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How to Conquer the Number Plane

An ascending 1-stair packing polynomial, which assigns an integer to each co-ordinate in the sector of the plane that has been cordoned off by the hobgoblin's velvet rope (in this example, the hobgoblin chose the sector bounded by 8/5).

Imagine dashing into a vast, Borgesian concert hall just before the curtain rises. There’s an infinite number of guests and an infinite number of seats, neatly arranged in rows and columns. Unfortunately, a mischievous hobgoblin has roped off a section of the auditorium with a velvet cord, putting some seats out of commission. How do you, Guest N, figure out where to sit?

Okay, it’s a far-fetched scenario, but math major Maddie Brandt ’15 is the first person in history to solve it in her paper “Quadratic Packing Polynomials On Sectors Of R2,” which she will present at a national conference in January.

The problem of assigning guests to seats is directly related to the problem of mapping the non-negative integers (those friendly, deceptively familiar objects such as 0,1,2,3, and their ilk) onto the co-ordinate plane (defined by pairs of integers such (0,0), (0,1), (0,2), etc.—think of the game of battleships). How do you map the integers to the co-ordinate pairs in such a way that you count all the pairs one after another, without skipping any?

Reed Math Prof Wins NSF Grant

A punctured torus being turned inside out. Topologists study these and similar vexing problems.

Prof. Kyle Ormsby [mathematics 2014–], who is set to start his tenure-track position at Reed this fall, is already bringing in the accolades. In May, Reed received a $172,146 research grant from the National Science Foundation for a project under Ormsby’s direction. The project “Structure and computations in motivic and chromatic homotopy” begins in September and continues through August 2017.

If the title leaves you scratching your head, Ormsby explains that the grant will provide support for his study of “some pieces of mathematics that lie at the intersection of topology and algebraic geometry.” Algebraic geometry, as you undoubtedly know, “narrows the focus of geometry, only studying shapes that are defined by polynomial equations.” Topology is the study of geometric properties that are unchanged by the continuous deformation of figures. For example, topologists consider doughnuts and coffee cups to belong to the same class (single-holed objects) because one could be stretched to resemble another.

“If topology’s objects are made out of saltwater taffy,” says Ormsby, “then algebraic geometry’s objects are constructed from peanut brittle—far more rigid and inflexible.”

Reedie Wants To Be a Millionaire

danielhermanmillionaire.jpg

Almost any Reedie would tell you that they did not embark on the life of the mind for its monetary potential. Yet few would turn down the opportunity to earn some quick cash by flexing their mental muscle. On this week's episode of Who Wants to be a Millionaire, Daniel Herman '15 did just that.

Daniel was well prepared for the show: having been on academic quiz teams in high school, and currently working towards a degree in math and physics he breezed through the first few questions. The question of which presidential couple had been married longest made him pause (answer: George and Barbara Bush), but he deployed a lifeline and continued on unabated. By the end of round one Daniel had $68,000 in the bank, and one lifeline left.

Reed Prof Finds Fractal Geometry in Mouse Cortex

Fractals, the bizarre geometrical shapes that undergird natural phenomena from snowflakes to lightning bolts, have been discovered in a new and striking location: the synapses of the brain.

In a recent paper, professor Richard Crandall '69 [physics 1978–] and colleagues at the Reed Center for Advanced Computation found intricate fractal patterns in synapses in the somatosensory neocortex of a mouse brain.

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