Hypercube House
Wednesday, June 28th, 2006Someone built a 4D hypercube house in Second Life. (I discussed hypercubes a while ago)
Archive for the ‘Mathematics’ Category
Someone built a 4D hypercube house in Second Life. (I discussed hypercubes a while ago)
Calculating The Length of a Path
Tuesday, June 20th, 2006When I learned calculus in high-school, integrals were introduced as a way of measuring the area below a function's graph. I was quite struck by this concept, and I tried to find other geometric properties of functions I could calculate. The first thing that came to mind was measuring the ...
Hypercube
Sunday, June 4th, 2006I was watching Cube 2: Hypercube the other day, and I started wondering about the nature of this object. The first thing I tried to figure out was how to define a hypercube. The prefix 'hyper' in Mathematics usually means 'in a higher dimension'. So a hypercube should be like ...
Two Envelopes: Part 2
Sunday, June 4th, 2006As promised, here's another solution to the two envelopes riddle: First, choose a descending list of probabilities p(n). When you receive a number n, say 'higher' with probability p(n) and 'lower' otherwise. That's the solution. Now let's prove that it works.
Two Envelopes
Saturday, May 27th, 2006Players A and B play a game. Player A somehow selects two different natural numbers and puts them in two envelopes. He then chooses one envelope at random and hands it to player B. Player B looks at the number, and has to guess whether the number in the other ...
Mathematics: Invention or Discovery?
Tuesday, May 23rd, 2006When I started studying Maths, the answer to this question became clear to me: Definitions are invented, while theorems are discovered. As Hardy said, Mathematics is the study of patterns. Practicing Math means basically two things: Defining interesting structures, and investigating their properties and inter-relations (proving theorems). When you define a structure, ...
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