Tuesday 15 August 2023

On This Day in Math - August 15

 voyager exits solar system 1990, see Events(2006)

The 227th day of the year; 227 is a prime number, but it can also be written as the sum of the sum and the product of the first four primes: (2 + 3 + 5 + 7)+(2 x 3 x 5 x 7) = 227. In a similar way, the first two primes work (2+3)+(2x3)=11 is prime. Can you find another? (Ben Vitale has found all the cases under 1000 for which p = (a + b + c + … ) + (a * b * c …) He even found another way to express 227. His blog also has lots of other number curiosities, so give it a look. Much fun.

The harmonic sequence, or sum of the reciprocals of the integers grows to infinity, but slowly. It takes the 227th term (1/227) to finally push it over the value 6.(And don't even think about trying to get to seven!)
A beauty about six primes, 227 + 251 + 257 = 233 + 239 + 263, and if you square each one, 227^2 + 251^2 + 257^2 = 233^2 + 239^2 + 263^2 *Prime Curios.

227 is also the largest odd day number of the year which can NOT be expressed as a prime added to twice a square. There are three others you might find, and three others larger than 366. Observe that these are all seven prime.[OEIS gives ten numbers that include 1, 5779, and 5993. These last two are composite. and that seems to be ALL of them that exist. if there are more, they are larger than 10^13.)
This problem is based on an original conjecture by C Goldbach that all ODD COMPOSITE numbers could be written as twice a square plus a prime. The last two show he was wrong.

227 is the 7^2 prime number *Prime Curios

The harmonic sequence, or sum of the reciprocals of the integers grows to infinity, but slowly. It takes the 227th term (1/227) to finally push it over the value 6.(And don't even think about trying to get to seven!)

A beauty about six primes, 227 + 251 + 257 = 233 + 239 + 263, and if you square each one, 227^2 + 251^2 + 257^2 = 233^2 + 239^2 + 263^2 *Prime Curios.

227 is a palindrome in base eight (343)

The number (7 * 10^227+71)/3 Forms a prime with the digit 2 followed by 225 digits of 3, then ending in 57
Students might try a few starting with 3, ,4, etc.

22/7 is a common approximation for Pi in middle school.

There are 227 composite days in a year. *Prime Curios

EVENTS

310 BC "Agathocles, who was already at the point of being overtaken and surrounded, gained unhoped for safety as night closed in. On the next day there occurred such an eclipse of the Sun that utter darkness set in and the stars were seen everywhere; wherefore Agathocles' men, believing that the prodigy portended misfortune for them, fell into even greater anxiety about the future. After they had sailed for six days and the same number of nights, just as day was breaking, the fleet of the Carthaginians was unexpectedly seen far away." From: Diodorus Siculus (Greek historian, 1st century BC), Library of History. Agathocles was a tyrant who had made his escape, with a fleet of sixty ships, from a blockade at Syracuse harbor by the Carthaginians. Quoted in Historical Eclipses and Earth's Rotation, by F Richard Stephenson, Cambridge University Press, 1997,

1665 Robert Hooke writes to Boyle in Oxford about his newly devised reflecting quadrant (also called octant), "My quadrant does to admiration for taking angles, so that thereby we are able from hence to tell the true distance between (St.) Paul's and any other church steeple in the city.... within the quantity of twelve foot." *Lisa Jardine, Ingenious Pursuits, pg 152

Two men independently developed the octant around 1730: John Hadley (1682–1744), an English mathematician, and Thomas Godfrey (1704–1749), a glazier in Philadelphia. While both have a legitimate and equal claim to the invention, Hadley generally gets the greater share of the credit. This reflects the central role that London and the Royal Society played in the history of scientific instruments in the eighteenth century.

1768 Lagrange, in a letter to D’Alembert, expressed his difficulty in solving the problem: Given a nonsquare positive integer n, to ﬁnd a square integer x2 such that nx2 +1 shall also be a square. *VFR
In the same letter, he showed that x2/3 could be expanded in a trigonometric series. D'Alembert had often used the function as an example that could not be so expanded. *Mathematical thought from ancient to modern times, Volume 2 , Morris Kline

1771 Benjamin Franklin writes to John Canton to share the news of Priestley's discovery that, unlike animals, a plant seemed to survive after months. He would later be inspired to place a life animal under the glass with the plant and realize that the animal survived longer. *Steven Johnson, The Invention of Air

1951 The Soviet Union issued a postage stamp with a portrait of Sofya Kovalevskaya. *VFR

1994  Microsoft Corp. decided to work to incorporate an Internet browser into its upcoming Windows 95 operating system in an effort to catch up to the Internet bandwagon it had missed. On August 15, Windows 95 programmer Benjamin Slivka sent an e-mail to his coworkers suggesting a World Wide Web browser as a feature for Windows 95. Microsoft has faced legal challenges for the way it bundled the result of the project - Internet Explorer - with Windows software. *CHS

2006 Voyager 1, the most distant man-made object, reached 100 astronomical units from the sun - meaning 100 times more distant from the sun than is Earth - about 15,000 million km (9,300 million miles) from the sun. At such great distance, the sun is a mere point of light, so solar energy is not an option, but having a nuclear power source, Voyager 1 continues to beam back information. The spacecraft, launched nearly 30 years earlier, on 5 Sep 1977, had flown beyond the outer planets and reached the heliosheath, the outer edge of our solar system, where the sun's influence wanes. Voyager 1 continues traveling at a speed of about one million miles per day and could cross into interstellar space before 10 years later.

BIRTHS

1720 Jean-Baptiste Le Roy (15 August 1720;Paris, France - 21 January 1800, Paris) Son of the renowned clockmaker Julien Le Roy, Jean-Baptiste Le Roy was one of four brothers to achieve scientific prominence in Enlightenment France; the others were Charles Le Roy (medicine and chemistry), Julien-David Le Roy (architecture), and Pierre Le Roy(chronometry). Elected to the Académie Royale des Sciences in 1751 as adjoint géomètre, Le Roy played an active role in technical as well as administrative aspects of French science for the next half-century. He was elected pensionnaire mécanicies in 1770 and director of the Academy for 1773 and 1778, and became both a fellow of the Royal Society and a member of the American Philosophical Society in 1773.
Le Roy’s major field of inquiry was electricity, a subject on which European opinion was much divided at mid-century. The most prominent controversy engaged the proponents of the Abbé Nollet’s doctrine of two distinct streams of electric fluids (outflowing and inflowing) and the partisans of Benjamin Franklin’s concept of a single electric fluid. This debate intensified in France in 1753 with an attack on Franklin’s views by Nollet. Le Roy, later a friend and correspondent of Franklin, defended his single-fluid theory and offered considerable experimental evidence in support thereof. He played an important role in the dissemination of Franklin’s ideas, stressing particularly their practical applications, and published many memoirs on electrical machines and theory in the annual Histoires and Mémoires of the Academy and in the Journal de Physique.
A regular contributor to the Encyclopédie, Le Roy wrote articles dealing with scientific instruments. The most important of these included comprehensive treatments of “Horlogerie,” “Télescope,” and “Électrométre” (in which Le Roy claimed priority for the invention of the electrometer). He also promoted the use of lightning rods in France, urged that the Academy support technical education, and was active in hospital and prison reform. After the Revolutionary suppression of royal academies, Le Roy was appointed to the first class of the Institut National (section de mécanique) at its formation in 1795. *Encycopedia.com

1795 Émile Léger (Born: 15 Aug 1795 in Lagrange-aux-Bois, France; Died: 15 Dec 1838 in Paris, France)Léger only published four mathematical papers but one contains possibly the first mention of what today is a well known fact about the Euclidean algorithm,

Émile Léger appears to have been the first (or second, if the work of de Lagny ... is counted) to recognise that the worst case of the Euclidean algorithm occurs when the inputs are consecutive Fibonacci numbers.  *SAU

1863 Aleksei N. Krylov, (15 Aug 1863 in Visyaga, Simbirskoy [now Ulyanovskaya], Russia - 26 Oct 1945 in Leningrad, USSR [now St Petersburg, Russia]) noted for mathematics, mechanics and engineering. *VFR Krylov made many mathematical advances in his applications of mathematics to shipbuilding. In hydrodynamics, among many advances, he made significant contributions to the theory of ships moving in shallow water. In 1904 he constructed a mechanical integrator to solve ordinary differential equations, being the first in Russia to make such an instrument. He improved Fourier's method for solving boundary value problems in a 1905 paper and gave many applications. *SAU

1865 Hantaro Nagaoka (15 Aug 1865; 11 Dec 1950)Japanese physicist who was influential in advancing physics in Japan in the early twentieth century. In 1904, he published his Saturnian model of the atom, inspired by the rings around the planet Saturn. He placed discrete, negatively charged electrons of the same tiny mass, spaced in a ring revolving around a central huge positive spherical mass at its centre. Considering the electrostatic forces, hee made a mathematical analogy to Maxwell's model of the stability of the motion of Saturn's rings in a huge central gravitational field. However, Nagaoka's theory failed in other ways, and he sidelined it in 1908. *TIS

1892 Louis Victor Pierre Raymond duc de Broglie (15 Aug 1892 -19 Mar 1987) was a French physicist best known for his research on quantum theory and for his discovery of the wave nature of electrons. De Broglie was of the French aristocracy - hence the title "duc" (Prince). In 1923, as part of his Ph.D. thesis, he argued that since light could be seen to behave under some conditions as particles (photoelectric effect) and other times as waves (diffraction), we should consider that matter has the same ambiguity of possessing both particle and wave properties. For this, he was awarded the 1929 Nobel Prize for Physics. *TIS

1893 Leslie (John) Comrie (15 Aug 1893-11 Dec 1950) was a New Zealand astronomer and pioneer in the application of punched-card machinery to astronomical calculations. He joined HM Nautical Almanac Office (1926-36), where he replaced the use of logarithm tables with desk calculators and punched card machines for the production of astronomical and mathematical tables. This made scientific use of these machines, made originally for only business uses. In 1938, he founded the Scientific Computing Service Ltd., the first commercial calculating service in Great Britain, to further his ideas of mechanical computation for the preparation of mathematical tables. His use of card processing systems prepared the way for electronic computers.*TIS

1905 Hermann Alexander Brück (15 August 1905 in Berlin, Germany – 4 March 2000 in Edinburgh, Scotland) was a German-born astronomer who spent the great portion of his career in the United Kingdom.
Upon graduation from Munich, Brück followed his friend Albrecht Unsöld to the Potsdam Astrophysical Observatory; Unsöld had earned his doctorate the year before, also under Sommerfeld. While there, he participated in the physics colloquium at the Humboldt University of Berlin with the physicists Max von Laue and Albert Einstein and the astronomer Walter Grotrian. With growing difficulties under National Socialism, Brück left Germany in 1936 to take a temporary research assistantship at the Vatican Observatory. In 1937 he moved to the University of Cambridge to join the circle of the modern astrophysicists around Arthur Eddington. In time, Brück became Assistant Director of the Observatories and John Couch Adams, specializing in solar spectroscopy. He taught a course in classical astronomy and started the student astronomical society, which fostered the careers of many astronomers.
In 1947, at the invitation of Éamon de Valera, Brück moved to Dublin to direct the Dunsink Observatory, which was part of the Dublin Institute for Advanced Studies, where he associated with Erwin Schrödinger. In 1950, the Observatory, along with the Royal Irish Academy, hosted the first meeting of the Royal Astronomical Society. In 1955, the International Astronomical Union held their triennial Assembly in Dublin. At this gathering, the Observatory demonstrated photoelectric equipment for photometry, which had been developed by M. J. Smyth, who had been Brück’s student in Cambridge. Also displayed was the UV solar spectroscopy which extended the Utrecht Atlas and formed part of the revised Rowland tables of the Solar spectrum; Brück’s wife, Dr. Mary Brück (née Conway), was a leading figure in this work.
In 1957, Brück moved to the University of Edinburgh. With his vision and drive, he transformed the Royal Observatory into an internationally-ranked center of research. He put together a team of astronomers and engineers headed initially by P. B. Fellgett and later by V. C. Reddish *Wik

1918 Jean Brossel ( 15 August 1918 in Périgueux , France - 4 February 2003 in France)developed with Alfred Kastler the technique of optical pumping at origin of lasers. *Arjen Dijksman ‏@materion

DEATHS

1758 Pierre Bouguer died (16 February 1698, Croisic – 15 August 1758, Paris). In 1727 he won the prize competition of the Acad´emie Royal des Sciences on the masting of ships. In this competition Euler only received the “accessit.” *vfr
Two days before (Aug 13)Charles-Etienne-Louis Camas was elected to the French Academy of Sciences because he had earlier won half the prize money in their competition for the best manner of masting vessels. (did Bouguer get the other half? Did Euler get any? is one, or more of these three pieces of information incorrect?)
French physicist whose work founded photometry, the measurement of light intensity. He was a child prodigy, a professor at age 15, following his father, Jean Bouguer, in hydrography - the study of bodies of water, both salt and fresh. He participated on the expedition to Peru (1735-44) to measure an arc of the meridian near the equator. In 1729, he invented a photometer to compare the intensity of two light sources illuminating separate halves of translucent paper. The eye itself, he determined, could not be used as a meter, but could establish the equality of brightness of adjacent surfaces. He determined the sun was 300 times brighter than the moon. Bouguer's law gives the attenuation of a beam of light by an optically homogeneous (transparent) medium.*TIS

1789 Jakob II Bernoulli, There seems to be confusion about his date of death, although it is well known that he drowned while swimming in the Neva River at the age of 29 and that he was married to one of Euler's granddaughters. Part of the confusion may be due to the fact that Russia did not switch to the modern Gregorian calendar until after the 1918 revolution. Alternate date given is July 2. Should be Aug 5 if converting the same day from Julian to Gregorian. Anyone?

1798 Edward Waring (ca. 1736 – 15 August 1798) was an English mathematician who gave many results about decomposing numbers into sums of powers and sums of primes.*SAU He entered Magdalene College, Cambridge as a sizar and became Senior wrangler in 1757. He was elected a Fellow of Magdalene and in 1760 Lucasian Professor of Mathematics, holding the chair until his death. He made the assertion known as Waring's Problem without proof in his writings Meditationes Algebraicae. Waring was elected a Fellow of the Royal Society in 1763 and awarded the Copley Medal in 1784.
In number theory, Waring's problem, proposed in 1770 by Edward Waring, asks whether for every natural number k there exists an associated positive integer s such that every natural number is the sum of at most s kth powers of natural numbers (for example, every number is the sum of at most 4 squares, or 9 cubes, or 19 fourth powers, etc.). The affirmative answer, known as the Hilbert–Waring theorem, was provided by Hilbert in 1909. *Wik

1927 Bertram Borden Boltwood (27 Jul 1870, 15 Aug 1927). was an American chemist and physicist whose work on the radioactive decay of uranium and thorium was important in the development of the theory of isotopes. Boltwood studied the "radioactive series" whereby radioactive elements sequentially decay into other isotopes or elements. Since lead was always present in such ores, he concluded (1905) that lead must be the stable end product from their radioactive decay. Each decay proceeds at a characteristic rate. In 1907, he proposed that the ratio of original radioactive material to its decay products measured how long the process had been taking place. Thus the ore in the earth's crust could be dated, and give the age of the earth as 2.2 billion years.*TIS

1953 Ludwig Prandtl (4 Feb 1875, 15 Aug 1953) German physicist who is remembered for his studies of both aerodynamics and hydrodynamics. He established the existence of the boundary layer adjoining the surface of a solid over which a fluid flows. The design of an efficient shape, weight, and mass for ships and aircraft owes much to his work, for which he is considered to be the father of aerodynamics. His made major studies on the effects of streamlining and the properties of aircraft wings. He made improvements to such constructions as wind tunnels. The Prandtl number is a dimensionless group used in the study of convection. The von Karman-Prandtl equation describes the logarithmic variation of water velocity within a channel from zero flow at the stream bed to a maximum velocity at the water surface.*TIS

1978 Viggo Brun (13 October 1885, Lier – 15 August 1978, Drøbak) was a Norwegian mathematician.
He studied at the University of Oslo and began research at the University of Göttingen in 1910. In 1923, Brun became a professor at the Technical University in Trondheim and in 1946 a professor at the University of Oslo. He retired in 1955 at the age of 70.
In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the Brun sieve, which addresses additive problems such as Goldbach's conjecture and the twin prime conjecture. He used it to prove that there exist infinitely many integers n such that n and n+2 have at most nine prime factors (9-almost primes); and that all large even integers are the sum of two 9 (or smaller)-almost primes.
In 1919 Brun proved that the sum of the reciprocals of the twin primes converges to Brun’s constant:
1⁄3 + 1⁄5 + 1⁄5 + 1⁄7 + 1⁄11 + 1⁄13 + 1⁄17 + 1⁄19 + . . . = 1.9021605 . . .by contrast, the sum of the reciprocals of all primes is divergent. He developed a multi-dimensional continued fraction algorithm in 1919/20 and applied this to problems in musical theory.
He also served as praeses of the Royal Norwegian Society of Sciences and Letters in 1946.
It was in 1994, while he was trying to calculate Brun’s constant,
that Thomas R. Nicely discovered a famous flaw in the Intel Pentium
microprocessor. The Pentium chip occasionally gave wrong answers
to a floating-point (decimal) division calculations due to errors in five
entries in a lookup table on the chip. Intel spent millions of dollars
replacing the faulty chips.
More recently, Nicely has calculated that the value of Brun’s constant
1s 1.902160582582 _ 0.000000001620.
*Wik

2002 Heinz Bauer (31 January 1928 – 15 August 2002) was a German mathematician.
Bauer studied at the University of Erlangen-Nuremberg and received his PhD there in 1953 under the supervision of Otto Haupt and finished his habilitation in 1956, both for work with Otto Haupt. After a short time from 1961 to 1965 as professor at the University of Hamburg he stayed his whole career at the University of Erlangen-Nuremberg. His research focus was the Potential theory, Probability theory and Functional analysis
Bauer received the Chauvenet Prize in 1980 and became a member of the German Academy of Sciences Leopoldina in 1986. Bauer died in Erlangen. *Wik

Credits :
*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