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#	Item
41	How Euler Did It by Ed Sandifer Propulsion of Ships February, 2004 Long before there were Fields Medals or Nobel Prizes, the great scientific academies of Europe regularly proposed problems, with lucrative cash prizes fo Add to Reading List Source URL: eulerarchive.maa.org Language: English - Date: 2013-11-04 12:20:24 Number theorists Leonhard Euler Euler Society Paddle steamer Steamboat Euler Propeller Paddle
42	How Euler Did It by Ed Sandifer Odd Perfect Numbers November 2006 The subject we now call “number theory” was not a very popular one in the 18th century. Euler wrote almost a hundred papers on the subject, but the fi Add to Reading List Source URL: eulerarchive.maa.org Language: English - Date: 2013-11-04 12:20:24 Integer sequences Number theory Divisor function Algebraic number theory Perfect number Modular arithmetic Amicable numbers Divisor Prime number Quadratic reciprocity Leonhard Euler Coprime integers
43	How Euler Did It by Ed Sandifer Finding logarithms by hand July 2005 Today, it is just as easy to take a square root as it is to find a logarithm. You just find your calculator, turn it on, and press a few buttons. The f Add to Reading List Source URL: eulerarchive.maa.org Language: English - Date: 2013-11-04 12:20:24 Logarithms Natural logarithm Common logarithm Geometric mean Exponentiation E Trigonometric functions Contributions of Leonhard Euler to mathematics Binary logarithm
44	How Euler Did It by Ed Sandifer Beyond Isosceles Triangles April, 2004 We know lots about triangles for which ∠A = ∠ B . Such triangles are isosceles, and we have known at least since Euclid that ∠A = ∠ B exactly Add to Reading List Source URL: eulerarchive.maa.org Language: English - Date: 2013-11-04 12:20:24 Triangle geometry Triangles Triangle Euler line Isosceles triangle Altitude Spherical geometry
45	How Euler Did It by Ed Sandifer St. Petersburg Paradox July 2007 If we knew what we were doing, it would not be called research, would it? -attributed to Albert Einstein) Add to Reading List Source URL: eulerarchive.maa.org Language: English - Date: 2013-11-04 12:20:24 Bernoulli family Number theorists Fellows of the Royal Society Leonhard Euler Jacob Bernoulli Nicolaus II Bernoulli St. Petersburg paradox Daniel Bernoulli Ars Conjectandi Nicolaus Bernoulli Utility
46	How Euler Did It by Ed Sandifer A Product of Secants May 2008 When an interesting illustration catches our eye, we sometimes stop to figure out what it is. But when I first saw this illustration I was in a hurry. I resol Add to Reading List Source URL: eulerarchive.maa.org Language: English - Date: 2013-11-04 12:20:24 Trigonometry Dimensionless numbers Ratios Planar graphs Platonic solids Trigonometric functions Sine Regular icosahedron E Triangle Inverse trigonometric functions Circumscribed circle
47	How Euler Did It by Ed Sandifer Density of air July 2009 Leonhard Euler did an immense amount of work in optics, but that work is not very well known among mathematicians. Seven volumes in Series III of the Opera omnia a Add to Reading List Source URL: eulerarchive.maa.org Language: English - Date: 2013-11-04 12:20:24 Mathematical constants Mathematical series Leonhard Euler E Swiss 1.2-metre Leonhard Euler Telescope Differential equation Pi Number theory Book:Leonhard Euler on Fluids Contributions of Leonhard Euler to mathematics
48	How Euler Did It by Ed Sandifer 2aa + bb January 2006 How do we know what to try to prove? A logician, or perhaps a Euclidean geometer, might try to say that we don’t try to prove Add to Reading List Source URL: eulerarchive.maa.org Language: English - Date: 2013-11-04 12:20:24 Integer sequences Leonhard Euler Prime number Number theory
49	How Euler Did It by Ed Sandifer Divergent series June 2006 Today we are fairly comfortable with the idea that some series just don’t add up. For example, the series Add to Reading List Source URL: eulerarchive.maa.org Language: English - Date: 2013-11-04 12:20:24 Divergent series Mathematical series Geometric series Real analysis Summability methods Series 1 2 + 3 4 + 1 + 2 + 3 + 4 + 1 + 2 + 4 + 8 + Taylor series Alternating series Natural logarithm
50	How Euler Did It by Ed Sandifer Euler and the Hollow Earth: Fact or Fiction? AprilIs the earth hollow? Is there a sun 600 miles in diameter at the center of the hollow earth? Is the Add to Reading List Source URL: eulerarchive.maa.org Language: English - Date: 2013-11-04 12:20:24 Earth Obsolete scientific theories Hollow Earth Subterranea Geodesy Leonhard Euler Precession Euler Society Astronomy Figure of the Earth Euler John Cleves Symmes Jr.