The seventeenth century philosopher Gottfried Leibniz wrote: 'Music is the pleasure the human mind experiences from counting without being aware that it is counting'. Mathematical structures have always provided the bare bones around which musicians compose music and have been vital to the very practical considerations of performance such as fingering and tempo.
But there is a more complex area in the relationship between maths and music which is to do with the physics of sound: how pitch is determined by force or weight; how the complex arrangement of notes in relation to each other produces a scale; and how frequency determines the harmonics of sound.
V.I. Warshawski is confronted with the mysterious death of a young woman at a local hospital and the preliminary investigation produces horrifying results.
A pair of ferocious forest fires rages out of control, threatening to destroy two American national parks and incinerate thousands of homes and park buildings. As the desperate battle to squelch the global warming-induced fires before they "blow up" reaches a fever-pitch, a mysterious string of violent airborne accidents among the air tanker fleet produces a mounting body count. The air tankers - the old aircraft used by pilots to bomb the fires with fire retardant slurry - have been literally falling apart in midair.
Teaching Young Children to Draw: Imaginative Approaches to Representational Drawing
This illustrated handbook on teaching young children to draw has been developed using what the authors call the "negotiated drawing approach". It presents this approach to teachers, demonstrating how it works, ideas for future work, and concrete evidence that it actually produces good results.
Photographers Linda and Robert Scarth have an incredible eye for that magic moment when small becomes beautiful. Matched with patience and skill, their eye for magic produces dazzling images of Iowa nature up close.
