Edward Sang is best remembered, when he is remembered at all, as " probably the greatest calculator of logarithms of the 19th century" in the words of Dennis Rogel. Wikipedia adds that he is, "best known for having computed large tables of logarithms, with the help of two of his daughters. (They did not mention the names of the daughters, but in Rogel's paper he cites Flora and Jane.) These tables went beyond the tables of Henry Briggs, Adriaan Vlacq, and Gaspard de Prony."
I first became acquainted with Sang while researching the history of near equilateral triangles, like 3,4,5 or 13,14,15, or 51,52,53. Sang found a Pell equation for the square root of three gave an infinite number of even middle sides for such triangles. He was looking at these triangles with a special focus, were the areas commensurable numbers, what he called a theory of commensurables. We could form a triangle with any three consecutive integers, but were the areas also integers (commensurable with the nits of the sides).
Sang even listed a 1,2, 3 triangle with area of zero. For the triangles above, the areas are all integers, 12, 84, and 1170.
Here is Sang's list:
But this was just one of the questions about commensurables. Sang begins his inquiry thinking about the incommensurables that might have sparked interest in early mathematicians about this problem. Consider the simple forms of geometry. The equilateral triangle with integer sides has an altitude that is not an integer. The square with integral sides has diagonals that are not integers. Regular hexagons, because they are made of equilateral triangles have their major diagonal as integers, twice the side length. Sang imagined exploring areas, and other features of each shape.
Sang opens his paper with this general statement, "The general proposition in the theory of commensurables is to determine the conditions under which lines, surfaces, or solidities, connected with prescribed figures or forms, may have their ratios expressible by integer numbers."
"Many problems of a similar nature may be proposed: thus we may require that the three sides of a trigon, and the line bisecting one of the angles, be all commensurable ; that the four sides and the two diagonals of a tetragon be all expressed by integer numbers, and so on.The methods of solving such problems may be said to constitute the theory of commensurables."
His first study is upon right triangles and what we today call primitive Pythagorean triangles, or PPT, and he proceeds to a number of interesting explorations. I think the article would be a great exploration for teacher and student alike.
Some proofs command assent. Others woo and charm the intellect.
They evoke delight and an overpowering desire to say, 'Amen, Amen'.
~Sir John William Strutt, Lord Rayleigh
The 316th day of the year; 316 can be written as the sum of 3 consecutive triangular numbers.
316 is also a centered triangular number (these two definitions turn out to be identical, all sums of 3 consecutive triangular numbers are centered triangular numbers, and vice-versa) The nth Centered triangle number has a single point at the center (the first centered triangular number) , and triangles surrounding it with 2,3,..., n dots on a side. The fourth centered triangular, 19 =3+6+10, number is shown
Students often enjoy finding cycles in the "sort then add" sequence. 316 is the only year date that does not reach a sorted number to terminate(at least we haven't found it yet) . [If a number is not sorted, then add n to sorted n, for example 21 is not sorted, so f(21)= 21+12=33 (a sorted number) 65 is not sorted, so f(65)= 65+56 = 121, still not sorted so do 121+112= 233, a sorted number so f(65) terminates in 233]
EVENTS
1673 Christopher Wren is appointed architect of the new St. Paul’s by Royal Warrant. Wren had been one asked for an opinion on the renovation needed on Old St Paul'sin 1663 and had recommended foundation work and a facelift. In a few years it would need a lot more. *Lisa Jardine, Ingenious Pursuits pg 71
1680 Leeuwenhoek writes to Hooke suggesting that all reproduction is sexual
But in my opinion we can now be assured sufficiently that no animals, however small they may be, take their origin in putrefaction, but exclusively in procreation... For seeing that animals, from the largest down to the little despised animal, the flea, have animalcules in their semen, seeing also that some of the vessels of the lungs of horses and cows consist of rings and that these rings can occur on the flea's veins, why cannot we come to the conclusion that as well as the male sperm of that large animal the horse and similar animals, and of all manner of little animals, the flea included, is furnished with animalcules (and other intestines, for I have often been astonished when I beheld the numerous vessels in a flea), why, I say should not the male sperm of the smallest animals, smaller than a flea may even the very smallest animalcules have the perfection that we find in a flea.
— Antonie van Leeuwenhoek * The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 3,
1733 Abraham DeMoivre privately presented to some friends the normal distribution curve. *School Science and Mathematics, vol. 62, p. 172
He privately presented the normal distribution curve to friends on November 12, 1733, in a seven-page pamphlet titled “Approximatio ad Summam Terminorum Binomii a + b in Seriem expansi” *PB
Although the context of De Moivre’s discovery had to do with binomial events (i.e., two possible outcomes) and gambling procedures, the curve has extensive application to errors of measurement, a fact that has made it useful for the work of observing the movements of planets and stars. In addition, the curve approximates all sorts of raw score distributions, such as the heights of adult males in a given homogeneous population, obtained IQ scores for a given population, some personality variables, as well as innumerable naturally occurring variables, including things like the weight of a given species of wild rabbits and even the widths of foreheads of crabs. It was De Moivre who worked-out the area under the curve for distances up to three standard deviations. Because he worked out the formula for the normal curve and the areas under the curve, De Moivre is duly credited with the normal curve’s discovery. However, other mathematicians deserve credit for popularizing it.*Paul Hesselroade
1792 After subscriptions to his Universal Tontine Association failed to meet expectations, Samual Blodgett met with the investors in the scheme and adopted articles of association forming the Insurance Company of North America (INA), the oldest stock insurance company in the United States, giving the company the ability to write fire, life, or marine insurance. Other fire insurance companies existed in Philadelphia, but INA was the first to include protection of the contents rather than just the building. The first policy was issued to Nesbitt's mercantile firm, Conyngham, Nesbitt & Co., for the ship America on its voyage from Philadelphia to Londonderry. The Universal Tontine was a sort of early annuity fund that also acted as a lottery for the members who survived beyond the 21 year limit, when they would share the remains.*Wik
INA firemark circa 1801–1830, as found on a house in the Society Hill neighborhood of Philadelphia, 2013.
In 1799, Andrew Ellicott wrote the first known record of a meteor shower observed in the U.S. He viewed the display from a ship off the coast of Florida Keys at full moon. He wrote: "In every instant the meteors were as numerous as the stars," and that the "whole heaven appeared as if illuminated with sky rockets, flying in an infinity of directions, and I was in constant expectation of some of them falling on the vessel. They continued until put out by the light of the sun after day break." His account was read to the American Philosophical Society on 16 Jan 1801. The Leonids meteor shower is an annual event that is greatly enhanced every 33 years when accompanied by the appearance of the comet Tempel-Tuttle. *TIS *History of Astronomy @hist_astro Image from The midnight sky, notes on the stars and planets By Edwin Dunkin
1802 The United States Military Philosophical Society was founded at West Point. Jonathan Williams, nephew of Benjamin Franklin and superintendent of the Academy was the first president. Members received an attractive certificate bearing a scene of the destruction of the Roman fleet at Syracuse by means of Archimedes’ mirror and the motto “Scientia in bello pax” (The use of science in war leads to peace). *VFR In 1833, the great shower of the Leonid Meteors was recorded. Many observers
clearly reported that the meteors seemed to radiate from a spot in Leo and that, as the constellation moved slowly westward during the night, the radiant point moved with it. Within weeks a Yale mathematician, Denison Olmsted, showed that this radiant point was simply an effect of perspective. The millions of meteors that fell that night had in fact been moving along parallel paths. They appeared to diverge from a point in Leo for the same reason that parallel lines on the ground (such as railroad tracks), appear to diverge from a point on the horizon. Following this realization, the meteors were given the Latin family name for their apparent place of origin: the Leonids.*TIS According to some sources, the 1934 jazz standard, "Stars Fell on Alabama", composed by Frank Perkins with lyrics by Mitchell Parish, refers to this occurrence of the Leonids. As reported by the Florence Gazette: "[There were] thousands of luminous bodies shooting across the firmament in every direction. There was little wind and not a trace of clouds, and the meteors succeeded each other in quick succession." *Wik In 1901, the first Nobel Prize for Physics was awarded to Wilhelm Roentgen for his discovery of X-rays.*TIS\
Wilhelm Röntgen discovered X-rays by accident in November 1895 while experimenting with cathode rays. He took the first medical X-ray image of his wife, Anna Bertha Ludwig's, hand just weeks after his discovery. The resulting image clearly showed the bones of her hand and her wedding ring, demonstrating the new technology's ability to see inside the human body. This simple image marked a pivotal moment in medical history, and Röntgen's work led to him winning the first Nobel Prize in Physics in 1901.
1906 Alberto Santos-Dumont, Brazilian aviation pioneer, flew his 14-BIS airplane a distance of 220 meters, height of 6 m. and speed of 37 km/h. to win the "Archdecon Prize." In 1909, he produced his famous "Demoiselle" or "Grasshopper" monoplanes, the forerunners of the modern light plane. *Wik
1906 “The unique strength of Cambridge, as a place of experimental research, and as a leader in the advancement of Science generally, has depended greatly on the mathematical foundations given a large portion of all the undergraduates by the mathematical Tripos.” So wrote William Thomson, by then Lord Kelvin. See H. W. Becher, “William Whewell and Cambridge Mathematics,” HSPS, 11(1980), p. 15. *VFR Kelvin was very confident of his own mathematical ability and the story is told that on the day of the examination results were released he sent his servant to find out, "Who is second wrangler?" He was devastated when the servant returned to answer, "You, Sir.". *Walter Gratzer, Eurekas and Euphorias, pg 21
1937 Alan Turing’s paper entitled On Computable Numbers with an Application to the Entscheidungs-problem appeared on November 12, 1937, somewhat contemporaneously with Konrad Zuse’s work on the first of the Z machines in Germany, John Vincent Atanasoff ‘s work on the ABC, George Stibitz’s work on the Bell Telephony relay machine, and Howard Aiken’s on the Automatic Sequence Controlled Calculator. Later renamed the Turing Machine, this abstract engine provided the fundamental concepts of computers that the other inventors would realize independently. So Turing provided the abstraction that would form the basic theory of computability for several decades, while others provided the pragmatic means of computation.*CHM
1950 Clarence Leonidas Fender (August 10, 1909 – March 21, 1991) was an American inventor and founder of the Fender Musical Instruments Corporation.
Fender designed the company's iconic early instruments: the Fender Telecaster, the first mass-produced solid-body electric guitar; the Fender Stratocaster, among the most iconic electric guitars; and the Fender Precision Bass, which set the standard for electric basses. He also designed the Fender Bassman amplifier, which became the archetype for later amplifiers (notably by Marshall and Mesa Boogie) that dominated rock and roll music.
Fender, who was not a guitarist himself, and although he developed electric instruments that revolutionized rock and roll, Leo Fender never learned how to play guitar. He was inducted posthumously into the Rock and Roll Hall of Fame in 1992.
First prototype of the Fender Esquire (1949)
In 1980, the space probe Voyager I traveled under the rings and within 77,000 miles of Saturn.*TIS
2002 Grigori Perelman posts the first of a series of eprints to the arXiv, in which he proves the century old Poincaré conjecture. On 22 December 2006, the journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year", the first such recognition in the area of mathematics. *Wik
BIRTHS
1746 Jacques-Alexandre-César Charles (12 Nov 1746; 7 Apr 1823) French mathematician, physicist, and inventor. When Benjamin Franklin visited France in 1779, Charles was inspired to study physics. He soon became an eloquent speaker to non-scientific audiences. His lectures and demonstrations attracted notable patrons and helped popularize Franklin's theory of electricity and other new scientific concepts. With Nicolas and Anne-Jean Robert, he made several balloon ascents, and was the first to use hydrogen for balloon inflation (1783). Charles invented most of the equipment that is still used in today's balloons. About 1787 he developed Charles's law concerning the thermal expansion of gases that for a gas at constant pressure, its volume is directly proportional to its absolute temperature. *TIS
For the record....He didn't. Among everything else, JAC Charles was almost incompetent at any mathematical level. Jacques Alexandre César Charles (1746–1823) did not technically “discover” Charles’s Law in the modern experimental sense, even though the law bears his name.
Around 1787, Charles observed that gases expand in proportion to temperature (at constant pressure). However, he never published his findings. His work was only mentioned secondhand by Joseph Louis Gay-Lussac in 1802. Gay-Lussac credited Charles, saying the idea was his earlier, and so the law became known as “Charles’s Law.” But the first careful measurements confirming the relationship between gas volume and temperature were actually done by Gay-Lussac himself, not by Charles.
*Linda Hall Org
1825 Mikhail Vashchenko-Zakharchenko (October 31 O.S.) (November 12) 1825 – August 14 (O.S.) (August 27) 1912 worked on the theory of linear differential equations, the theory of probability and non-euclidean geometry.*SAU
From the start of 1870s Vaschenko-Zakharchenko began to read the course of the projection geometry, and from 1878 — the course of non-Euclidean geometry (basics of the Lobachevsky geometry). In 1880 he published the translation of Beginnings of Euclid with a big introduction where were viewed the main principles of the hyperbolic geometry.
He is an author of more than dozen textbooks on the analytical geometry, projection geometry, algebra, calculus of variations, and including an important work on the history of mathematics in which he discussed the history of mathematics up to the 15th century.*Wik
1835 Hugues Charles Robert Méray (November 12, 1835, Chalon-sur-Saône, Saône-et-Loire - February 2, 1911, Dijon) was a French mathematician. Méray sought to establish rigorously that any Cauchy sequence converges.He is noted as the first to publish an arithmetical theory of irrational numbers.
In 1869, he was the first to give a rigorous construction of real numbers . This construction is based on the consideration of the equivalence class of Cauchy sequences of rational numbers . Georg Cantor gave a similar construction of real numbers . Karl Weierstrass started from the notion of "aggregates" to construct 𝑅
.Richard Dedekind , finally, will start from the notion of cutting the set of rationals for his construction of 𝑅
{\displaystyle \mathbb {R} }"arithmetization of analysis."
His work did not have much of a role in the history of mathematics because France, at that time, was less interested in such matters than Germany.*Wik
1842 John William Strutt, 3rd Baron of Rayleigh (of Terling Place) (12 Nov 1842; 30 Jun 1919) was an English physical scientist who made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He received the Nobel Prize for Physics in 1904 for his investigations into the densities of the most important gases and his successful isolation of argon, an inert atmospheric gas. *TIS
A favorite quote from Strutt, Some proofs command assent. Others woo and charm the intellect. They evoke delight and an overpowering desire to say, "Amen, Amen".1891 Seth Barnes Nicholson (12 Nov 1891; 2 Jul 1963) was an American astronomer best known for discovering four satellites of Jupiter. As a graduate student at the University of California, while photographing the recently-discovered 8th moon of Jupiter with the 36-inch Crossley reflector, he discovered a 9th (1914). During his life career at Mt.Wilson Observatory, he discovered two more Jovian satellites (1938) and the 12th (1951), as well as a Trojan asteroid, and computed orbits of several comets and of Pluto. His main assignment at Mt. Wilson was observing the sun with the 150-foot solar tower telescope, and he produced annual reports on sunspot activity and magnetism for decades. With Edison Pettit, he measured the temperatures of the moon, planets, sunspots, and stars in the early 1920s. *TIS
1910 Hua Luogeng (12 November 1910 – 12 June 1985) was a Chinese mathematician born in Jintan, Jiangsu. He was the founder and pioneer in many fields in mathematical research. He wrote more than 200 papers and monographs, many of which became classics. Since his sudden death while delivering a lecture at the University of Tokyo, Japan, many mathematics secondary education programs have been named after him. His book on additive prime number theory influenced many subsequent number theorists in China, including the renowned Chen Jingrun who obtained the best result so far towards the binary Goldbach conjecture.*Wik
1923 Irving Stoy Reed (November 12, 1923 in Seattle, Washington- September 11, 2012) is a mathematician and engineer. He is best known for co-inventing a class of algebraic error-correcting and error-detecting codes known as Reed-Solomon codes in collaboration with Gustave Solomon. He also co-invented the Reed-Muller code. Reed has made many contributions to areas of electrical engineering including radar, signal processing, and image processing. He was part of the team that built the MADDIDA, guidance system for Northrop's Snark cruise missile - one of the first digital computers. He developed and introduced the now-standard Register Transfer Language to the computer community while at M.I.T. Lincoln Laboratory. He had been a faculty member of the Electrical Engineering-Systems Department of the University of Southern California from 1962 to 1993. *Wik
1927 Yutaka Taniyama (November 12, 1927, Kisai near Tokyo – November 17, 1958, Tokyo) was a Japanese mathematician known for the Taniyama-Shimura conjecture. Taniyama was best known for conjecturing, in modern language, automorphic properties of L-functions of elliptic curves over any number field. A partial and refined case of this conjecture for elliptic curves over rationals is called the Taniyama-Shimura conjecture or the modularity theorem whose statement he subsequently refined in collaboration with Goro Shimura. The names Taniyama, Shimura and Weil have all been attached to this conjecture, but the idea is essentially due to Taniyama. In 1986 Ribet proved that if the Taniyama-Shimura conjecture held, then so would Fermat's last theorem, which inspired Andrew Wiles to work for a number of years in secrecy on it, and to prove enough of it to prove Fermat's Last Theorem. Due to the pioneering contribution of Wiles and the efforts of a number of mathematicians the Taniyama-Shimura conjecture was finally proven in 1999. The original Taniyama conjecture for elliptic curves over arbitrary number fields remains open, and the method of Wiles and others cannot be extended to provide its proof.*Wik
1948 Gerard J. Murphy (12 November 1948 – 12 October 2006) MRIA was a prolific Irish mathematician. His textbooks are internationally acclaimed, and translated into different languages. He died from cancer in October 2006, at the age of 57.
Gerard's research was in functional analysis. In recent times his research was on quantum groups and non-commutative geometry, subjects of importance both for mathematics and physics. He authored more than 70 original mathematical papers, singly or with colleagues in Ireland, Europe and North America. He will also be remembered for his book, C*-algebras and Operator Theory, which was published in 1990 to worldwide acclaim.
Gerard's principal interests were in the general theory of C*-algebras, the spectral and index theory of Toeplitz operators on Hardy spaces of ordered groups and bounded symmetric domains, and the C*-algebra approach to quantum groups.
"Gerard Murphy, like Pythagoras and Boole before him, discovered new mathematical truths, truths that will last forever. Generations of future students and researchers will build on and develop these results." Associate Professor Des MacHale, University College Cork *Wik
DEATHS
1793 Jean-Sylvain Bailly (15 Sep 1736, 12 Nov 1793) French astronomer, first Mayor of Paris (1789-91), was guillotined in Paris during the French Revolution. Noted for his computation of an orbit for Halley's Comet (1759) and for his studies of the four satellites of Jupiter then known. *TIS 1916 Percival Lowell (13 Mar 1855, 12 Nov 1916) American astronomer who predicted the existence of the planet Pluto and initiated the search that ended in its discovery. Lowell was also passionately committed to finding proof of intelligent life on Mars. In 1894, he founded the Lowell Observatory, atop Mars Hill, at Flagstaff as Arizona's first astronomical observatory. Studying Mars, Lowell drew in intricate detail, the network of several hundred fine, straight lines and their intersection in a number of "oases." Lowell concluded that the bright areas were deserts and the dark ones were patches of vegetation. He believed further, that water from the melting polar cap flowed down the canals toward the equatorial region to revive the vegetation. *TIS
*Wik
1944 Ludwig Otto Blumenthal (20 July 1876 – 12 November 1944) was a German mathematician and professor at RWTH Aachen University.
He was born in Frankfurt, Hesse-Nassau. A student of David Hilbert, Blumenthal was an editor of Mathematische Annalen. When the Civil Service Act of 1933 became law in 1933, after Hitler became Chancellor, Blumenthal was dismissed from his position at RWTH Aachen University. He was married to Amalie Ebstein, also known as 'Mali' and daughter of Wilhelm Ebstein.
Blumenthal, who was of Jewish background, emigrated from Nazi Germany to the Netherlands, lived in Utrecht and was deported via Westerbork to the concentration camp, Theresienstadt in Bohemia (now Czech Republic), where he died.
In 1913, Blumenthal made a fundamental, though often overlooked, contribution to applied mathematics and aerodynamics by building on Joukowsky's work to extract the complex transformation that carries the latter's name, making it an example of Stigler's Law of eponymy. *Wik
1944 George David Birkhoff (21 Mar 1884, 12 Nov 1944) American mathematician, foremost of the early 20th century, who formulated the ergodic theorem. As the first American dynamicist, Birkhoff picked up where Poincaré left off, gaining distinction in 1913 with his proof of Poincaré's Last Geometric Theorem, a special case of the 3-body problem. Although primarily a geometer, he discovered new symbolic methods. He saw beyond the theory of oscillations, created a rigorous theory of ergodic behavior, and foresaw dynamical models for chaos. His ergodic theorem transformed the Maxwell- Boltzmann ergodic hypothesis of the kinetic theory of gases (to which exceptions are known) into a rigorous principle through use of the Lebesgue measure theory. He also produced a mathematical model of gravity. *TIS
1969William F. Friedman (24 Sep 1891; 12 Nov 1969) one of the world's greatest cryptologists, who helped decipher enemy codes from World War I to World War II. He was born as Wolfe Friedman.in Kishinev, Russia. He emigrated to the U.S. in 1893. Originally trained as an agricultural geneticist, he had become interested in cryptology. During World War I, with his wife Elizebeth, he set up a cryptology school for military personnel, which led to appointment by the U.S. as head of the Signal Intelligence Service (1930). He broke the Japanese "Purple" code (1937-40), thus allowing Americans to read much of Japan's secret messages during World War II. *TIS There is a bust of him at the National Cryptologic Museum in Fort Meade Maryland on which he is identified as the "Dean of American Cryptology". There is an interesting biography here .
1974 Seishi Kikuchi (August 25, 1902 – November 12, 1974) was a Japanese physicist, known for his explanation of the Kikuchi lines that show up in diffraction patterns of diffusely scattered electrons.
Seishi Kikuchi was born and grew up in Tokyo. He graduated in 1926 from Tokyo Imperial University.
In 1928, Kikuchi and Shoji Nishikawa observed and gave a theoretical explanation of the electron backscatter diffraction pattern from a calcite cleavage face. In 1929, he went to Germany as a student and stayed at the University of Göttingen and Leipzig University. In 1934, he was appointed as professor at Osaka Imperial University and directed the construction of Japan's first DC high voltage Cockcroft-Walton accelerator.
In 1955, he was appointed as the first director of the Institute of Nuclear Research at the University of Tokyo, and successfully presided over the completion of the variable energy cyclotron.
Between 1959 and 1964, he was chairman of the Japan Atomic Energy Research Institute.
*Wik
2000 Jacob Willem "Wim" Cohen (27 August 1923 Leeuwarden – 12 November 2000) was a Dutch mathematician, well known for over hundred scientific publications and several books in queuing theory.
Having acquired an autodidact knowledge of mathematics while in hiding during World War II, Cohen got an Engineer's degree (1949) and Ph.D. degree (1955) in mechanical engineering at Delft University, on a dissertation titled Stress Calculations in Helicoidal Shells and Propeller Blades. He worked as teletraffic engineer with the Telecommunications group at Philips (1950–57), at the applied mathematics department at Delft (1957–73) and University of Utrecht (1973-1998). He was buried in Haifa.
Some of his many works:
The single server queue (1969)
Statistical Power Analysis for the Behavioural Sciences (Academic Press, 1969)
On regenerative processes in queueing theory
Boundary value problems in queueing systems (Elsevier, 1983). Editor with Onno J. Boxma.
Analysis of random walks (IOS Press, 1992)*Wik
*CHM=Computer History Museum *FFF=Kane, Famous First Facts *NSEC= NASA Solar Eclipse Calendar *RMAT= The Renaissance Mathematicus, Thony Christie *SAU=St Andrews Univ. Math History *TIA = Today in Astronomy *TIS= Today in Science History *VFR = V Frederick Rickey, USMA *Wik = Wikipedia *WM = Women of Mathematics, Grinstein & Campbell
Ephraim McDowell (November 11, 1771 – June 25, 1830) was an American physician and pioneer surgeon. The first person to successfully remove an ovarian tumor, he has been called "the father of ovariotomy" as well as founding father of abdominal surgery.
McDowell was born in Rockbridge County, Virginia, the ninth child of Samuel and Mary McDowell. His father was a veteran of the French and Indian War and a colonel during the American Revolution. In 1784 Samuel McDowell was appointed land commissioner and moved his family to Danville, Kentucky. There, he presided over ten conventions that resulted in the drafting of the Kentucky Constitution.[4][page needed] Samuel was the 2nd great-grandfather of First Lady Mary Todd Lincoln, making her Ephraim McDowell's great-grandniece.
McDowell received his early education at the classical seminary of Worley and James, then spent three years as a medical student under Dr. Alexander Humphreys in Staunton, Virginia. He attended lectures in medicine at the University of Edinburgh, Scotland, from 1793 to 1794 and studied privately with John Bell. He never received a diploma, but in 1825, the University of Maryland conferred on him an honorary M.D. degree.
In 1795, McDowell returned from Scotland, settled in Danville, Kentucky, and began his practice as a surgeon. McDowell perfected the modern surgical technique of lithotomy for removal of stones obstructing the urinary bladder. One of his most famous patients was James K. Polk, for whom he removed a urinary stone and repaired a hernia.
On December 13, 1809, McDowell was called to see Jane Todd Crawford in Green County, Kentucky, 60 miles from Danville. Her physicians thought that Mrs. Crawford was beyond term pregnant. McDowell diagnosed an ovarian tumor. Mrs. Crawford begged him to keep her from a slow and painful death. He then described her condition and that an operation for cure had never been performed. He said that the best surgeons in the world thought it impossible. Mrs.Crawford said she understood and wanted to proceed. McDowell told her he would remove the tumor if she would travel to his home in Danville. She agreed and rode the 60 miles on horseback.
On Christmas morning, 1809, McDowell began his operation. The surgery was performed without benefit of anesthetic or antisepsis, neither of which was then known to the medical profession. The tumor McDowell removed weighed 22.5 pounds (10.2 kg). He determined that it would be difficult to remove completely, so he tied a ligature around the fallopian tube near the uterus and cut open the tumor. He described the tumor as the ovarium and fimbrious part of the fallopian tube that was very much enlarged. The whole procedure took 25 minutes. Crawford made an uncomplicated recovery. She returned to her home in Green County 25 days after the operation and lived another 32 years. This was the first successful removal of an ovarian tumor in the world.
All attempts at abdominal exploration before 1809 had resulted in peritonitis and death. Descriptions of McDowell include phrases like "neat and clean" or "scrupulously clean." He was not only neat, but meticulous. In his report on the operation, he described the removal of blood from the peritoneal cavity and bathing the intestines with warm water.
McDowell did not publish a description of his procedure until 1817, after he had performed two more such operations. This was widely criticized in the English surgical literature. There is evidence that he performed at least 12 operations for ovarian pathology.
"Having never seen so large a substance extracted, nor heard of an attempt, or success attending any operation such as this required, I gave to the unhappy woman information of her dangerous situation. The tumor appeared full in view, but was so large we could not take it away entire. We took out fifteen pounds of a dirty, gelatinous looking substance. After which we cut through the fallopian tube, and extracted the sac, which weighed seven pounds and one half. In five days I visited her, and much to my astonishment found her making up her bed."
From 1809 and 1818, McDowell wrote about four separate ovariotomies following Crawford's. All four were performed on enslaved women, three of whom survived and one of whom died. It is unclear whether the enslaved women he performed surgeries on gave consent or received sufficient time to recover following the procedure.
A commemorative stamp honoring Ephraim McDowell, was issued December 3, 1959, the 150th anniversary of successful ovarian operation
In 1802, McDowell married Sarah Shelby, daughter of war hero and two-time Kentucky governor Isaac Shelby. They had two sons and four daughters.
McDowell played a prominent role in his community. He was also a founder, original corporator, and member of the primary board of trustees of Centre College in Danville. McDowell became a member of the Philadelphia Medical Society in 1817. McDowell was the great-great-grandfather of General John Campbell Greenway, whose statue was placed in the National Statuary Hall Collection by the state of Arizona in 1930. He was cousin to woman's suffrage leader Madeline McDowell Breckinridge.
McDowell was a Presbyterian but became an Episcopalian and founded Trinity Episcopal Church in Danville, Kentucky, having donated the land for its first building.
0, McDowell was stricken with an acute attack of violent pain, nausea, and fever. He died on June 25, most likely a victim of appendicitis. His wife died 18 years later. They were buried at "Traveller's Rest", the homestead of Isaac Shelby, south of Danville, Kentucky but were reinterred in 1879, near a monument dedicated to him in Danville.
In 1879, a monument in his honor was erected by the Medical Society of Kentucky in Danville.
In 1929, Isaac Wolfe Bernheim donated a bronze statue of McDowell by Charles Henry Niehaus to the state of Kentucky for placement in the U.S. Capitol's National Statuary Hall Collection. The statue depicts the ovarian tumor that McDowell removed from Jane Crawford, sitting in a bowl on the table behind McDowell. An identical statue by the same artist stands in the rotunda of the Kentucky State Capitol in Frankfort, Kentucky. *Wik
I have live back to back with Jerry and Martha (McDowell) Hinton for 16 years. Two incredible people who seemed to be best friends with everyone in Western Kentucky. Today while having an art day in my wife, Jeannie's studio, she shared the early details of this post . It is hard to believe that any of his decedents could better represent the character and civility of Ephraim McDowell than his third great grand niece.
As I mentioned before, I'm re-posting some of the most popular blogs of recent years. This one, "Surprisingly Constant" was from 2010, but I've added a bit at the end from the amazing graphics mathematical posts of "3Blue 1 Brown."
Some things never change... and some of the things that don’t change are pretty remarkable. I was recently reminded of two that always seemed non-intuitive, and therefore quite pleasing. Both of these can be proved toward the end of a first year calculus course, and at least one can be explained with a little hand-waving, by a good pre-calc student.
The first is the simple fact that if you take a slice a sphere with a pair of parallel planes that are some distance, d, apart; the surface area of the part of the sphere between those planes is the same no matter where the slices are made. Near the “poles” or near the “equator”, the area is the same. It is nice to be able to tell students that this incredibly interesting fact was known to Archimedes in the first Century of the modern era when he proved that the surface area of a sphere is the same as the lateral area of a cylinder that contains the sphere. This image is part of an explanation provided at a math site at the University of Regina
The essence of the explanation uses nothing beyond similar triangles. If we approximate the sphere’s surface between the slicing planes as a frustum of a cone, then the slant height (AP) can be shown to be in the same proportion to the height (AB)as the radius of the frustum (QP) is to the radius of the sphere(KP)). This image is also from the U Regina site mentioned above.Another nice thing about this relation is that when you set up the rather fearsome looking integral for the surface area, it reduces through simple algebra to a constant.
For a different look at this with some beautiful graphics, as well as several nice explanations of why the formula for the surface area of a sphere is four times the area of a circle, see this 3Blue, 1Brown video on YouTube.
The second similarly interesting idea is about the volume of a shape I call a bead, for lack of a more precise term. The bead is the solid remaining when you drill through the center of a sphere.The unexpected constant here is that for any radius sphere you start with, the volume of the bead depends only on the height. And perhaps even less expected, is that the volume is the same as the volume of an un-drilled sphere with the same height (i.e., when 2r = h).
I have found a beautiful non-calculus proof of this using an idea from Mamikon Mnatsakanian work with his visual geometry.
