3 citations · 3 across the 7 of their papers we have counts for
10 papers
The Diagonal of a Regular Pentagon
Dan McQuillan
We demonstrate the well-known fact that the diagonal of a unit regular pentagon has length the golden ratio. While similar to other proofs, we provide a novel figure that we believ…
Drawings of complete graphs in the projective plane
Alan Arroyo, Dan McQuillan, R. Bruce Richter +2
Hill's Conjecture states that the crossing number of the complete graph in the plane (equivalently, the sphere) is $\frac{1}{4}\lfloor\frac{n}{2}\rfloor\lflo…
Convex drawings of the complete graph: topology meets geometry
Alan Arroyo, Dan McQuillan, R. Bruce Richter +1
In this work, we introduce and develop a theory of convex drawings of the complete graph in the sphere. A drawing of is convex if, for every 3-cycle of , t…
Specialization, generalization, and a new proof of Vivinai's Theorem
Addie Armstrong, Dan McQuillan
We provide a new proof of Vivinai's Theorem using what George Polya calls a 'leading particular case.' Our proof highlights the role of generalization in mathematics.
Drawings of Kn with the same rotation scheme are the same up to Reidemeister moves. Gioan's Theorem
Alan Arroyo, Dan McQuillan, R. Bruce Richter +1
A {\em good drawing\/} of is a drawing of the complete graph with vertices in the sphere such that: no two edges with a common end cross; no two edges cross more than onc…
Levi's Lemma, pseudolinear drawings of , and empty triangles
Alan Arroyo, Dan McQuillan, Bruce Richter +1
There are three main thrusts to this article: a new proof of Levi's Enlargement Lemma for pseudoline arrangements in the real projective plane; a new characterization of pseudoline…
Bishellable drawings of
Bernardo M. Ábrego, Oswin Aichholzer, Silvia Fernández-Merchant +6
The Harary--Hill conjecture, still open after more than 50 years, asserts that the crossing number of the complete graph is $ H(n) = \frac 1 4 \left\lfloor\frac{\mathstrut n}…
A Remark on Baserunning risk: Waiting Can Cost You the Game
Peter MacDonald, Dan McQuillan, Ian McQuillan
We address the value of a baserunner at first base waiting to see if a ball in play falls in for a hit, before running. When a ball is hit in the air, the baserunner will usually w…
On the crossing number of K_13
Dan McQuillan, Shengjun Pan, R. Bruce Richter
Since the crossing number of K_{12} is now known to be 150, it is well-known that simple counting arguments and Kleitman's parity theorem for the crossing number of K_{2n+1} combin…
Witt's cancellation theorem seen as a cancellation
Sunil K. Chebolu, Dan McQuillan, Jan Minac
The year 2017 marks the 80th anniversary of Witt's famous paper containing key results, including the Witt cancellation theorem, which form the foundation for the algebraic theory…