Cumulative / Accumulate The words accumulate and cumulative both refer to the grouping together of other objects or sets and both come from the ancient Indo-European root kou from which we also get words like cave, cage, cavity and excavate. By the time the Romans adopted cumulare for a heap or collection of objects, the meaning had apparently extended to the pile made in creating a cave or cavity. Today cumulative often refers to successive additions, as in the statistical use, while accumulate often suggests collecting all at once. A cumulus cloud is so called because it looks like a heaped mass, a pile of cloud. Which prompts me to provide a note on cloud names from The Weather DoctorCirrus, stratus, cumulus. We take these terms to describe the clouds above us pretty much for granted these days, often assuming they are names of ancient origin. While great age can be ascribed to their Latin roots, the specific terms for various basic cloud forms are not yet two centuries old and were only accepted as the international standards during the Twentieth Century. The man whom we must credit with developing the basis for our cloud classification system was Luke Howard (1772-1864), an English manufacturing chemist and pharmacist. Like many who observed and studied the workings of the atmosphere at that time, Howard was an amateur meteorologist. Despite that fact he produced several landmark works including On the Modification of Clouds, The Climate of London, and Seven Lectures on Meteorology, the first textbook on weather.
Friday 1 November 2024
On This Day in Math - November 1
If you walk along the street you will encounter a number of scientific problems. Of these, about 80 per cent are insoluble, while 19½ per cent are trivial. There is then perhaps half a per cent where skill, persistence, courage, creativity and originality can make a difference. It is always the task of the academic to swim in that half a per cent, asking the questions through which some progress can be made.
~Sir Hermann Bondi
The 305th day of the year; 305 is the smallest odd composite which is the average of two consecutive Fibonacci numbers. *Number Gossip
305 has two representations as a sum of two squares: 305 = 17^2 + 4^2 = 16^2 + 7^2
305 has two representations as a sum of two squares: 305 = 17^2 + 4^2 = 16^2 + 7^2
It also has two representations as the difference of two squares, 153^2 - 152^2 = 33^2 - 28^2 = 305
".....I beg you most emphatically to communicate your discovery to the learned world, and to send me as soon as possible your theories about the Universe, together with the tables and whatever else you have pertaining to the subject. I have instructed Dietrich von Rheden to make a fair copy of this at my expense and send it to me. If you will do me these favors, you will find that you are dealing with a man who has your interests at heart, and wishes to do full justice to your excellence. Farewell.
1772, Antoine Lavoisier reported in a note to the Secretary of the French Academy of Sciences that in the previous week he had discovered that sulphur and phosphorus when burned increased in weight because they absorbed "air," while the metallic lead formed when litharge was heated with charcoal weighed less than the original litharge because it had lost "air." The exact nature of the airs concerned in the processes he could not yet explain, and he proceeded to study the question extensively. Lavoisier's investigation of the role of air in combustion would change the way chemists viewed combustion. *TIS
1809 Louis Poinsot (1777–1859) named assistant professor of analysis and mechanics at the Ecole Polytechnique. In 1794 he was admitted to the first class at the university despite insufficient knowledge of algebra. *VFR
1812 On 1st November 1812, Davy writes to Jane (his wife), worried that she’ll hear this story from some other source: ‘Yesterday I began some new experiments to which a very interesting discovery & a slight accident put an end. I made one of those compounds more powerful than gunpowder destined perhaps at some time to change the nature of war & influence the state of Society, an explosion took place which has done me no other harm than that of preventing me from working this day & the effects of which will be gone tomorrow & which I should not mention at all, except that you may hear some foolish exaggerated account of it for it really is not worth mentioning’. *Sharon Ruston Blog
1818 Whewell wrote John Herschel that he “would not be surprised if in a short time we were only to read a few propositions of Newton, as a matter of curiosity.” See H. W. Becher, “William Whewell and Cambridge mathematics,” *HSPS, 11(1980), p. 15.
1826 John Boole an amateur mathematician of some ability, would pencil into the cover of the sixth book of Leslie's Geometry, "George Boole finished this book on 1 Nov. 1826." The following day would be George's eleventh birthday. *Desmond MacHale, The Life and Works of George Boole
1844 Gauss in a letter to Schumacher, “I am rather surprised that you expect clarity from a professional philosopher. Muddled concepts and definitions are nowhere more at home than among philosophers who are not mathematicians ... Just look around at today’s philosophers, Schelling, Hegel, Nees von Esenbeck and Co. Don’t their definitions make your hair stand on end? Or, in classical philosophy, read the kinds of things which “stars” like Plato and others (I except Aristotle) gave as explanations. Even Kant is often not much better: his distinction between analytic and synthetic propositions is, I believe, one of those which either turns on a triviality or is false.” [The Mathematical Intelligencer, 1(1978), p. 18]*VFR
1848 in 1848 Boston, Massachusetts, the first medical school for women, Boston Female Medical School (which later merged with the Boston University School of Medicine), opens. *the painter flynn
1884 The International Meridian Conference referenced mean solar time to the 24 standard meridians each of 15 degrees longitude. The international date line was then established to generally follow the 180th meridian in the Pacific Ocean. Previously Lewis Carroll had badgered officials with the question: Leave London at noon and travel with the sun directly overhead, returning the next day. When does the new day begin? *VFR Greenwich Mean Time (GMT) was (more or less) universally adopted at this conference.
1927 40 pfennig violet stamp featuring Leibniz is issued in Germany. According to a 1960 article in Mathematics Magazine by Maxey Brooke of Sweeny Texas this was the first stamp featuring a mathematician in Philatelic history.
1951 Cuba commemorated the 30th anniversary of the winning of the World Chess title by Jose Raul Capablanca by issuing a stamp picturing the resignation play of Dr. Emanuel Lasker (1868-1941). [Scott #C44]. *VFR (The match began March 15, 1921, and ended (prematurely) on April 21, when Lasker retired from the match. At this point he was down 0-4, with 10 draws. Lasker had been champion since 1894. Capablanca retained the title until 1927, when he lost to Alexander Alekhine.)
1957 the Mackinac Bridge, the world's longest suspension bridge between anchorages at the time, opens to traffic connecting Michigan's upper and lower peninsulas. Familiarly known as "Big Mac" and "Mighty Mac" is still the longest suspension bridge between anchorages in the Western Hemisphere. (I regularly use my MacPass for quicker passage through the long holiday lines at the booths.) The name is drawn from the native name for the popular Mackinac Island, which they called Michilimackanac (which many think meant "Great Turtle", but others disagree.)
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| *Wik |
1963 The Arecibo Observatory in Arecibo, Puerto Rico, with the largest radio telescope ever constructed, officially opens. *the painter flynn
2005 A software error related to a system upgrade halted stock and bond trading on the Tokyo Stock Exchange. Problems came to light before the market's opening at 9 a.m. local time and delayed the start of trading until 1:30 p.m. The glitch was the most serious to hit the exchange since 1999, when floor trading was scrapped so that an all-electronic trading system could be installed.
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2017 A nice number fact about today from John Cook at Algebra Fact @AlgebraFact
Today's date is prime if you write it as 11/1/2017, 11/01/2017, or 11/1/17.
i.e. 1112017, 11012017, and 11117 are all prime.
BIRTHS
1535 Giambattista della Porta (1 November 1535 Vico Equense (near Naples), Italy
- 4 February 1615 Naples, Italy) was an Italian scholar who worked on cryptography and also on optics. He claimed to be the inventor of the telescope although he does not appear to have constructed one before Galileo.
In 1563, della Porta published De Furtivis Literarum Notis, a work about cryptography. In it he described the first known digraphic substitution cipher. Charles J. Mendelsohn commented, "He was, in my opinion, the outstanding cryptographer of the Renaissance. Some unknown who worked in a hidden room behind closed doors may possibly have surpassed him in general grasp of the subject, but among those whose work can be studied he towers like a giant."
Della Porta invented a method which allowed him to write secret messages on the inside of eggs. During the Spanish Inquisition, some of his friends were imprisoned. At the gate of the prison, everything was checked except for eggs. Della Porta wrote messages on the egg shell using a mixture made of plant pigments and alum. The ink penetrated the egg shell which is semi-porous. When the egg shell was dry, he boiled the egg in hot water and the ink on the outside of the egg was washed away. When the recipient in prison peeled off the shell, the message was revealed once again on the egg white.
Della Porta was the founder of a scientific society called the Academia Secretorum Naturae (Accademia dei Segreti). This group was more commonly known as the Otiosi, (Men of Leisure). Founded sometime before 1580, the Otiosi were one of the first scientific societies in Europe and their aim was to study the "secrets of nature." Any person applying for membership had to demonstrate they had made a new discovery in the natural sciences.
His private museum was visited by travelers and was one of the earliest examples of natural history museums. It inspired the Jesuit Athanasius Kircher to begin a similar, even more renowned, collection in Rome.
*SAU *Wik
i.e. 1112017, 11012017, and 11117 are all prime.
1535 Giambattista della Porta (1 November 1535 Vico Equense (near Naples), Italy
- 4 February 1615 Naples, Italy) was an Italian scholar who worked on cryptography and also on optics. He claimed to be the inventor of the telescope although he does not appear to have constructed one before Galileo.
In 1563, della Porta published De Furtivis Literarum Notis, a work about cryptography. In it he described the first known digraphic substitution cipher. Charles J. Mendelsohn commented, "He was, in my opinion, the outstanding cryptographer of the Renaissance. Some unknown who worked in a hidden room behind closed doors may possibly have surpassed him in general grasp of the subject, but among those whose work can be studied he towers like a giant."
Della Porta invented a method which allowed him to write secret messages on the inside of eggs. During the Spanish Inquisition, some of his friends were imprisoned. At the gate of the prison, everything was checked except for eggs. Della Porta wrote messages on the egg shell using a mixture made of plant pigments and alum. The ink penetrated the egg shell which is semi-porous. When the egg shell was dry, he boiled the egg in hot water and the ink on the outside of the egg was washed away. When the recipient in prison peeled off the shell, the message was revealed once again on the egg white.
Della Porta was the founder of a scientific society called the Academia Secretorum Naturae (Accademia dei Segreti). This group was more commonly known as the Otiosi, (Men of Leisure). Founded sometime before 1580, the Otiosi were one of the first scientific societies in Europe and their aim was to study the "secrets of nature." Any person applying for membership had to demonstrate they had made a new discovery in the natural sciences.
His private museum was visited by travelers and was one of the earliest examples of natural history museums. It inspired the Jesuit Athanasius Kircher to begin a similar, even more renowned, collection in Rome.
*SAU *Wik
1585 Jan Brożek (Ioannes Broscius, Joannes Broscius or Johannes Broscius;) (1 November 1585 – 21 November 1652) was a Polish polymath: a mathematician, astronomer, physician, poet, writer, musician and rector of the Kraków Academy.
Brożek was born in Kurzelów, Sandomierz Province, and lived in Kraków, Staszów, and Międzyrzec Podlaski. He studied at the Kraków Academy (now Jagiellonian University) and at the University of Padua. He served as rector of Jagiellonian University.
He was the most prominent Polish mathematician of the 17th century, working on the theory of numbers (particularly perfect numbers) and geometry. He also studied medicine, theology and geodesy. Among the problems he addressed was why bees create hexagonal honeycombs; he demonstrated that this is the most efficient way of using wax and storing honey.
He contributed to a greater knowledge of Nicolaus Copernicus' theories and was his ardent supporter and early prospective biographer. Around 1612 he visited the chapter at Warmia and with the knowledge of Prince-Bishop Simon Rudnicki took from there a number of letters and documents in order to publish them, which he never did. He contributed to a better version of a short biography of Copernicus by Simon Starowolski. "Following his death, his entire collection was lost"; thus "Copernicus' unpublished work probably suffered the greatest damage at the hands of Johannes Broscius."
Brożek died at Bronowice, now a district of Kraków. One of the Jagiellonian University's buildings, the Collegium Broscianum, is named for him. *Wik
1828 Balfour Stewart (1 Nov 1828; 19 Dec 1887) Scottish meteorologist and geophysicist noted for his studies of terrestrial magnetism and radiant heat. His researches on radiant heat contributed to foundation of spectrum analysis. He was the first to discover that bodies radiate and absorb energy of the same wavelength. In meteorology, he pioneered in ionospheric science, making a special study of terrestrial magnetism. He proposed (1882) that the daily variation in the Earth's magnetic field could be due to air currents in the upper atmosphere, which act as conductors and generate electrical currents as they pass through the Earth's magnetic field. He also investigated sunspots. In 1887, he died, age 59, soon after suffering a stroke while crossing to spend Christmas at his estate in Ireland. *TIS
1828 William Henry Besant FRS (1 November 1828, Portsea, Portsmouth – 2 June 1917, Cambridge) was a British mathematician, brother of novelist Walter Besant.
In a competition, William won a scholarship to Corpus Christi College, Cambridge in 1844. He took part in Cambridge Mathematical Tripos in 1850, gaining the title of Senior Wrangler. He was also winner of Smith's Prize.
In 1853 William became a Fellow of Saint John's College, Cambridge where he was a lecturer in mathematics until 1889. His pupils included William Burnside, A. W. Flux and G. B. Mathews. Besant served as an examiner for Tripos in 1856, 1857, and 1885. He was also an examiner for University of London from 1859 to 1864. Besant was also a coach for students taking the Tripos; twenty-one of his students placed in the ranks of top ten wranglers. According to Mathews, "he had the great advantage (for a coach) of being equally good in geometry, analysis, and dynamics."
In 1859 Besant vacated his Fellowship with Saint John's college to marry Margaret Elizabeth Willis, daughter of Rev. Robert Willis, a professor of natural philosophy at Cambridge. They had two sons and a daughter. In 1863 Besant published Elementary Hydrostatics, a textbook on fluid statics containing mathematical exercises such as students might face in examination. The book was reprinted several times, and revised in 1892. He also wrote Treatise on Hydromechanics (1867) covering fluid mechanics. His book Elementary Conics came out in 1901.
Besant was a Fellow of the Royal Astronomical Society from 10 February 1854. He became a Fellow of the Royal Society in 1871. In 1883 Cambridge University bestowed upon him, and Edward Routh, the degree Sc.D.. He died on 2 June 1917 and is buried at the Parish of the Ascension Burial Ground in Cambridge. He created the term Glissettes for his studies on the objects for Notes on Roulettes and Glissettes(1871). He writes in the preface:
1864 Ludwig Schlesinger was a mathematician, born in what is now Slovakia, who worked on differential equations *SAU
1880 Alfred L. Wegener (1 Nov 1880; Nov 1930) Alfred Lothar Wegener was a German meteorologist and geophysicist who first gave a well-developed hypothesis of continental drift. He suggested (1912) that about 250 million yrs ago all the present-day continents came from a single primitive land mass, the supercontinent Pangaea, which eventually broke up and gradually drifted apart. (A similar idea was proposed earlier by F.B. Taylor in 1910.) Others saw the fit of coastlines of South America and Africa, but Wegener added more geologic and paleontologic evidence that these two continents were once joined. From 1906, interested in paleoclimatology, he went on several expeditions to Greenland to study polar air circulation. He died during his fourth expedition. *TIS (The hypothesis that continents 'drift' was first put forward by Abraham Ortelius in 1596 * Wik)
1913 Andrzej Mostowski was a Polish mathematician who worked on logic and the foundations of mathematics.*SAU
1919 Sir Hermann Bondi (1 Nov 1919; 10 Sep 2005) Austrian-born British mathematician and cosmologist who, with Fred Hoyle and Thomas Gold, formulated the steady-state theory of the universe (1948). Their theory addressed a crucial problem: "How do the stars continually recede without disappearing altogether?" Their explanation was that the universe is ever-expanding, without a beginning and without an end. Further, they said, since the universe must be expanding, new matter must be continually created in order to keep the density constant, by the interchange of matter and energy. The theory was eclipsed in 1965, when Arno Penzias and Robert Wilson discovered a radiation background in microwaves giving convincing support to the "big bang" theory of creation now accepted.*TIS
1920 Claude Ambrose Rogers FRS (1 November 1920 – 5 December 2005) was an English mathematician who worked on analysis and geometry, and in particular found the Rogers bound for dense packings of spheres and a counterexample to the Busemann–Petty problem. *Wik
1950 Robert B. Laughlin (1 Nov 1950, ) American physicist who (with Daniel C. Tsui and Horst Störmer) received the Nobel Prize for Physics in 1998 for research on the fractional quantum Hall effect. In a current-carrying conductor, the classic Hall effect is the voltage produced at right angles to a magnetic field, as first discovered in 1879. A century later the German physicist Klaus von Klitzing discovered that in a powerful magnetic field at extremely low temperatures the Hall resistance of a semiconductor is quantized in integral "steps". Using even stronger magnetic fields and lower temperatures, Störmer and Tsui discovered fractional steps, explained by Laughlin's theory that the electrons can form a new type of quantum fluid with quasiparticles carrying fractions of an electron's charge. *TIS
1943 Alexander George McAdie (4 Aug 1863, 1 Nov 1943) American meteorologist who was a pioneer in employing kites in the exploration of high altitude air conditions. As a college graduate, McAdie in Jan 1882 joined the Army Signal Service, which preceded the civilian U.S. Weather Bureau. He invented and patented devices to protect fruit from frost. He examined the influence of smoke pollution on the atmosphere, McAdie studied the relation between atmospheric electricity and auroral phenomena, and wrote about lightning as a hazard both in the air and on the ground. He believed that the units used in meteorology should be standardized by adoption of the metric system. McAdie was a founder of the Seismological Society of America. Mt. McAdie (13,799 ft.) in the Sierra Nevada was named for him.*TIS
1962 Thomas MacRobert (4 Apr 1884 - 1 Nov 1962) studied at Glasgow and Cambridge universities. He returned to Glasgow to a series of posts culminating in the professorship. He worked on Complex Analysis. He became President of the EMS in 1921 and was a founder member of the Glasgow Mathematical Association. *SAU
1971 Leonard Jimmie Savage (20 November 1917 – 1 November 1971) was an American mathematician and statistician. Nobel Prize-winning economist Milton Friedman said Savage was "one of the few people I have met whom I would unhesitatingly call a genius." His most noted work was the 1954 book Foundations of Statistics, in which he put forward a theory of subjective and personal probability and statistics which forms one of the strands underlying Bayesian statistics and has applications to game theory.
During World War II, Savage served as chief "statistical" assistant to John von Neumann, the mathematician credited with building the first electronic computer.
One of Savage's indirect contributions was his discovery of the work of Louis Bachelier on stochastic models for asset prices and the mathematical theory of option pricing. Savage brought the work of Bachelier to the attention of Paul Samuelson. It was from Samuelson's subsequent writing that "random walk" (and subsequently Brownian motion) became fundamental to mathematical finance.
In 1951 he introduced the minimax regret criterion used in decision theory.
The Hewitt–Savage zero-one law is (in part) named after him, as is the Friedman–Savage utility function. *Wik
1989 Gerrit Bol (May 29, 1906 in Amsterdam, Nov 1, 1989) was a Dutch mathematician, who specialized in geometry. He is known for introducing Bol loops in 1937, and Bol’s conjecture on sextactic points.
Bol earned his PhD in 1928 at Leiden University under Willem van der Woude. In the 1930s, he worked at the University of Hamburg on the geometry of webs under Wilhelm Blaschke and later projective differential geometry. In 1931 he earned a habilitation.
In 1942–1945 during World War II, Bol fought on the Dutch side, and was taken prisoner. On the authority of Blaschke, he was released. After the war, Bol became professor at the Albert-Ludwigs-University of Freiburg, until retirement there in 1971. *Wik
2000 Ruth I. Michler (March 8, 1967 to November 1, 2000) was an American-born mathematician of German descent who lived and worked in the United States. She earned her Ph.D. in Mathematics from the University of California, Berkeley,[5] and she was a tenured associate professor at the University of North Texas. She died at the age of 33 while visiting Northeastern University, after which at least three memorial conferences were held in her honor, and the Ruth I. Michler Memorial Prize was established in her memory.
Michler earned her Ph.D. in Mathematics in 1993 from the University of California, Berkeley. Her dissertation is titled "Hodge components of cyclic homology of affine hypersurfaces."[5][7] Her advisors were Mariusz Wodzicki and Arthur Ogus. She spent the academic year 1993-1994 as a postdoc at Queen's University working with Leslie Roberts. In 1994, she joined the tenure-track faculty at the University of North Texas where she earned tenure in 2000.
Michler was killed in an accident in Boston on November 1, 2000, when she was struck by a construction vehicle while riding her bicycle.
Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*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
Albert Geoffrey Howson (9 May, 1931 – 1 November 2022) was a British mathematician and educationist.
He started to work as algebraist and in 1954 published the Howson property of groups and proved it for some types of groups. Later he devoted himself to the mathematics education and participated in reforms of mathematics education in the Great Britain and internationally. He was the editor-in-chief and chairman of Trustees of the School Mathematics Project in Great Britain and was involved in many other national and international projects. He worked at University of Southampton as head of the Department of Mathematics and Dean of the Faculty of Mathematical Studies and served as president of the Mathematical Association of Great Britain, and two terms as Secretary of the International Commission on Mathematical Instruction.[1]
Howson died on 1 November 2022, aged 91.
Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*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