Tag Archives: differential geometry

Calculus is topology. The reason is that the matrix of the exterior derivative is equivalent to the transpose of the matrix of the boundary operator. That fact has been known for some time, but its practical consequences have only been … Continue reading

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Robert Bryant – The Idea of Holonomy

The Idea of Holonomy by Robert Bryant from the MAA: “Can I roll the ball from any point to any other point and have it wind up in a given orientation that we want?” Bryant asked. If I draw a dot … Continue reading

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More drawings by Robert Ghrist. Point-set topology, differential topology, geometric topology, symplectic topology, algebraic topology illustrated. From his (free) notes on applied homology. GLOSSARY Topology = connections between things. Manifolds come in a wide variety of shapes, but they’re all tame. Vector fields = arrows on … Continue reading

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A beautiful depiction of a 1-form by Robert Ghrist. You never thought understanding a 1→1-dimensional ODE (or a 1-D vector field) would be so easy! What his drawing makes obvious, is that images of Phase Space wear a totally different meaning … Continue reading

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Radiolab – Bird’s-Eye View

<![CDATA[// <![CDATA[ // <![CDATA[ // <![CDATA[ // <![CDATA[ // <![CDATA[ (function(){var s=function(){__flash__removeCallback=function(i,n){if(i)i[n]=null;};window.setTimeout(s,10);};s();})(); // ]] // ]] // ]] // ]]]]]]> // ]]]]>]]> In gradeschool calculus I learnt that derivative = slope. That was a nice teacher’s lie (like the Bohr … Continue reading

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arXiv

Hola Nerds, Have you ever found yourself browsing tumblr and thinking to yourself: “Instead of looking at pictures of dyed hair, I should really be thinking about chirped dissipative solitons” ? Well, now you can. I ported the following arXiv feeds … Continue reading

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Clouds

You can see the “edge” of a cloud from far away so it should be obvious what ∂cloud means. But up close (from an airplane) you can see there is no edge. The mist fades gradually into blue sky. Here’s another job … Continue reading

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