Mathematics
Why the Determinant Measures Area and Volume
A clear explanation of why the determinant of a matrix tells us how a linear map scales area, volume, and orientation.
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5 posts tagged "Geometry"
Mathematics
Karen Uhlenbeck: Geometry, Physics, and the Abel Prize
The story of Karen Uhlenbeck, a pioneer of geometric analysis who overcame gender barriers in mathematics, made fundamental contributions to gauge theory and minimal surfaces, and became the first woman to win the Abel Prize.
Mathematics
Bernhard Riemann: The Geometry of the Universe
The life and revolutionary ideas of Bernhard Riemann, whose short career produced some of the most profound concepts in mathematics — from Riemannian geometry to the Riemann hypothesis, the greatest unsolved problem in mathematics.
Mathematics
The Banach-Tarski Paradox: Doubling a Sphere with Pure Mathematics
We explain the Banach-Tarski paradox — how a solid ball in three-dimensional space can be decomposed into finitely many pieces and reassembled into two balls identical to the original — and explore the role of the Axiom of Choice.
Mathematics
Maryam Mirzakhani: The First Woman to Win the Fields Medal
The inspiring story of Maryam Mirzakhani, an Iranian mathematician who made groundbreaking contributions to the geometry of Riemann surfaces and moduli spaces, becoming the first woman to receive the Fields Medal.