The figure above illustrates an example of a Steinmetz solid, a shape formed by the symmetric intersection of two or more cylinders. You can think of the solid shown on the right as the amount of metal you remove when you use a drill of a given radius to bore a hole through a solid pipe of equal radius. A good place to learn more about Steinmetz solids is Martin Gardner's wonderful recreational math book The Unexpected Hanging and Other Mathematical Diversions, which features a Steinmetz solid on its cover.
The Steinmetz solid was named after the legendary Charles Proteus Steinmetz, a mathematician, inventor, electric engineer, educator, and political leader who started up the first GE research lab in the back of his home in a historic neighborhood we'll see on Wednesday's walk, and who later moved it to the GE Realty Plot neighborhood we'll walk through on Tuesday.
An immigrant who had arrived in this country penniless, he brought with him the treasures of a rich mathematical education, including participating in a math circle in his native Germany. (Interestingly, he also added the middle name "Proteus" after coming to this country, choosing a somewhat mathematically-themed name after the Greek god who could change his shape!)
A prolific inventor with 200 patents to his name, Steinmetz once said, "I want to say that absolutely all the success I have had has been due to my thorough study of mathematics." He liked to work on his mathematical calculations on papers spread out on a board across his canoe as he went up and down the Mohawk River.
Steinmetz is best known for a mathematically beautiful formula he invented that uses complex numbers to elegantly simplify the computations needed for alternating current applications. Because of that beautiful formula, he is known as the "the wizard of Schenectady who generated electricity from the square root of negative one."
Despite all his inventions and discoveries, he realized that his greatest power to make a difference in the world lay in his ability to educate others, so he left General Electric to become a professor at Union College and also to lead the Schenectady School Board, providing much needed educational leadership at a time when the city public schools were bursting at the seams. His campaign slogan was "a seat for every child."
Here's what science historian George Wise has to say about Steinmetz.
In the life of the great electrical engineer Charles Proteus Steinmetz (April 9, 1865- October 23, 1923) truth really is stranger than fiction. He's best remembered today for the many myths that grew up around him. Most are pure fiction, or at best gross exaggerations. For example, it's a myth that Steinmetz invented alternating current. Or that when one of his bosses pointed first to Steinmetz's ever-present cigar and then to the "no smoking sign" and told him to put the stogie out, Steinmetz replied: "no smoking, no Steinmetz". Or that Steinmetz was so valuable to his employer, General Electric, that GE gave him not a salary, but a blank checkbook. Or that GE had bought a whole company just to acquire Steinmetz. Or that when Steinmetz, who suffered from scoliosis so severe that he was cruelly called a "hunchback" by the insensitive, was asked why he accepted the post of professor at Union College rather than at a famous Midwest university, he answered" "The choice was simple-- it was either to become the electrical genius of Union College, or the hunchback of Notre Dame."
All that is fiction. The truth is better. The scoliosis, its destructive effects on his stature, and the taunts it inspired were real-- and so was his triumph over disability, a story deservedly celebrated alongside that of the physicist Stephen Hawking. Growing up in Germany, Steinmetz studied mathematics and philosophy-- but also acquired a devotion to socialism that led him to leave the country one step ahead of the police and shortly before completing a Ph.D. thesis in mathematics. Steinmetz really did arrive in America with no money or reputation, but he had letters of introduction and an academic background from the University of Breslau that quickly won him a job in the infant electrical industry. There he made his name by developing his Law of Hysteresis, an important tool for predicting energy losses in equipment using magnetic fields, such as electric motors. GE acquired him by good luck, not design. But his GE bosses were smart enough to recognize his greatness and soon made him their chief consulting engineer. He did not invent alternating current or even invent the mathematics for analyzing alternating current. But he educated the world about that mathematics. His ability to define and solve complicated problems involving the generation, transmission and control of alternating currents in a pre-computer age earned him the nickname "the Supreme Court"-- the final authority on such matters. His own recognition that his greatness was as an educator rather than as a scientist or inventor led him in 1902 to join the Union faculty. He rejuvenated Union's engineering program, and was the first chair of its Electrical Engineering Department. In his spare time, he founded the first research laboratory in the US (now GE Global Research), pioneered environmentalism and electric cars, helped organize a successful Socialist Party that won control of Schenectady city government and installed such improvements as better schools and a park system, and, daring the unpopularity of a German-American appearing to take the German side in World War I, chaired a mass meeting in 1916 calling for neutrality and peace.
His mathematical and educational leadership legacy is a great inspiration to contemplate as we walk through his old stomping grounds on our early morning walking tours of Schenectady.
Our Chapter MATHCOUNTS competition actually takes place on the huge and sprawling GE Global Research Campus in nearby Niskayuna. That 525-acre facility traces its origins to the rather modest quarters in Steinmetz home. I think Steinmetz would be very happy to see all the enthusiastic young problem solvers who come together in those facilities each February.