Philadelphia Area Seminar on History of Mathematics

The Philadelphia Area Seminar on History of Mathematics will meet on Thursday, October 20, 2016, from 6:00 p. m. to 8:00 p.m., in Saint Augustine Center Room 300.

We begin with conversation and a light supper (donation: $10.00). When the discussion lags, about 6:30 to 6:45, Toke Knudson of SUNY, Oneonta will speak on:

During the first decades of the 20th century in Denmark the didactic method of geometry was discussed intensely. Early on it became clear that there were only two possible paths when it came to the teaching of geometry. One path was to uphold the Euclidean ideal and teach geometry according to the axiomatic method. The other path was to accept geometry as a natural science in which connections are seen through experiments. The “experimental method” was outlined in textbooks already from 1904. According to this method, the pupils were to get as far as they could through experiments, then switch to deduce new results from the set of “axioms” brought forth by the experiments. Johannes Hjelmslev, who was professor of mathematics at the University of Copenhagen, went further and constructed what he called “the geometry of reality,” which had as its only axioms the existence of graphing paper and rectangular blocks. Hjelmslev’s geometry directly contradicted classical geometry, which Hjelmslev considered a crude and poor approximation to the actual conditions of reality—the opposite view of a classical mathematician, who tells us that what we draw in geometry is only a crude approximation to pure geometry. Some of Hjelmslev’s claims, including that a tangent of a circle has a line segment in common with the circle, were rejected by some, but others took to his ideas. In particular, his followers wrote school textbooks according to his geometry. My talk will trace the discussion of geometry’s didactics in Denmark with an emphasis on the contributions by Hjelmslev.

Directions: Villanova University is located on route 30, Lancaster Avenue, just east of I-476. If you drive to the meeting, enter Villanova by the main gate on Ithan Avenue. By order of the Parking Office, all parking is now in the Saint Augustine Center lot, newly refurbished to a multistory structure. You will need to display a parking pass, which is attached to this email. You can get in touch with me (Alan Gluchoff) at 610-905-1376 if you need help.

Public transportation: Take SEPTA's Paoli - Thorndale train to the Villanova station. If outbound from center city go down through the tunnel to the inbound side. From the inbound platform a few steps lead to the Mendel parking lot. Proceed as above to Saint Augustine 300.