## Archive for the ‘geometry’ Category

### Diagrams

The diagram above is from a paper of mine which, as I found out today, was published last year! It is in ACM Transactions on Algorithms, although their website still lists the “current issue” as 2010 and they didn’t tell me when it went to press. The paper, joint with Ramki Thurimella, is about using a […]

Filed under: diagrams, geometry, LaTeX, toc | Leave a Comment

### Fold-Fashioned

Continuing on last week’s post, there were a couple of hands-on activities led by Joseph O’Rourke at the geometry minicourse that I attended. In one of them, you start by printing out the following sheet of paper (available at howtofoldit.org): The red and green lines indicate mountain and valley folds and at this point your […]

Filed under: b.k.a.t., geometry | 1 Comment

### Joint Meeting

No, this is not about sharing joints (even in moderation). This week I am at the joint meeting of the American Math Society and Math Association of America in Boston, MA. It is a huge conference with around 7000 participants, but more cohesive than many other mega-conferences including Informs and ISMP that I have visited. The […]

Filed under: CS Circles, geometry, math, travel | Leave a Comment

### Depth and Violation

Over the last year or so I became interested in a family of problems related to linear programming. In ordinary linear programming, we are given some collection of linear constraints, say {ai x ≥ bi} for i=1, …, n, and the x represents a d-dimensional variable. A central result in optimization says that there is […]

Filed under: complexity, computer science, geometry, math | Leave a Comment

### Valentine Convex Sets

Here’s a problem which I was introduced to in 1997 in Halifax, failed miserably to solve (along with some other students), and then mentioned at a bar and got many people very confused last week. You need to know the definition of a convex set: a set is convex if for each two points u, […]

Filed under: geometry, math, problems | 3 Comments

### Houston

I’m in Houston right now and am posting a couple of pictures from the Houston Space Centreer. One is of me as an astronaut. The second one is a picture of a toy they have in the gift shop that reminded me of my earlier “roundahedra” post… the toy is made out of 5 interlocked […]

Filed under: geometry, travel | Leave a Comment

### More Roundahedra

After figuring out why the equation in the last post described a tetrahedron, I was able to apply the same technique to generate the four other Platonic solids. By popular demand, here they are! The rounded cube has equation (1-x2)(1-y2)+(1-y2)(1-z2)+(1-z2)(1-x2)=0 and the rounded octahedron is 1-2(x2+y2+z2)-2(x2y2+z2x2+y2z2)+x4+y4+z4=0. I won’t post the icosahedron and dodecahedron’s formulas because […]

Filed under: geometry, polyhedra | Leave a Comment