A collection of mathematical fascinations, not strictly limited to the subject itself but also people's interactions and interpretations. My curiosity for the subject is infinite, but I try to stay away from the sciences. The thrill lies in the purity, not the application.
Info on my icon can be found here.
In the academic world Dover Publications is widely known for publishing standard texts in mathematics. To me they’re known for publishing books with the best cover designs around, which truly make them stand out among the boring rest.
“How many mathematical logicians does it take to replace a lightbulb??
None: They can’t do it, but they can prove that it can be done.
How many numerical analysts does it take to replace a lightbulb??
3.9967: (after six iterations).
How many classical geometers does it take to replace a lightbulb??
None: You can’t do it with a straight edge and a compass.
How many constructivist mathematicians does it take to replace a lightbulb??
None: They do not believe in infinitesimal rotations.
How many simulationists does it take to replace a lightbulb??
Infinity: Each one builds a fully validated model, but the light actually never goes on.
How many topologists does it take to screw in a lightbulb??
Just one. But what will you do with the doughnut?
How many analysts does it take to screw in a lightbulb??
Three: One to prove existence, one to prove uniqueness and one to derive a nonconstructive algorithm to do it.
How many Bourbakists does it take to replace a lightbulb: ?
Changing a lightbulb is a special case of a more general theorem concerning the maintain and repair of an electrical system. To establish upper and lower bounds for the number of personnel required, we must determine whether the sufficient conditions of Lemma 2.1 (Availability of personnel) and those of Corollary 2.3.55 (Motivation of personnel) apply. Iff these conditions are met, we derive the result by an application of the theorems in Section 3.1123. The resulting upper bound is, of course, a result in an abstract measure space, in the weak-* topology.”
“Another picture from our wonderful blackboard artist Ryan Budney in Victoria, Canada. He’s taken a 4-dimensional sphere and removed a knotted 2-dimensional sphere (i.e. the surface of a beach ball), and tried to triangulate the resulting space. Triangulation means breaking up a complicated space into simpler pieces – triangles! – and then explaining how these pieces fit together. The triangulation here has precisely one vertex (a 0-dimensional triangle), one edge (a 1-dimensional triangle), 4 triangles (i.e. your usual garden-variety triangles), 5 tetrahedra (3D triangles) and the two pentachora (4-dimensional triangles). The bottom picture shows how the pieces are glued together. The top picture is completely unrelated.
The knotted 2-dimensional sphere is called a Cappell-Shaneson knot because it is sitting inside a ‘homotopy 4-sphere’. That is, the space the knot is sitting in looks like a normal sphere from a distance but might turn out not to be upon closer inspection. If it isn’t, then it would provide a counterexample to the Poincaré Conjecture, which is still open in 4 dimensions (but was famously solved for 3 dimensions by Grigori Perelman in 2003).” Via What’s On My Blackboard?
Next time you’re at a party and want to leave an impression on someone say: “I bet you don’t know how to slice a doughnut into 13 pieces with just three cuts!” (This puts a very vivid image in my head of Ryan Gosling saying: “Hey Girl, do you know how to slice a doughnut into 13 pieces with only three cuts?”)
From “The 2nd Scientific American Book of Mathematical Puzzles & Diversions” via the Reanimation Library, a really great project looking to resurrect “cultural debris.” They have some amazing images.
This is a much more elegant representation of the problem on last week’s assignment that I was most proud of. My explanation wasn’t terribly clear, but at least it was correct, and I don’t know that anybody else managed that much. Oh, and if the problem isn’t clear, it’s to continuously deform a double torus into a double torus with linked arms, all without tearing or cutting anything, and without identifying and specific points. The way I was able to wrap my head around it involved stretching one lobe of the torus until it looks sort of like a thick coffee cup with no bottom and one handle. Then if you pinch the area where the handle connects (between the two connections really, you’re grabbing the inside of the hole of that lobe of the torus) and then pull it halfway through, so the two lobes are looped over each other. This shape is fairly easy to mold into the linked double torus.
image credit to the dying love grape, which seems to be a pretty interesting blog at least somewhat about maths.
Recreational mathematician and aspiring teacher. Grew up a math nerd and consider the subject a major part of my identity. Fascinated by just about everything. Here's hoping this blog will open me up to some more creative outlets. That might be good for me at this juncture in my life :)
