The Fibonacci sequence Modulo 50, has a period length of 300. As an example for a smaller number, mod 2, the numbers 1, 1, 2, 3, 5, 8, 13 Mod 2 have residues 1, 1, 0, 1, 1, 0, 1, for a repeating pattern of 3.
EVENTS
1725 Nicolaus II and Daniel Bernoulli arrived in St. Petersburg on October 27, 1725 (OS)
In 1780, the first U.S. astronomical expedition to record an eclipse of the sun observed the event which lasted from 11:11 am to 1:50 pm. The observers left about three weeks earlier, on 9 Oct from Harvard College, Cambridge, Mass., for Penobscot Bay, led by Samuel Williams. A boat was supplied by the Commonwealth of Massachusetts the four professors and six students. Although the U.S. was at war with Britain, the British officer in charge of Penobscot Bay permitted the expedition to land and set up equipment to observe the predicted total eclipse of the sun. The expedition was shocked to find itself outside the path of totality. They saw a thin arc of the sun instead of its complete obscuration by the moon. *TIS
1859 The spectroscope was invented on this day. A spectroscope is a prism-based device which separates light into its different wavelengths. Gustav Kirchhoff initially used it to study the spectral “signature” of various chemical elements, allowing the identification of a new element if a new spectrum was observed. *rsc.org
1980 The first major network crash, the four-hour collapse of the ARPANET, occurred
The ARPANET, predecessor of the modern Internet, was set up by the Department of Defense Advanced Research Projects Agency (DARPA). Initially it had linked four sites in California and Utah, and later was expanded to cover research centers across the country.
The network failure resulted from a redundant single-error detecting code that was used for transmission but not storage, and a garbage-collection algorithm for removing old messages that was not resistant to the simultaneous existence of one message with several different time stamps. The combination of the events took the network down for four hours. *CHM
2011 EPL (Europhysics Letters) went beyond Earthly limits by publishing its first ever paper submitted from space: a landmark for both European and physics-based research. Concerned with the properties of complex plasma in almost zero gravity conditions, the paper represents collaborative research of 29 individual missions performed over the last 10 years by German and Russian researchers aboard the International Space Station (ISS).
The experiments detailed in the paper were performed on the ISS in July 2010 by Alexander Alexandrovich Skvortsov and were submitted on 27 October 2011 by Skvortsov’s colleague, Sergey Alexandrovich Volkov, who remains on the ISS.
IOP Blog
BIRTHS1678 Pierre Rémond de Montmort (27 Oct 1678 in Paris, France, 7 Oct 1719 in Paris, France) was a French mathematician who wrote an important work on probability. Montmort's reputation was made by his book on probability Essay d'analyse sur les jeux de hazard which appeared in 1708. The book, which is a collection of combinatorial problems, is a systematic study of games of chance and shows that there is important mathematics in this area.
Montmort collaborated with Nicolaus(I) Bernoulli and he was also a friend of Taylor. At a time of high feelings in the Newton-Leibniz controversy it says a lot for Montmort that he could be friends with followers of both camps.
In addition to those mentioned above, Montmort corresponded with Craig, Halley, Hermann and Poleni.
Montmort was elected to be a Fellow of the Royal Society in 1715, when he was on a trip to England. The following year he was elected to the Académie Royal des Sciences. *SAU
1728 James Cook (27 Oct 1728; 14 Feb 1779) English seaman who was the first of the really scientific navigators. Captain Cook spent several years surveying the coasts of Labrador and Newfoundland. He observed a solar eclipse on 5 Aug 1766 near Cape Ray, Newfoundland. On the first of three expeditions into the Pacific (1768) he took Joseph Banks as the ship's botanist to study the flora and fauna discovered. (This practice of carrying a naturalist took place some 75 years before Charles Darwin's famous voyage.) Cook observed the transit of Venus on this voyage from the island of Tahiti on 3 Jun 1769. This would help scientists plot the distance between the sun to the earth. His geographical discoveries made him the most famous navigator since Magellan. He was killed by cannibal natives in Hawaii.*TIS
1798 Heinrich Ferdinand Scherk (27 Oct 1798 in Poznań, Poland - 4 Oct 1885 in Bremen, Germany) was a mathematician born in what is now Poland who discovered an important example of a minimal surface. Scherk discovered the third non-trivial examples of a minimal surface which appeared in his paper Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen published in Crelle's Journal. The first two examples, the catenoid and the helicoid (also called the screw surface), had been found by the Frenchman Jean Baptiste Marie Meusnier in 1776. The catenoid arises from rotating the catenary curve about a horizontal line. Scherk's result was certainly seen as a major breakthough and brought him considerable fame; two surfaces, Scherk's First Surface and Scherk's Second Surface, as they are named today, are studied in the paper. Scherk's doubly periodic surface is the first example of a complete, embedded, doubly periodic minimal surface. His minimal surfaces have recently been the basis of sculptures by the American artist Brent Collins who has based many of his works on Scherk's second minimal surface.
Another contribution by Scherk is still important today, namely his work on the distribution of the prime numbers. *SAU
1827 Pierre-Eugène-Marcellin Berthelot (27 Oct 1827, 18 Mar 1907 at age 79) was a French chemist and science historian and government official whose creative thought and work significantly influenced the development of chemistry in the late 19th century. He helped to found the study of thermochemistry, introduced a standard method for determining the latent heat of steam, measured hundreds of heats of reactions and coined the words exothermic and endothermic. Berthelot systematically synthesized organic compounds, including some not found in nature. His syntheses of many fundamental organic compounds helped to destroy the classical division between organic and inorganic compounds. *TIS
1856 Ernest William Hobson (27 Oct 1856 in Derby, England, -19 April 1933 in Cambridge, Cambridgeshire, England) wrote the first English book on the measure theory and integration of Baire, Borel and Lebesgue. *SAU
1890 Olive Clio Hazlett (October 27, 1890 - March 8, 1974) was an American mathematician who spent most of her career working for the University of Illinois. She mainly researched algebra, and wrote seventeen research papers on subjects such as nilpotent algebras, division algebras, modular invariants, and the arithmetic of algebras.*Wik She was the most prolific of the US-born women of her time who worked in pure mathematics and was recognized for her research accomplishments when, in 1927, she became the second US-born woman to be ranked as one of American’s leading mathematicians by her peers, a distinction marked by a “star” in American Men of Science. *Natl Museum of American History
1915 Robert Alexander Rankin (27 Oct 1915 in Garlieston, Wigtownshire, Scotland, - 27 Jan 2001 in Glasgow, Scotland) studied at Cambridge University. His fellowship there was interrupted by his wartime work on rockets. He became Professor of Mathematics at Birmingham before moving to the professorship at Glasgow, a post he held for 27 years. His most important work was on Number Theory. He became President of the EMS in 1957 and 1978 and an honorary member in 1990. *SAU
DEATHS1449 Ulugh Beg (22 Mar 1394- 27 Oct 1449) The only important Mongol scientist, mathematician, and the greatest astronomer of his time. His greatest interest was astronomy, and he built an observatory (begun in 1428) at Samarkand. In his observations he discovered a number of errors in the computations of the 2nd-century Alexandrian astronomer Ptolemy, whose figures were still being used. His star map of 994 stars was the first new one since Hipparchus. After Ulugh Beg was assassinated by his son, the observatory fell to ruins by 1500, rediscovered only in 1908. Written in Arabic, his work went unread by the world's next generation of astronomers. When his tables were translated into Latin in 1665, telescopic observations had surpassed them. *TIS
1553 Michael Servetus (/sərˈviːtəs/; Spanish: Miguel Serveto as real name, French: Michel Servet), also known as Miguel Servet, Miguel de Villanueva, Michel Servet, Revés, or Michel de Villeneuve (Tudela, Navarre, 29 September 1511 – 27 October 1553), was a Spanish theologian, physician, cartographer, and Renaissance humanist. He was the first European to correctly describe the function of pulmonary circulation, as discussed in Christianismi Restitutio (1553). He was a polymath versed in many sciences: mathematics, astronomy and meteorology, geography, human anatomy, medicine and pharmacology, as well as jurisprudence, translation, poetry and the scholarly study of the Bible in its original languages.
He is renowned in the history of several of these fields, particularly medicine. He participated in the Protestant Reformation, and later rejected the Trinity doctrine and mainstream Catholic Christology. After being condemned by Catholic authorities in France, he fled to Calvinist Geneva where he was burnt at the stake for heresy by order of the city's governing council.
1616 Johann Richter or Johannes Praetorius (1537 Jáchymov, Bohemia – 27 October 1616, Altdorf bei Nürnberg) was a Bohemian German mathematician and astronomer. From 1557 he studied at the University of Wittenberg, and from 1562 to 1569 he lived in Nuremberg. His astronomical and mathematical instruments are kept at Germanisches Nationalmuseum in Nuremberg.
In 1571 be became Professor of mathematics (astronomy) at Wittenberg where he met Valentinus Otho(Otto) and Joachim Rheticus. When Otho came to Wittenberg in 1573, he suggested to him the fraction |( \frac{355}{113}\) as an approximation to pi. Although known much earlier in the Orient, this is the first known time it was introduced in Europe.
He taught Copernicus' theory of astronomy initially as a means of eliminating the equant from Ptolemy's account, and later moving to a proto-Tychonic system.
He died in Altdorf bei Nürnberg, aged about 79. *Wik
1845 Jean-Charles-Athanase Peltier (22 Feb 1785, 27 Oct 1845) French physicist who discovered the Peltier effect (1834), that at the junction of two dissimilar metals an electric current will produce heat or cold, depending on the direction of current flow. In 1812, Peltier received an inheritance sufficient to retire from clockmaking and pursue a diverse interest in phrenology, anatomy, microscopy and meteorology. Peltier made a thermoelectric thermoscope to measure temperature distribution along a series of thermocouple circuits, from which he discovered the Peltier effect. Lenz succeeded in freezing water by this method. Its importance was not fully recognized until the later thermodynamic work of Kelvin. The effect is now used in devices for measuring temperature and non-compressor cooling units. *TIS
1675 Gilles Personne de Roberval (8 Aug 1602- 27 Oct 1675) French mathematician who developed powerful methods in the early study of integration, writing Traité des indivisibles. He computed the definite integral of sin x, worked on the cycloid and computed the arc length of a spiral. Roberval is important for his discoveries on plane curves and for his method for drawing the tangent to a curve, already suggested by Torricelli. This method of drawing tangents makes Roberval the founder of kinematic geometry. In 1669 he invented the Roberval balance with an articulated parallelogram is now almost universally used for weighing scales of the balance type. He studied the vacuum and designed apparatus which was used by Pascal in his experiments and also worked in cartography. *TIS
1968 Lise Meitner (7 Nov 1878, 27 Oct 1968)Austrian physicist who shared the Enrico Fermi Award (1966) with the chemists Otto Hahn and Fritz Strassmann for their joint research beginning in 1934 that led to the discovery of uranium fission. She refused to work on the atom bomb. In 1917, with Hahn, she had discovered the new radioactive element protactinium. She was the first to describe the emission of Auger electrons. In 1935, she found evidence of four other radioactive elements corresponding to atomic numbers 93-96. In 1938, she was forced to leave Nazi Germany, and went to a post in Sweden. Her other work in the field of nuclear physics includes study of beta rays, and study of the three main disintegration series. Later, she used the cyclotron as a tool. *TIS
1980 John Hasbrouck Van Vleck (13 Mar 1899, 27 Oct 1980) was an American physicist and mathematician who shared the Nobel Prize for Physics in 1977 with Philip W. Anderson and Sir Nevill F. Mott. The prize honoured Van Vleck's contributions to the understanding of the behaviour of electrons in magnetic, noncrystalline solid materials. *TIS
1999 Robert L. Mills (15 Apr 1927 - 27 Oct 1999)American physicist who shared the 1980 Rumford Premium Prize with his colleague Chen Ning Yang for their "development of a generalized gauge invariant field theory" in 1954. They proposed a tensor equation for what are now called Yang-Mills fields. Their mathematical work was aimed at understanding the strong interaction holding together nucleons in atomic nuclei. They constructed a more generalized view of electromagnetism, thus Maxwell's Equations can be derived as a special case from their tensor equation. Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories. *TIS
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
Looking through the Gazette of the Australian Mathematical Society, and found their puzzle corner (July 2009 , so the exponents in the first problem are explained) ... really nice problems. I think I have this one, but I didn't prove it.... 
where dLat and dLong are the differences in the latitiudes and longitudes. Tables for Navigation contained both Hav(x) and its inverse invHav(x) and the logs of these values to assist in