Friday 12 April 2024

On This Day in Math - April 12


"If equations are trains threading the landscape of numbers,
then no train stops at pi. "
~Richard Preston

The 102nd day of the year; I wrote that the number 102 may be the most singularly uninteresting number so far this year, but was corrected. Within an hour David Brooks sent me a list of items about 102. I really liked, and don't know how I missed, that "The sum of the cubes of the first 102 prime numbers is a prime number." Thanks David. It might be interesting for students to examine for which n is the cube of the first n primes also a prime.) 

 He also included that 102 is the name of a river in the state of Missouri. To French explorers the native American name for the river sounded like cent deux, the French words for 102. ( It is near the Iowa border, a tributary of the Platte River of Missouri that is approximately 80 miles long) *******

Another writer wrote to tell me that 102 is the sum of four consecutive primes, 102 = 19 + 23 + 29 + 31,
And there used to be a US 102 in Michigan, but they changed the number,

If you remember the four-fours game, here is a solution for 102 = .4 * 4^4 -.4

It is a sphenic number, since it is the product of 3 distinct primes. 2 x 3 x 17.  From the ancient Greek σφήν (sphḗn, “wedge”), +‎ -ic. 

 see math facts on every year day (1-365) at **************


In 1633 Galileo Galilei’s investigation by the Roman Inquisition began. At its conclusion, his belief that the Earth was not the center of the Universe was pronounced heretical.*Thony Christie, *TIS

In 1992, thirteen years after it was appointmented, a commission of historic, scientific and theological inquiry brought the pope a "not guilty" finding for Galileo, who in 1633, at age 69, was forced to repent by the Roman Inquisition and spent the last eight years of his life under house arrest. (Even in 1979-1992 it took 13 years to admit they messed up?)

 VATICAN CITY, OCT. 31 -- It's official: The Earth revolves around the sun, even for the Vatican.

The Roman Catholic Church has admitted to erring these past 359 years in formally condemning Galileo Galilei for formulating scientific theories it considered heresy.

1749 Euler succeeded in proving Fermat's theorem on sums of two squares in 1749, when he was forty-two years old. He communicated this in a letter to Goldbach #OTD.
Fermat's theorem on sums of two squares asserts that an odd prime number can be expressed as

p = x^2 + y^2

with integer x and y if and only if p is congruent to 1 (mod 4).   Euler add The statement was announced by Fermat in 1640, but he supplied no proof.  Fermat's famous Last Theorem, this one was written in the margin of Bachet's translation of Diophantos.   *Wik   *Oystein Ore

1803 A letter from Dalton to "Respected Friend" describes his theory that "If a quantity of water thus freed from air be agitated in any kind of gas, not chemically uniting with water, it will absorb its bulk of the gas, or otherwise a part of it equal to some one of the following fractions, namely, 1/8, 1/27, 1/64, 1/125, &c. these being the cubes of the reciprocals of the natural numbers " He then goes on to add that " I am just upon the point of discovering something superior to any of those already published, & which may be of as much importance to science as that of Gravitation itself. I mean the nature of Heat & all its combinations with substances." This may be the earliest note by Dalton of his atomic theory as it precedes his first lab notebook entry of 6 September by five months. This would be the basis for a paper read to the Literary and Philosophical Society of Manchester on Oct. 21, 1803.

1804 Gauss is made a fellow of the Royal Society of  London

1888, a French newspaper mistakenly published an obituary for Alfred Nobel, inventor of dynamite, calling him “"a merchant of death.” The mistake was that it was actually Alfred's brother, Ludwig Nobel, who had just died (at age 56, due to heart trouble). However, shocked by the newspaper's report,  Nobel began to seek a change in public opinion, which led to his decision to establish the Nobel Prizes.*TIS

In 1898, Marie Curie observed a meeting of the French Academy of Sciences, where one of her teachers, Prof. Gabriel Lippmann announced her discovery of substances much more radioactive than uranium. Working since Dec 1897, she had verified that the radiant activity of various compounds was directly related to the amount of uranium present, whether solid, powdered, or in a wet state. She proposed the radiant activity was an atomic property, for it was independent of physical or chemical state. She announced that in pitchblende and charcolite she had discovered compounds even more active than uranium. (She had not, in fact, found a new element, but was the first to identify thorium's powerful radioactivity.*TIS

1842 The first mutual life insurance company in the U.S. was chartered. Since such companies must employee many actuaries, this provides a good source of jobs for individuals with a knowledge of mathematics. *FFF

1933 Hanger One at Moffett Field was commissioned on this day. Originally called Airbase Sunnyvale CAL, although it was actually in Mtn. View, but that was a name that the backers feared might scare off the Navy. The two communities banded together to bring the air station to Mountain View. Originall y built for the USS Macon, the Akron's sister ship (Which delivered the firt Coast to Coast Air Mail, See May 9, 1932). Admiral William Moffett (the founder of the Navy airship effort) perished when the USS Akron went down 8 days before our commission, and we were named in his honor. *@MoffettHangar1
Image : Cover carried on the May 1932 "Coast to Coast" flight and later autographed by the only three survivors of the April 1933 crash of USS Akron *Wiki

In 1954, the American Atomic Energy Commission (AEC) began hearings to revoke Robert Oppenheimer's security clearance, thereby severing him from the commission's work. Although he had led the scientists making the atomic bombs during the WW II Manhattan Project, he had been affected by the bombs' death toll and chilling descriptions of radiation sickness. When the Soviet Union detonated an atom bomb in 1949, Edward Teller and Ernest Lawrence lobbied feverishly to develop the hydrogen bomb. Oppenheimer chaired the General Advisory Committee AEC, repudiated the hydrogen bomb as a weapon of “genocide.” In May 1953, when Lewis Strauss accepted the chair of the AEC, he regarded Oppenheimer as a security risk, and wanted him to be dismissed. *TIS
In his testimony, Isador Rabi would say in Oppenheimer's defense: "there he was; he is a consultant, and if you don't want to consult the guy, you don't consult him, period. Why you have to then proceed to suspend clearance and go through all this sort of thing,...We have an A-bomb and a whole series of it, and what more do you want, mermaids? This is just a tremendous achievement. If the end of that road is this kind of hearing, which can't help but be humiliating, I thought it was a pretty bad show. I still think so." *atomicarchive

1961 In Syracuse, Italy, the scientific festivities began to celebrate the memory of Archimedes who was born in the city in 287 BC and was killed there in 212 BC by a Roman soldier. His last words, according to Livy, were “Nolitangere circulos meos” (Don’t touch my circles). [Scripta Mathematica, 26(1961), 143] *VFR

1961 Yuri Gagarin became the first man in space, orbiting the earth in 108 minutes in the Soviet spacecraft Vostok. (or did he... )

1977 Fiji issued a stamp showing a world map in sinusoidal projection. [Scott #374] *VFR
The sinusoidal projection is a pseudocylindrical equal-area map projection, sometimes called the Sanson-Flamsteed or the Mercator equal-area projection. It is defined by:

x = \left(\lambda - \lambda_0\right) \cos \phi
y = \phi\,
where \phi\, is the latitude, \lambda\, is the longitude, and \lambda_0\, is the central meridian.
The north-south scale is the same everywhere at the central meridian, and the east-west scale is throughout the map the same as that; correspondingly, on the map, as in reality, the length of each parallel is proportional to the cosine of the latitude; thus the shape of the map for the whole earth is the area between two symmetric rotated cosine curves. The true distance between two points on the same meridian corresponds to the distance on the map between the two parallels, which is smaller than the distance between the two points on the map. There is no distortion on the central meridian or the equator.  *Wik

1979  On the UNICEF International Children's day, the African nation of Guinea-Bissau issues an education stamp depicting the inscribed angle theorem.  
1981 HP-41 calculator used in space:
HP-41 calculator used on board NASA's first space shuttle flight. The HP-41 allowed astronauts to calculate the exact angle at which they needed to re-enter the Earth's atmosphere. *CHM


1994, the first Internet spamming program was used by an attorney in Arizona. Laurence Canter created the software program, a simple Perl script, that flooded Usenet message board readers with a notice for the "Green Card Lottery" to solicit business for his law firm of Canter & Siegel (with wife, Martha Siegel.) The reaction from the online community was vigorously critical, condemning such a form of advertising. Thousands of recipients complained, but a new, burgeoning business of unsolicited mass Internet advertising had been spawned. 
What made them different was that they did not hide the fact that they were spammers. They were proud of it, and thought it was great advertising. They even went on to write the book "How to Make a Fortune on the Information Superhighway : Everyone’s Guerrilla Guide to Marketing on the internet and Other On-Line Services". They planned on opening a consulting company to help other people post similar advertisements, but it never took off.
In 1997, the Supreme Court of Tennessee disbarred Canter in part for illegal advertising practices.
The term "spam" was coined from a sketch in the "Monty Python's Flying Circus" BBC television show in which a waitress offered a menu full of variations of spam to an unwilling patron. *TIS
The Monty Python skit is here

Spam filled inbox


1794 Germinal Pierre Dandelin (12 April 1794 – 15 February 1847) was a mathematician, soldier, and professor of engineering. He was born near Paris to a French father and Belgian mother, studying first at Ghent then returning to Paris to study at the École Polytechnique. He was wounded fighting under Napoleon. He worked for the Ministry of the Interior under Lazare Carnot. Later he became a citizen of the Netherlands, a professor of mining engineering in Belgium, and then a member of the Belgian army.
He is the eponym of the Dandelin spheres, of Dandelin's theorem in geometry (for an account of that theorem, see Dandelin spheres), and of the Dandelin–Gräffe numerical method of solution of algebraic equations. He also published on the stereographic projection, algebra, and probability theory.*Wik

1851 Edward Walter Maunder (12 Apr 1851, 21 Mar 1928 at age 76) English astronomer who was the first to take the British Civil Service Commission examination for the post of photographic and spectroscopic assistant at the Royal Observatory, Greenwich. For the next forty years that he worked there, he made extensive measurements of sunspots. Checking historical records, he found a period from 1645 to 1715 that had a remarkable lack of reports on sunspots. Although he might have questioned the accuracy of the reporting, he instead attributed the shortage of report to an actual dearth of sunspots during that period. Although his suggestion was not generally accepted at first, accumulating research has since indicated there are indeed decades-long times when the sun has notably few sunspots. These periods are now known as Maunder minima.*TIS

On the far side of the Moon lies the Maunder crater, named after two British astronomers - Annie and Walter Maunder.
Annie worked alongside her husband at the end of the 19th Century, recording the dark spots that pepper the Sun.
The name Maunder is still known in scientific circles, yet Annie has somehow slipped from history.
"I think the name Maunder is there and we have all rather forgotten that that's two people," says Dr Sue Bowler, editor of the Royal Astronomical Society magazine, Astronomy and Geophysics.
"She was acknowledged on papers, she published in her own name as well as with her husband, she wrote books, she was clearly doing a lot of work but she also clearly kept to the conventions of the day, I think." *By Helen Briggs BBC News
She is known to have worked closely with her husband on the study of sunspots, and she is often credited with discovering the butterfly pattern. *LH
Annie Scott Dill Maunder (née Russell) FRAS (14 April 1868 – 15 September 1947)*PBnotes

1852 Carl Louis Ferdinand von Lindemann(12 Apr 1852; 6 Mar 1939 at age 86) He showed π is transcendental (not the root of any algebraic equation with rational coefficients), consequently the circle cannot be squared  (constructing a square with the same area as a given circle using ruler and compasses alone.) In 1873, Lindemann visited Hermite in Paris and discussed the methods which Hermite had used in his proof that e, the base of natural logarithms, is transcendental. Following this visit, Lindemann was able to extend Hermite's results to show that  was also transcendental.  *TIS
(the image is of his tombstone.... note the square and  circle with Pi inside.)

1883 Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. First a noted logician, he later branched into epistemology, and during the last 20 years of his life, he wrote much on ethics. The New York Times memorialized him as "a leading authority on symbolic logic and on the philosophic concepts of knowledge and value." He was the first to coin the term "Qualia" as it is used today in philosophy, linguistics, and cognitive sciences. *Wik
(In philosophy of mind, qualia (/ˈkwɑːliə, ˈkweɪ-/; sg.: quale /-li/) are defined as instances of subjective, conscious experience. The term qualia derives from the Latin neuter plural form (qualia) of the Latin adjective quālis (Latin pronunciation: [ˈkʷaːlɪs]) meaning "of what sort" or "of what kind" in relation to a specific instance, such as "what it is like to taste a specific apple — this particular apple now".)

1903 Jan Tinbergen (April 12, 1903 – June 9, 1994), was a Dutch economist. He was awarded the first Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel in 1969, which he shared with Ragnar Frisch for having developed and applied dynamic models for the analysis of economic processes. Tinbergen was a founding trustee of Economists for Peace and Security.
Tinbergen became known for his 'Tinbergen Norm', which is the principle that, if the difference between the least and greatest income in a company exceeds a rate of 1:5, that will not help the company and may be counterproductive.*Wik


1817 Charles Messier (26 Jun 1730, 12 Apr 1817 at age 86)French astronomer who discovered 15 comets. He was the first to compile a systematic catalog of "M objects." The Messier Catalogue (1784), containing 103 star clusters, nebulae, and galaxies. (In Messier's time a nebula was a term used to denote any blurry celestial light source.) He established alphanumeric names for the objects (M1, M2, etc.), which notation continues to be used in astronomy today.*TIS
Image:  M1, the Crab Nebula 


1919 Friedrich Otto Rudolf Sturm (6 Jan 1841 in Breslau, Germany (now Wrocław, Poland) -12 April 1919 in Breslau, Germany (now Wrocław, Poland)) Sturm wrote extensively on geometry and, other than the teaching textbook on descriptive geometry and graphical statics which we mentioned above and one other teaching text Maxima und Minima in der elementaren Geometrie which he published in 1910, all his work was on synthetic geometry.
He wrote a three volume work on line geometry published between 1892 and 1896, and a four volume work on projective geometry, algebraic geometry and Schubert's enumerative geometry the first two volumes of which he published in 1908 and the second two volumes in 1909. These two multi-volume works collect together most of his life's research. *SAU

1971  Wolfgang Krull proved the Krull-Schmidt theorem for decomposing abelian groups and defined the Krull dimension of a ring.

1971 Igor Yevgenyevich Tamm (8 Jul 1895, 12 Apr 1971 at age 75)Soviet physicist who shared the 1958 Nobel Prize for Physics with Pavel A. Cherenkov and Ilya M. Frank for his efforts in explaining Cherenkov radiation. Tamm was an outstanding theoretical physicist, after early researches in crystallo-optics, he evolved a method for interpreting the interaction of nuclear particles. Together with I. M. Frank, he developed the theoretical interpretation of the radiation of electrons moving through matter faster than the speed of light (the Cerenkov effect), and the theory of showers in cosmic rays. He has also contributed towards methods for the control of thermonuclear reactions. *TIS 
And one of my favorite math stories is from George Gamow's autobiography and is about the Nobel Laureate, Igor Tamm.
 "Here is a story told to me by one of my friends who was at that time a young professor of physics in Odessa. His name was Igor Tamm (NobelPrize laureate in Physics, 1958). Once when he arrived in a neighboring village, at that period when Odessa was occupied by the Reds, and was negotiating with a villager as to how many chickens he could get for half a dozen silver spoons, the village was captured by one of the Makhno bands, who were roaming the country, harassing the Reds. Seeing his city clothes (or what was left of them), the capturers [sic] brought him to the Ataman, a bearded fellow in a tall black fur
hat with machine-gun cartridge ribbons crossed on his broad chest and a couple of hand grenades hanging on the belt.
'You son-of-a-bitch, you Communist agitator, undermining our Mother Ukraine! The punishment is death.'

'But no,' answered Tamm, 'I am a professor at the University of Odessa and have come here only to get some food.'

'Rubbish!' retorted the leader. 'What kind of professor are you ?'

'I teach mathematics.'

'Mathematics?' said the Ataman. 'All right! Then give me an estimate of the error one makes by cutting off Maclaurin's series at the nth term. Do this, and you will go free. Fail, and you will be shot!'

Tamm could not believe his ears, since this problem belongs to a rather special branch of higher mathematics. With a shaking hand, and under the muzzle of the gun, he managed to work out the solution and handed it to the Ataman.

'Correct!' said the Ataman. 'Now I see that you really are a professor. Go home!'

Who was this man? No one will ever know. If he was not killed later, he may well be lecturing now on higher mathematics in some Ukrainian university."

I tell this story every other year or so to my physics students when they cannot be bothered to remember the form of the remainder in Taylor expansions...."

2000 David George Crighton FRS (15 November 1942, Llandudno, Wales - 12 April 2000, Cambridge) was a British mathematician and physicist. In his first paper, Crighton studied the sound wave associated with turbulent flow over a discontinuous surface formed by two semi-infinite flexible planes.
Over the years he worked broadly in the fields of acoustics, equation theory and quasi-diabatic systems including solitons. This included on the generalized Burgers' equation and inverse scattering theory. *Wik
In 1974, he was appointed as a research fellow in the Department of Engineering at the University of Cambridge. However, he never took up this post, but instead accepted the chair in applied mathematics at the University of Leeds, which he held until 1986.
He then returned to Cambridge as Professor of Applied Mathematics in succession to George Batchelor.
Later, he became a well-loved Master of Jesus College (1997–2000), and was head of the Applied Mathematics and Theoretical Physics Department (DAMTP) in Cambridge between 1991 and 2000, where he was held in huge regard by the faculty and students.

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

Thursday 11 April 2024

The Prime Game


Ulam Prime Spiral

150x150 spiral with prime "ley lines"

I read a post some time ago called "Math Notes" by Greg Ross at Futility Closet, and as always, it was very interesting.

One part in particular got my mind turning. He wrote:








19793393 and

197933933 are all prime.

(OK, we don't use 1 as prime anymore, but it was common a century ago)    

It struck me that this could be a great student game/project.

Such numbers are called right truncatable primes, since you can continuously chop off the last digit  and still have a prime.  There are similar types for  left truncatable, and even some left/right truncatable.  

Player one picks a number, a single prime digit.

Player two must pick a second digit so that the two form a two digit prime.

Play continues until one can not make a prime.

An interesting alternative rule cold be to allow the subsequent numbers to be added at either the front or the end of the string.

It might also be interesting to create a "map" of the strings possible..

For example the one above would be on a mapping that starts with one and then branches to 11, 13, 17, and 19 The 11 could go to 113 but then would be a dead end as 1131, 1133, 1135, and 1137 (and 1139) are all factorable. The 13 node can be extended to 131, 137, 139.

Students might amaze themselves with the long strings they could create.

For the string that started all this above, one might add 1979339333 is also prime, but if you wished, you could use 1979339339 which is prime as well.  That's a quick ten digit string of primes.  It is not easy for students to test if either of those is the end of the string, but along the way they have learned something about testing primes.

A good solitaire version might be to start with the digits 1,2,3,4,5,6,7,8,9 and try to build a tree that leads to a ten digit prime with all the numerals by adding one digit at a time.

And a footnote, Greg had this ten digit prime which isn't truncatable, but has the digits 1 through 9 in order...1234567891.  

Thought people might wonder about left truncatable primes, so here are the three  largest found so far by 

The Prime Glossary page : The three largest left-truncatable primes are:

 959 18918 99765 33196 93967,

 966 86312 64621 65676 29137, and

3576 86312 64621 65676 29137.

If you want to learn more, here is a paper that might be of interest  

C. Caldwell, "Truncatable primes," J. Recreational Math., 19:1 (1987) 30--33. [A recreational note discussing left truncatable primes, right truncatable primes, and deletable primes.]


On This Day in Math - April 11


Bayeux Tapestry with Halley's Comet *Heraldic

I will stop here.
Concluding the lecture in which he claimed to have proved the Taniyama-Weil Conjecture for a class of examples, including those necessary to prove Fermat's Last Theorem. (1993)
~Andrew Wiles

The 101st day of the year; 101 is the sum of five consecutive primes, but even more exciting, 101 = 5! - 4! + 3! - 2! + 1! (What would be the next number created in a sequence like this?)

There are six ways you can pick two of the four smallest primes, 2, 3, 5, and 7.  Form all six pairs, multiply each pair, and add all the products....boom, 101

101 is the largest known prime of the form 10+ 1.

There are 101 digits in the product of the 39 successive primes produced by the formula n2 + n + 41, where n = 1 to 39. This formula was used by Charles Babbage to demonstrate the capabilities of his Difference Engine (1819-1822). *Prime Curios

and The last five digits of 101101 are 10101.

1 + 6 + 8 = 15 = 2 + 4 + 9, and the sets remain equal if you square them before adding, 1^2 + 6^2 + 8^2 = 2^2 + 4^2 + 9^2 = 101
Folks in Kentucky know that  Wild Turkey bourbon's most common production is its 101 proof. Brewed just down the road in Lawrenceburgh, Ky . Jump on the Bourbon Tour and stop by, and tell 'em Pat B sent ya'.

Wonowon, British Columbia i so named because it is at Mile Marker 101 on Highway 97, the Alaska Highway.

More Math facts on 101,  and more... here

1594, the twenty-two-year-old Kepler arrived in southern Austria to take up his duties as teacher and as provincial mathematician. In the first year he had few pupils in mathematical astronomy and in the second year none, so he was asked to teach Vergil and rhetoric as well as arithmetic. But the young Kepler made his mark in another way; soon after coming to Graz, he issued a calendar and prognostication for 1595, which contained predictions of bitter cold, peasant uprisings, and invasions by the Turks. All were fulfilled, to the great enhancement of his local reputation. Five more calendars followed in annual succession, and later in Prague he issued prognostications for 1602 to 1606. These ephemeral items are now extremely rare, some surviving in unique copies; and all the copies of nearly half the editions are totally lost. *
In the On the new star (1606) Kepler explicated the meaning of the new star of 1604 as the conversion of America, downfall of Islam and return of Christ. The De cometis libelli tres (1619) is also replete with astrological predictions.

Kepler's De Cometis , and De Stella Nova opened to display image with the Supernova located in the foot of the serpent bearer.

In 1751, Ebenezer Kinnersley advertised in the Pennsylvania Gazette that he was to give a lecture on "The Newly Discovered Electrical Fire." His lectures were the first of the kind in America or Europe. The announcement read: "Notice is hereby given to the Curious, that Wednesday next, Mr. Kinnersley proposes to begin a course of experiments on the newly discovered Electrical Fire, containing not only the most curious of those that have been made and published in Europe, but a considerable number of new ones lately made in this city, to be accompanied with methodical Lectures on the nature and properties of that wonderful element." Thus, Kinnersley was one of the earliest popularizers of science. *TIS
Electrical air thermometer by E. Kinnersley. From a letter to B. Franklin,

1816 Gauss writes to Gerling from Goettingen. Gerling had written to Gauss in March about Legendre’s theory of parallels in the book elemens de geom. Gauss responded that Legendre’s argument does not carry the weight of proof for him, and then comments on what happens if Euclidean geometry is not correct.
It is easy to show that if Euclid’s geometry is not the true one then there are no similar figures: the angles in an equilateral triangle depend on the size of the edges, in which I do not find anything absurd. Then the angle is a function of the side, and the side a function of the angle, naturally such a function in which a linear constant appears. It seems somewhat paradoxical that a linear constant can be a priori possible; but I don’t find anything contradictory in this. It would be even desirable that Euclid’s geometry is not true, for then we would have a general measure a priori, for example, one could assume as the unit of space the side of the equilateral triangle whose angle = 59o 59’ 59’’.99999….
*Stan Burris, Notes on Euclidean Geometry

Lambert wrote his Theorie der Parallellinien in an attempt to prove, by contradiction, the parallel postulate. He deduced remarkable consequences including this one, from the negation of that postulate. These consequences make his memoir one of the closest (probably the closest) text to hyperbolic geometry, among those that preceded the writings of Lobachevsky, Bolyai and Gauss. His conclusions include (6) below, and preceded Gauss' by about 50 years:

"(1) The angle sum in an arbitrary triangle is less than 180◦.
(2) The area of triangles is proportional to angle defect, that is, the
difference between 180◦
and the angle sum.
(3) There exist two coplanar disjoint lines having a common perpendicular
and which diverge from each other on both sides of
the perpendicular.
(4) Given two lines coplanar d1 and d2 having a common perpendicular,
if we elevate in the same plane a perpendicular d3 to
d1 at a point which is far enough from the foot of the common
perpendicular, then d3 does not meet d2.
(5) Suppose we start from a given point in a plane the construction
of a regular polygon, putting side by side segments having the
same length and making at the junctions equal angles having a
certain value between 0 and 180◦
(see Figure 2 below). Then,
the set of vertices of these polygons is not necessarily on a circle.
Equivalently, the perpendicular bisectors of the segment do not
necessarily intersect.
(6) There exist canonical measures for length and area."

1936 Zuse patent filed for automatic execution of calculations. German computer pioneer Konrad Zuse files for a patent for the automatic execution of calculations, a process he invents while working on what would become the Z-1, Germany's first computer. In the patent application, Zuse offers the first discussion of programmable memory, using the term ""combination memory"" to describe breaking programs down into bit combinations for storage. This is the first device to calculate in binary with translation to decimal. Zuse goes on to build a series of computers. *CHM (Christopher Sears sent a comment last year to tell me that, "There was a character in Tron: Legacy named "Zuse". I thought is was "Zeus" during the movie, but I saw it was spelled differently in the credits . Now I know where the reference came from.")
 This became the first device to calculate in binary with translation to decimal.

Zuse went on to establish one of the earliest computer businesses in 1941 and produced the Z3, the world’s first programmable computer and the Z4, the world’s first commercial computer. Because of his achievements he is often referred to as the inventor of the modern computer.

Zuse Z3

1970 France issued a stamp honoring the physicist Maurice de Broglie (1875–1960). He is pictured with a spectrograph. [Scott #B439] *VFR He made advances in the study of X-ray diffraction and spectroscopy. In 1971, the government of Nicaragua issued a series of stamps entitled "Ten Equations That Changed the Face of the World".  De Broglie's famous equation, \( \lambda = \frac{h}{mv} \) was one of them.

1970 Apollo 13 lifted off, an on-board computer and large computers on Earth performed the critical guidance and navigation calculations necessary for a successful journey. In addition, crews carried a slide rule for more routine calculations. NASA chose a 5-inch, metal rule, model "N600-ES," manufactured by the Pickett Company for their use. It was a model that was popular among engineers, scientists and students at the time. No modifications were needed for use in space.

This rule used by the crew of Apollo 13, in April 1970 was transferred from NASA to the National Air and Space Museum in 1984. *

1986, Halley's Comet made its closest approach to Earth this trip, 63 million kilometers (39 million mi), on its outbound journey. Many observers were disappointed because the famous comet was barely visible to the naked eye. Some years are simply better than others, as in 1066 when the comet was so bright that it terrified millions of Europeans. Comet Halley isn't officially scheduled to visit Earth again until 2061 when it returns on its 76-year orbit. This comet's closest known approach to the Earth was 3 million miles on 10 Apr 837 AD). Its perihelion (the closest point to the Sun) occurred earlier in the year, on 9 Feb 1986, when it was 88 million km (55 million mi) from the Sun, between the orbits of Mercury and Venus. *TIS 


1798 Macedonio Melloni (11 Apr 1798; 11 Aug 1854 at age 56) Italian physicist who was the first to extensively research infrared radiation. Sir William Frederick Herschel discovered infrared radiation in 1800, but research stalled until the invention of a thermopile in 1830. That instrument was a series of strips of two different metals that produced electric current when one end was heated. Melloni improved the thermopile and used it to detect infrared radiation. In 1846, from an observation point high on Mount Vesuvius, he measured the slight heating effect of moonlight. He showed also that rock salt, being transparent to infrared, made suitable lenses and prisms to demonstrate the reflection, refraction, polarization and interference of infrared in the same manner as visible light.*TIS  
He is notable for demonstrating that radiant heat has similar physical properties to those of light.

1829 Alexander Buchan (11 Apr 1829; 13 May 1907 at age 78) British meteorologist, eminent in his field, who first noticed what became known as Buchan spells - departures from the normally expected temperature occurring during certain seasons. They are now believed by meteorologists to be more or less random. Buchan is credited with establishing the weather map as the basis of weather forecasting as a result of his tracing (1868) the path of a storm across North America and the Atlantic into northern Europe. *TIS
Buchan prepared meteorological and oceanographic reports for the Challenger Expedition.
His niece, Jessie Hill Buchan, an expert calculator, was his assistant until her death in 1905.

1862 William Wallace Campbell (11 Apr 1862 near Findlay in Hancock county, Ohio; 14 Jun 1938 at age 76) American astronomer known particularly for his spectrographic determinations of the radial velocities of stars--i.e., their motions toward the Earth or away from it. In addition, he discovered many spectroscopic binary stars, and in 1924 he published a catalog listing more than 1,000 of them.*TIS
 After a few years of local schooling he entered in 1882 the University of Michigan to study civil engineering, graduating Bachelor of Science in 1886. Whilst at university he developed his interest in astronomy when he read Simon Newcomb's Popular Astronomy.
After graduating he was appointed Professor of Mathematics at the University of Colorado but soon moved back to Michigan as an instructor in astronomy. In 1891 he was invited to work on spectroscopy at Lick Observatory in California. Campbell was a pioneer of astronomical spectroscopy and catalogued the radial velocities of stars. He was also recognized for his work in solar eclipse photography. In 1893 he discovered the Wolf–Rayet star HD 184738 (also known as Campbell's hydrogen envelope star). He was made a director of Lick Observatory from 1901 to 1930.

1894 Paul Finsler (born 11 April 1894, in Heilbronn, Germany, died 29 April 1970 in Zurich, Switzerland) was a German and Swiss mathematician.
Finsler's thesis work concerned differential geometry, and Finsler spaces were named after him by Élie Cartan in 1934. The Hadwiger–Finsler inequality, a relation between the side lengths and area of a triangle in the Euclidean plane, is named after Finsler and his co-author Hugo Hadwiger. Finsler is also known for his work on the foundations of mathematics, developing a non-well-founded set theory with which he hoped to resolve the contradictions implied by Russell's paradox. *Wik 
In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane. It states that if a triangle in the plane has side lengths a, b and c and area T, then
 a^2+b^2+c^2  ≥ (a-b)^2+(b-c)^2+(c-a)^2+4 sqrt {3}T

1901 Donald Howard Menzel (11 Apr 1901 in Florence, Colorado; 14 Dec 1976 at age 75) was an American astronomer who was best known for his arguments against the existence of extraterrestrial UFO's. Menzel was one of the first practitioners of theoretical astrophysics in the United States and pioneered the application of quantum mechanics to astronomical spectroscopy. An authority on the sun's chromosphere, he discovered with J. C. Boyce (1933) that the sun's corona contains oxygen. With W. W. Salisbury he made (1941) the first of the calculations that led to radio contact with the moon in 1946. He supervised the assignment of names to newly discovered lunar features. *TIS

1904 Phillip Hall (11 April 1904, Hampstead, London, England – 30 December 1982, Cambridge,England) was the main impetus behind the British school of group theory and the growth of group theory to be one of the major mathematical topics of the 20th Century was largely due to him. *SAU
He was educated first at Christ's Hospital, where he won the Thompson Gold Medal for mathematics, and later at King's College, Cambridge. He was elected a Fellow of the Royal Society in 1951 and awarded its Sylvester Medal in 1961. He was President of the London Mathematical Society in 1955–1957, and awarded its Berwick Prize in 1958 and De Morgan Medal in 1965. *Wik

1914 Dorothy Lewis Bernstein (April 11, 1914 – February 5, 1988) was an American mathematician known for her work in applied mathematics, statistics, computer programming, and her research on the Laplace transform.
Dorothy Bernstein was born in Chicago, the daughter of Russian immigrants to the US. She was a member of the American Mathematical Society and the first woman elected president of the Mathematical Association of America. Due in great part to Bernstein's ability to get grants from the National Science Foundation, Goucher College (where she taught for decades) was the first women's university to use computers in mathematics instruction in the 1960s.*Wik

1921 Leo Moser (April 11, 1921, Vienna—February 9, 1970, Edmonton) was an Austrian-Canadian mathematician, best known for his polygon notation.
A native of Vienna, Leo Moser immigrated with his parents to Canada at the age of three. He received his Bachelor of Science degree from the University of Manitoba in 1943, and a Master of Science from the University of Toronto in 1945. After two years of teaching he went to the University of North Carolina to complete a Ph.D., supervised by Alfred Brauer. There, in 1950, he began suffering recurrent heart problems. He took a position at Texas Technical College for one year, and joined the faculty of the University of Alberta in 1951, where he remained until his death at the age of 48. *Wik In mathematics, Steinhaus–Moser notation is a means of expressing certain extremely large numbers. It is an extension of Steinhaus’s polygon notation.
n in a triangle a number n in a triangle means nn.
n in a square a number n in a square is equivalent with "the number n inside n triangles, which are all nested."
n in a pentagon a number n in a pentagon is equivalent with "the number n inside n squares, which are all nested."

1953 Sir Andrew John Wiles, KBE, FRS (born 11 April 1953) is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory. He is most famous for proving Fermat's Last Theorem in 1995 (and my proof was nearly complete, ;-{ )  for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal and for which he was appointed a Knight Commander of the Order of the British Empire in 2000. In 2018, Wiles was appointed the first Regius Professor of Mathematics at Oxford. Wiles is also a 1997 MacArthur Fellow.

1626 Marino Ghetaldi (2 Oct 1568 in Ragusa, Dalmatia (now Dubrovnik, Croatia)- 11 April 1626 in Ragusa, Dalmatia (now Dubrovnik, Croatia)) Marino Ghetaldi was a Croatian mathematician who published work with early applications of algebra to geometry.*SAU
Ghetaldi was a mathematician and physicist who studied in Italy, England and Belgium, his best results are mainly in physics, especially optics, and mathematics. He was one of the few students of François Viète and friend of Giovanni Camillo Glorioso.

1734 Thomas Fantet de Lagny (7 Nov 1660 in Lyon, France - 11 April 1734 in Paris, France was a French mathematician who is well known for his contributions to computational mathematics, calculating π to 120 places. [V F Rickey has this as the 12th of April.... and shares], using Gregory’s series, Maupertius was called to de Lagny’s deathbed, and finding the poor man unconscious, asked him for the square of 12. Like an automaton, de Lagny rose in bed, gave the answer, and immediately passed away. [Eves, Circles, 238◦ and Allen Debus, World Who’s Who in Science] *VFR
In 1686, he went to Paris and became a mathematics tutor to the Noailles family. He collaborated with de l'Hospital under the name of de Lagny, and at that time he started publishing his first mathematical papers.
He came back to Lyon when, on 11 December 1695, he was named an associate of the Académie Royale des Sciences. Then, in 1697, he became professor of hydrography at Rochefort for 16 years.*Wik

1875 Samuel Heinrich Schwabe (25 Oct 1789, 11 Apr 1875 at age 85) Amateur German astronomer who discovered the 10-year sunspot activity cycle. Schwabe had been looking for possible intramercurial planets. From 11 Oct 1825, for 42 years, he observed the Sun virtually every day that the weather allowed. In doing so he accumulated volumes of sunspot drawings, the idea being to detect his hypothetical planet as it passed across the solar disk, without confusion with small sunspots. Schwabe did not discover any new planet. Instead, he published his results in 1842 that his 17 years of nearly continuous sunspot observations revealed a 10-year periodicity in the number of sunspots visible on the solar disk. Schwabe also made (1831) the first known detailed drawing of the Great Red Spot on Jupiter. *TIS

1907 Christian Gustav Adolph Mayer (February 15, 1839 – April 11, 1907) was a German mathematician. Mayer studied at Heidelberg, and submitted his habilitation thesis to the University of Heidelberg. He gained the permission to teach at universities in 1866. He taught mathematics at the University of Heidelberg for the rest of his life. He did research on differential equations, the calculus of variations and mechanics. His research on the integration of partial differential equations and a search to determine maxima and minima using variational methods brought him close to the investigations which Sophus Lie was carrying out around the same time.
Several letters were exchanged between Mayer and mathematician Felix Klein from 1871 to 1907. Those letters provide insights into the scientific and personal relations among Felix Klein, Mayer and Lie over the period.
Mayer's students included : Friedrich Engel, Felix Hausdorff and Gerhard Kowalewski. *Wik

1974 Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics.  Nearly half of Robinson's papers were in applied mathematics rather than in pure mathematics.  He is the creator of non-standard analysis.
He became known for his approach of using the methods of mathematical logic to attack problems in analysis and abstract algebra. He "introduced many of the fundamental notions of model theory". Using these methods, he found a way of using formal logic to show that there are self-consistent nonstandard models of the real number system that include infinite and infinitesimal numbers. 

1989 Emil Grosswald (December 15, 1912 – April 11, 1989) was a Romanian-American mathematician who worked primarily in number theory. His career is closely associated with that of his teacher, Hans Rademacher. Grosswald completed some works of his teacher Hans Rademacher, who died in 1969. Rademacher had prepared notes for an Earle Raymond Hedrick Lecture in Boulder, Colorado in 1963 on Dedekind sums, but fell ill, and Grosswald gave the lecture for him. After Rademacher's death, Grosswald edited and completed the notes and published them in the Carus Mathematical Monographs series as Dedekind Sums. He also edited for publication Rademacher's posthumous textbook Topics in Analytic Number Theory.*Wik
Emil Grosswald (right) and Fred van der Blij in 1968.

2015 Carmen Adelina Gutiérrez Alonso (aka Adelina Gutiérrez, May 27, 1925 – April 11, 2015) was a Chilean scientist, academic and professor of astrophysics. She was the first Chilean to obtain a doctoral degree in astrophysics and the first woman to become a member of the Chilean Academy of Sciences.

Gutiérrez began working as a science teacher at the Liceo Dario Salas and the Faculty of Physical and Mathematical Sciences (FCFM) of the University of Chile. From June 1, 1949, Gutiérrez worked at National Astronomical Observatory of Chile. At that observatory, her work was initially restricted to analyzing astronomical data obtained by other scientists. While working there, Gutiérrez developed an interest in the photoelectric photometry of austral stars, a subject which she addressed in numerous publications. During the time that she was working at the National Astronomical Observatory, Gutiérrez also became a full faculty member in Faculty of Physical and Mathematical Sciences of the University of Chile.

In the late 1950s, Gutiérrez traveled to the United States to study for a PhD in astrophysics, which has obtained in June 1964, becoming the first Chilean to obtain such a degree. In 1965, after having returned to Chile, Gutiérrez, Hugo Moreno León and Claudio Anguita founded a bachelor's degree course in astronomy at the University of Chile. Gutiérrez was responsible for overseeing the course. In 1976, Gutiérrez also founded a master's degree course in astronomy at the University of Chile.

In 1967, Gutiérrez began working with Hugo Moreno León in the newly opened Cerro Tololo Observatory. That same year she was named a full member of the Chilean Academy of Sciences Institute. She was the first woman and the first astronomer to join that select group of scientists.

2020 John Horton Conway ceases to play the game of life.
John Horton Conway (born 26 December 1937, died  April 11, 2020 ) was a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life.
Conway is currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He received the Berwick Prize (1971),[1] was elected a Fellow of the Royal Society (1981), was the first recipient of the Pólya Prize (LMS) (1987), won the Nemmers Prize in Mathematics (1998) and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society. He has an Erdős number of one.*Wik
Conway was known for his sense of humor, and the last proof in his "On Numbers and Games" is this:
Theorem 100; This is the last Theorem in this book.
The Proof is Obvious.
Conway was exposed to the corona virus and took a fever around the 8th of April.  He had suffered from ill health for an extended time, and in three days, on April 11, 2020 he died at his home in New Jersey.

I really enjoyed Siobhan Roberts biography of Conway.  You may, too.

The horned sphere

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

Solution to 101 coins