Download Slicing Pizzas, Racing Turtles, and Further Adventures in by Robert B. Banks PDF

By Robert B. Banks

Have you daydreamed approximately digging a gap to the opposite aspect of the area? Robert Banks not just entertains such rules yet, higher but, he provides the mathematical information to show fantasies into problem-solving adventures. during this sequel to the preferred Towing Icebergs, Falling Dominoes (Princeton, 1998), Banks offers one other selection of puzzles for readers drawn to sprucing their pondering and mathematical talents. the issues diversity from the wondrous to the eminently functional. in a single bankruptcy, the writer is helping us be certain the whole variety of those who have lived on the earth; in one other, he exhibits how an realizing of mathematical curves will help a thrifty lover, armed with building paper and scissors, retain charges down on Valentine's Day.

In twenty-six chapters, Banks chooses issues which are particularly effortless to investigate utilizing quite basic arithmetic. The phenomena he describes are ones that we come upon in our day-by-day lives or can visualize with no a lot difficulty. for instance, how do you get the main pizza slices with the least variety of cuts? to head from aspect A to indicate B in a downpour of rain, for those who stroll slowly, jog reasonably, or run as quick as attainable to get least rainy? what's the size of the seam on a baseball? If the entire ice on the planet melted, what may take place to Florida, the Mississippi River, and Niagara Falls? Why do snowflakes have six sides?

Covering a extensive diversity of fields, from geography and environmental reviews to map- and flag-making, Banks makes use of easy algebra and geometry to unravel difficulties. If well-known scientists have additionally meditated those questions, the writer stocks the old information with the reader. Designed to entertain and to stimulate considering, this publication should be learn for sheer own leisure.

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Extra resources for Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics

Example text

A curve γ = γ(t) in a contact manifold is called a Legendre curve if η(β (t)) = 0 along β. Let S 2n+1 (c) denote the hypersphere in Cn+1 with curvature c centered at the origin. Then S 2n+1 (c) is a contact manifold endowed with a canonical contact structure which is the dual 1-form of the characteristic vector field Jξ, where J is the complex structure and ξ the unit normal vector on S 2n+1 (c). g. a diffeomorphism of a contact manifold is a contact transformation if and only if it maps Legendre curves to Legendre curves.

23) holds identically if and only if the following four statements hold: ˜ (a) NT is a totally geodesic holomorphic submanifold of M; ˜ with −∇(ln fi ) (b) For each i ∈ {2, . . , k}, Ni is a totally umbilical submanifold of M as its mean curvature vector; ˜ and (c) f2 N2 × · · · ×fk Nk is immersed as mixed totally geodesic submanifold in M; (d) For each point p ∈ N, the first normal space Im hp is a subspace of J(Tp N⊥ ). Remark 1 B. 13 to the following. 19 There exist no warped product submanifolds of the type Mθ ×f MT and MT ×f Mθ in a Kaehler manifold, where Mθ is a proper slant submanifold and ˜ MT is a holomorphic submanifold of M.

6 ([2]) Let N be an anti-holomorphic submanifold in a complex space ˜ 1+p (4c) with h = rank C D = 1 and p = rank D⊥ ≥ 2. Then, we have form M δ(D) ≤ (p − 1)(p + 2)2 2 p H + (p + 3)c. -Y. 46) holds identically if and only if c = 0 and either (i) N is a totally geodesic anti-holomorphic submanifold of Ch+p or, (ii) up to dilations and rigid motions, N is given by an open portion of the following product immersion: φ : C × S p (1) → C1+p ; (z, x) → (z, w(x)), z ∈ C, x ∈ S p (1), where w : S p (1) → Cp is the Whitney p-sphere.

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