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Chapter 5 explores how technical ingenuity featured in the act of religious dedication in ancient Greek religion. Two epigrams (describing the Bes rhyton and the Lykon thēsauros) are taken alongside descriptions of pneumatic inventions in Philo of Byzantium and Hero of Alexandria’s technical manuals. Though not typically read together, Hellenistic epigram, and Philo and Hero’s texts all describe pneumatically enhanced dedications, and demonstrate, within the confines of their genres, how religious awe and technological capabilities were co-constructed and mutually reinforcing. The chapter then turns to the material record, examining traces of technically enhanced dedications in practice. Two examples are explored: wheeled tripods and articulated figurines. Both categories of votive objects show different ways in which the mechanical, human, and divine were configured. Both also stretch further back chronologically than the discussion of preceding chapters, allowing for discussion of texts including Iliad 18 on Hephaistos’ tripods, and Prometheus Bound, to think about the (mythic) prehistory of the phenomenon at hand.
Thomassen’s chord conjecture from 1976 states that every longest cycle in a $3$-connected graph has a chord. The circumference $c(G)$ and induced circumference $c'(G)$ of a graph G are the length of its longest cycles and the length of its longest chordless cycles, respectively. Harvey [‘A cycle of maximum order in a graph of high minimum degree has a chord’, Electron. J. Combin.24(4) (2017), Article no. 4.33, 8 pages] proposed the stronger conjecture: every $2$-connected graph G with minimum degree at least $3$ has $c(G)\geq c'(G)+2$. This conjecture implies Thomassen’s chord conjecture. We observe that wheels are the unique Hamiltonian graphs for which the circumference and the induced circumference differ by exactly one. Thus, we need only consider non-Hamiltonian graphs for Harvey’s conjecture. We propose a conjecture involving wheels that is equivalent to Harvey’s conjecture on non-Hamiltonian graphs. A graph is $\ell $-holed if all its holes have length exactly $\ell $. We prove that Harvey’s conjecture and hence also Thomassen’s conjecture hold for $\ell $-holed graphs and graphs with a small induced circumference.
Before the taming of horses, human lives and activities were limited by the speed of walking or boats, and without the wheeled vehicle transport of goods was restricted to human strength. All this would change when humans had finally established control of the horse, breeding, training and using this unique species, and in due course attaching it to haul chariot, cart and wagon.
We live in an era of major technological developments, post-pandemic social adjustment, and dramatic climate change arising from human activity. Considering these phenomena within the long span of human history, we might ask: which innovations brought about truly significant and long-lasting transformations? Drawing on both historical sources and archaeological discoveries, Robin Derricourt explores the origins and earliest development of five major achievements in our deep history, and their impacts on multiple aspects of human lives. The topics presented are the taming and control of fire, the domestication of the horse,and its later association with the wheeled vehicle, the invention of writing in early civilisations, the creation of the printing press and the printed book, and the revolution of wireless communication with the harnessing of radio waves. Written in an engaging and accessible style, Derricourt's survey of key innovations makes us consider what we mean by long-term change, and how the modern world fits into the human story.
This paper gives a number which is used to determine the component number of links from their associated planar graphs. In particular, we use this number to determine the component numbers of links whose associated planar graphs are fans, wheels and 2-sums of graphs.