Monday, November 15, 2010

Circle equations formulas and calculator

If you have one unknown variable:
  • circumference (c)
  • area (A)
  • radius  (r)
  • or diameter of the circle (d)
just type it in the calculator below. Other values will be calculated quickly using the following formulas:

where π is calculated to 10 significant digits.

Radius r
Diameter d
Circumference c
Area A

Yabba dabba do :)

Wednesday, November 10, 2010

Heart Curve

Each of us probably knows how to draw a heart, but draw a heart with a mathematical formula is certainly a huge challenge. Look down this formulas and the corresponding graphs, or perhaps try to calculate another :)

And even more fascinating three-dimensional heart!

All you need is love...

Sunday, November 07, 2010

Magic square

A magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2.

So let's look at a 3x3 magic square . You should write the numbers 1 to 9 in a square, so that the sum of the rows, the columns, and the diagonals is 15.

I'll show you a trick to solve magic square with odd length.

The first step is to draw squares up, down, left and right as shown. The second step is to enter numbers 1-9, starting from the top and moving it down-right (every second diagonal).

The final third step is to switch the numbers that are outside of the initial square in the following way:
number from the top must be entered into a free space at the bottom of the square,
number from the left must be entered into the gap on the right and so on...
Look at the picture, it's more understandable. :)

Let's look at a 5x5 magic square and how to enroll additional squares.

The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. The magic constant of a normal magic square depends only on n and has the value:
M = (n3 + n) / 2

Remember, this method can only solve the magic square of any odd-sized lengths (3,5,7,9...)

Cheerful greetings to all until next time! ;)

Thursday, November 04, 2010

Nines to infinity

In mathematics, the repeating decimal 0.999... which may also be written as 0.9̇ or 0.(9), denotes a real number that can be shown to be the number one. In other words, the symbols 0.999... and 1 represent the same number.


Confusing :S? Or not ? ;)

Wednesday, November 03, 2010

"Proof" that the sum of the angles in a triangle is equal to 180 degrees

I made this simple applet to show everyone why the sum of the angles in a triangle is excatly 180 degrees. You can also move points A, B and C. I hope you like it ;)

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Made with GeoGebra

Tuesday, November 02, 2010

Multiplication using vedic mathematics

Hello math lovers. In the following clip you can see how multiplication can be easy if you use Vedic math.
Have fun:)