By Julian Havil
ISBN-10: 0691148228
ISBN-13: 9780691148229
Math--the program of moderate good judgment to average assumptions--usually produces moderate effects. yet occasionally math generates spectacular paradoxes--conclusions that appear thoroughly unreasonable or simply simple most unlikely yet which are however demonstrably actual. were you aware wasting activities staff can turn into a successful one via including worse avid gamers than its competitors? Or that the 13th of the month is prone to be a Friday than the other day? Or that cones can roll unaided uphill? In Nonplussed!--a delightfully eclectic selection of paradoxes from many various parts of math--popular-math author Julian Havil finds the maths that exhibits the reality of those and plenty of different incredible ideas.
Nonplussed! can pay particular awareness to difficulties from likelihood and statistics, components the place instinct can simply be mistaken. those difficulties comprise the vagaries of tennis scoring, what could be deduced from tossing a needle, and disadvantageous video games that shape successful combos. different chapters handle every little thing from the traditionally vital Torricelli's Trumpet to the mind-warping implications of items that live to tell the tale excessive dimensions. Readers find out about the colourful heritage and other people linked to lots of those difficulties as well as their mathematical proofs.
Nonplussed! will attract an individual with a calculus history who enjoys well known math books or puzzles.
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Additional info for Nonplussed!: Mathematical Proof of Implausible Ideas
Sample text
Images were real if they were concrete or real-world such as "sun" for energy. Model images were abstractions such as "electron density" for orbital. The total number of images recalled and the level of abstraction of the images increased with the experience of the subjects (faculty had better recall than graduate students and graduate students had better recall than undergraduates). 8) were associative whereas only 10% (average of 3 out of 31) of the images reported by faculty were associative.
Problem solving was stressed in one section, but not in the other. The instruction was loosely based on Polya's problem-solving model: (a) understanding the problem, (b) designing the plan, (c) carrying out the plan, and (d) looking back (Polya, 1957). However, the first two stages were combined into one called "planning the solution," partly because Yackel's (1984) work had shown that these stages are not done separately or sequentially. 37 38 HERRON Students were encouraged to ask questions such as, "What is the unknown?
For example, the inclusion of air resistance and other nonlinear phenomena makes possible consideration of more realistic situations in mechanics. Are students sufficiently motivated by real-world examples to warrant using them in place of problems that are conceptually simpler and more readily understood? CONCLUSIONS It is a consequence of the broad scope of activity in research in physics education that the brief overview presented here has omitted so much of what has been done in the last few years.
Nonplussed!: Mathematical Proof of Implausible Ideas by Julian Havil
by Thomas
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