Braeden Sweder
Braeden Sweder
Finding the geometry behind the algebra
One of my favorite things about mathematics is when two ideas that look completely different turn out to be connected. Cubic equations, for example, can be approached with algebra, trigonometry, and even a rotating equilateral triangle.
Here I’ve collected some of those mathematical investigations, the book I’m writing, and a few other projects.
The same mathematics can have more than one picture.
Selected work
MATHEMATICAL RESEARCH
Completing the Square in 3D
What happens if we try to extend completing the square into three dimensions? I explored cubic equations using the volumes of pieces that fit together into a larger cube.
THE BEAUTY OF MATHEMATICS
The Beauty of Mathematics
An illustrated exploration of the connections between algebra, geometry, trigonometry, and complex numbers.
Other mathematical investigations
Solving Cubic Equations Using a Triangle
A rotating equilateral triangle provides a geometric view of the real roots of a cubic equation.
The Geometry of Polynomials
An ongoing investigation of the shapes that appear when polynomial equations are viewed geometrically.