Contain Yourself

I can’t say I’ve ever been known as the most organized person in the world. Likely due to clothing littered around my bed and papers sprawled across my desk, my living space is usually greeted with the phrase, “Well, it definitely looks lived-in.” Feeling fed-up with my clutter and inspired by a bout of Spring Fever, I took my first trip to the The Container Store this past weekend. I was overwhelmed and excited by the immense amount of gadgets and boxes that existed to compartmentalize any and every aspect of my life. They really have it all from jewelry organizers to specially designed coffee filter holders. I found myself extremely comforted by the possibility of having individual boxes to hold all of my worldly possessions so that I may be able to neatly pack them away and only retrieve them when it became necessary. [excerpt

Testing Programs That Contain OpenMP Directives

OpenMP is a standard of compiler directives for C and Fortran programs that allow a developer to parallelize existing code. In this master\u27s project, the topic of tests for code that has been parallelized using OpenMP is addressed. How should a developer test a program to make sure that the directives have not modified the expected results of the code

Sets that contain their circle centers

Say that a subset S of the plane is a "circle-center set" if S is not a subset of a line, and whenever we choose three noncollinear points from S, the center of the unique circle through those three points is also an element of S. A problem appearing on the Macalester College Problem of the Week website was to prove that a finite set of points in the plane, no three lying on a common line, cannot be a circle-center set. Various solutions to this problem that did not use the full strength of the hypotheses appeared, and the conjecture was subsequently made that every circle-center set is unbounded. In this article, we prove a stronger assertion, namely that every circle-center set is dense in the plane, or equivalently that the only closed circle-center set is the entire plane. Along the way we show connections between our geometrical method of proof and number theory, real analysis, and topology.Comment: 12 pages, 4 figure

Smooth rationally connected threefolds contain all smooth curves

We show that if X is a smooth rationally connected threefold and C is a smooth projective curve then C can be embedded in X. Furthermore, a version of this property characterises rationally connected varieties of dimension at least 3. We give some details about the toric case.Comment: Version 1 was called "Any smooth toric threefold contains all curves". This version is completely rewritten and proves a much stronger result, following suggestions of Janos Kolla