What do they Study? • A mathematician studies quantity, structure, space, change, and patterns. • Math is not just about learning what is known, it is about exploring the unknown.
Are there different types of Mathematicians? • Mathematicians study many different things, and there are many different kinds of mathematicians.
Who are some famous mathematicians? • Isaac Newton developed calculus to explain his laws of motion and gravity. • Carl Gauss is considered to be one of the greatest mathematicians of all time, with contributions too numerous to name.
Who cares about math? • There are several mathematics problems called the Millennium Prize Problems. Anyone who solves one of these problems will receive $1,000,000. • Every piece of technology you use (computers, video games, televisions, etc.) required an understanding of math to invent and build.
Some fun math! • What is the area of a square? • How about a triangle? • What about this shape? l w h b
Pick’s Theorem • There’s an easy way to find the area of any flat shape! • Area = (# of inside points) + ½(# of boundary points) – 1 • http://www.cut-the-knot.org/ctk/Pick.shtml
Try it for yourself! • Take your sheet of graph paper and draw a shape using only straight lines. • Now calculate the area using Pick’s Theorem! A = I + B/2 -1
Further Questions. • Once mathematicians prove something we always try and ask what happens if we change things just a little. Does our theorem still work? Or do we need to modify it before it works again? • Pick’s theorem worked for area (flat objects). Does it work for 3-D objects? (Spheres, cylinders, cubes)
My research • It turns out that Pick’s theorem doesn’t actually work in 3-D. • This doesn’t mean we give up! • In the 1960’s Eugene Ehrhart created Ehrhart polynomials which work for shapes in higher dimension. • Now, 40 years later we still don’t completely understand them.