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What Do Triangles and Hockey Sticks Have in Common?
What Do Midpoints and Hockey Sticks Have in Common?
Nothing
Except for Triangles!
- Polish mathematician
- He published 724 papers and 50 books
involving mathemtaical theory
- Graduated from the University of Warsaw in 1904
- worked as a school teacher of mathematics and physics in Warsaw
- In 1949 Sierpiński was awarded Poland's Scientific Prize, first degree
To draw the triangle...
- start with any triangle and use the midpoints of each side as the vertices of a new triangle
- remove the original or "middle" triangle
- 3 triangles are left
http://www.lutanho.net/fractal/sierpa.html
Pascal Triangle Hockey Stick
The sum of any diagonal that starts on a 1 on the edge of the triangle is equal to the number under the termination of the diagonal, creating a hockey stick shape.
Sierpinski's Triangle and Hockey Stick
Brooke Gann and Angie Palm
Waclaw Sierpinski
Sierpinski's Triangle
a fractal described in 1915 by Waclaw Sierpinski
The Hockey Stick pattern is found in Pascal's Triangle,
which was known and used long before Pascal. The
triangle was used:
- In India in the 10th century: binomial coefficients
- In Persia and Iran in the 10th and 11th centuries
- In China in the 13th century
- In Europe in the 15th century
China:
In China in the eleventh century
Pascal's Triangle was used by the
mathematician Chia Hsien to
extract square and cube roots of numbers.
Cheese is gooooood
- dimensions are 1/2 the dimensions of the original triangle
- area exactly 1/4 of the original area
- each remaining triangle is similar to the original
Sierpinski's triangle can also work with squares
Persia:
In Persia Pascal's Triangle was used
by Omar Khayyam to also extract
roots. In Persia and China the
triangle was discovered separately
Citations
All You Ever Wanted to Know About Pascal's Triangle and More. Web. 12 May 2011. <http://ptri1.tripod.com/>.
- "Pascal's Triangle." Math Is Fun - Maths Resources. Web. 12 May 2011. <http://www.mathsisfun.com/pascals-triangle.html>.
- "Sierpinski Triangle." Jim Wilson's Home Page. Web. 12 May 2011. <http://jwilson.coe.uga.edu/EMAT6680/Parsons/MVP6690/Essay1/sierpinski.html>.
- "The Sierpinski Triangle." Web. 12 May 2011. <http://math.bu.edu/DYSYS/chaos-game/node2.html>.
- "Sierpinski Triangle." Web. 12 May 2011. <http://www.zeuscat.com/andrew/chaos/sierpinski.html>.