# A Speck on the Sea: Epic Voyages in the Most Improbable by William H. Longyard

By William H. Longyard

*A gripping compendium of noteworthy small-boat voyages revamped the centuries."* --John Harland, writer of *Seamanship within the Age of Sail*

*A Speck at the Sea* chronicles the best ocean voyages tried within the littlest boats. those feats include:

• Diego Mendezs voyage to rescue Columbus

• William Okeley's get away from slavery in a folding rowboat

• Ernest Shackleton's death-cheating journeys

• And extra.

**Read Online or Download A Speck on the Sea: Epic Voyages in the Most Improbable Vessels PDF**

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**Extra resources for A Speck on the Sea: Epic Voyages in the Most Improbable Vessels**

**Sample text**

No statement should be accepted as true unless it has been logically demonstrated beyond a shadow of a doubt. In light of this, there is no place in a mathematical proof for fuzziness or ambiguities. There can be no loopholes. Unfortunately, the need for formality and rigor in the writing of proofs often masks the ideas that ultimately led to the proof. Throughout this book, you will often be required to either read or write proofs. In doing so, you will be forced to write in a very formal and rigorous way.

Presumably, you will observe that in each of the cases you looked at, two colors sufﬁced. The question is, how would you go about proving that two colors always sufﬁce? The proof will proceed by Mathematical Induction. Proof. We need to show that no matter how many lines are used to divide up the plane, we can color the plane using only two colors. To this end, we let T = n ∈ N | whenever a plane is divided up by n lines, it can be colored with 2 colors . We will be done if we can show that T contains all positive integers, and we will do this by applying Mathematical Induction.

X: −4 k(x): −3413 −3 −987 −2 −1 0 −207 −35 −9 1 2 −3 13 3 213 4 1155 Find the smallest positive integer n such that this table can be produced by a polynomial of degree n. ) 18. com = a b + . x+7 x+4 What This Book Is about and Who This Book Is for 17 19. Find real numbers a, b, and c such that 11x2 − 2x + 4 a bx + c = + 2 . x3 + x x x +1 20. When decomposing a rational function into a sum of partial fractions, all the denominators we use are powers of polynomials that cannot be factored any further.