Blaise Pascal was a French Mathematician who lived in the 17th century. Amongst other (more complex) work he did he is probably best known for the simple set of numbers that are written in the shape of a triangle.
The first row (the tip) of the triangle is '1' - because that seems like a good place to start if any.
Each subsequent row is generated by placing the sum of two adjacent numbers in the row, below and between them into the next. (0 is used if no number exists)
So if we have a row...
* 8 1 6 2 3 * * * 9 7 8 5 * * |
The triangle itself comes in very handy in mathematics, however, the form below just produces very nice patterns...
You will need Netscape3.0 or higher to view the triangles.
First select how many rows or the triangle you wish the program to calculate.
Next select a divisor factor. It is preset to 2 - this will colour all the even numbers in Pascal's triangle white and the rest black.
To see the triangle just click the VIEW TRIANGLE button.
The default pattern is called the Sierpinski Gasket. It happens that it can be drawn in three other completely different ways! Making it a very special image.
How long it takes to draw the triangle appears depends on how many rows are to be produced and on whether you are using another browser window to perform other operations.
63 rows take about 22-24 seconds to produce if the browser is not being used in that time.
BEFORE using this form, be sure to have loaded the images below
by either clicking the 'Load Images' button or on the images themselves
ALWAYS close each 'triangle window' before viewing a new one
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