Reading the Lost Folia of the Archimedean Palimpsest: The Last Proposition of the "Method"

The Method is the work in which Archimedes sets out his way of finding the areas and volumes of various figures. It can be divided into three parts. The first part is the preface addressed to Eratosthenes, in which Archimedes explains his motivation for writing the work. We find that he was sending demonstrations of results that he had communicated before—the volume of two novel solids, which we call hoof and vault in this article. As Archimedes thought that it was a good occasion to reveal his way of finding results that he had previously published with rigorous demonstration, he decided to include an exposition of this “way” (tropos in Greek, not method, as is usually assumed in modern accounts.) Thus, the first eleven propositions show how the results in his previous works (Quadrature of the Parabola, Sphere and Cylinder and Conoids and Spheroids) were found. We call this group of propositions the second part of the work. The third and last part, beginning with Prop. 12, treats the two novel solids and gives a demonstration of their volumes. Unfortunately, the end of the Method is lost. As is well known, the Method is known only through the palimpsest found in 1906, and some pages had already been lost. The text of the Method breaks off definitively near the end of the demonstration of the volume of the hoof, the first of the two novel solids announced in the preface. We have no testimony concerning how Archimedes demonstrated the volume of the vault, the second novel solid. In this article, we try to reconstruct this lost demonstration, based on recent studies

Ultrafast photocurrent measurement of the escape time of electrons and holes from carbon nanotube PN junction photodiodes

Ultrafast photocurrent measurements are performed on individual carbon nanotube PN junction photodiodes. The photocurrent response to sub-picosecond pulses separated by a variable time delay {\Delta}t shows strong photocurrent suppression when two pulses overlap ({\Delta}t = 0). The picosecond-scale decay time of photocurrent suppression scales inversely with the applied bias VSD, and is twice as long for photon energy above the second subband E22 as compared to lower energy. The observed photocurrent behavior is well described by an escape time model that accounts for carrier effective mass.Comment: 8 pages Main text, 4 Figure