letter to the Swiss mathematician Leonhard Euler in 1742.
Amicable Numbers
Are two different numbers related in such a way that the sum of the proper divisors of each is equal to the other number.
The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220. (A proper divisor of a number is a positive factor of that number other than the number itself.