Sierpinski Investigation Waclaw Franciszek Sierpinski was a famous Polish Mathematician who made many innovations in Math. His work is used to this day as a foundation for many current mathematical theories. His most compelling work was with set theories, number theories, theories of functions, and topology. In his life time he published over 700 papers and 50 books. Sierpinski was born in Warsaw, Poland, on March 14 of 1882. At the age of 21, he won his first medal for writing an essay on Georgy Feodosevich Voronoy’s contribution to number theory. Sierpinski’s most worked with mathematical topic was definitely with set theories. A set theory is the study of mathematics that studies sets, or collections of objects, in this case, objects that are relevant to mathematics. Sierpinski first became interested in 1907 when he came upon a certain theory. A college professor told him look at set theories for an explanation to this theory. The study of set theories was first discovered by Cantor and Dedekind in the 1870s. Set theory is the most commonly used system for mathematics. It is used in mathematical ideas such as functions, learned in high school, all the way to Venn diagrams introduced in elementary school. Set theories are used to find a common relationship two elements. There are six techniques that one can use to find such relationships; they are union, intersection, complement, symmetric difference, Cartesian product, and powerset. Sierpinski wrote a book on set theory called Outline of Set Theory in 1912. He died on October 21 of 1969 in Warsaw, Poland. The Sierpinski Triangle is an example of a fractal that was created by Waclaw Sierpinski. There are many stages of this fractal in stage one, there is one shaded triangle within the triangle. In stage two, there are three shaded triangles. In stage three, there are nine shaded triangles. In stage four there are 27. After studying this pattern, I was able to come up with a function for finding the number...