According to Pickover, " if humans attempt to read such data in the form of numbers and letters, they will take in the information at a snail's pace.

According to Vepstas ( 1997 ) " Pickover hit on the novel concept of looking to see how closely the orbits of interior points come to the x and y axes.

According to Pickover ( 1999 ) in summary, he " described an algorithm which could be used for the creation of diverse and complicated forms resembling invertebrate organisms.

According to Mark Bollman, a mathematics and calculator historian and associate professor of mathematics at Albion College, the " Construction Master is the first in a long and profitable line of CI construction calculators " which carried them through the 1980s, 1990s, and to the present.

According to the formalist, mathematics is manipulation of symbols according to agreed upon formal rules.

According to Husserl, this view of logic and mathematics accounted for the objectivity of a series of mathematical developments of his time, such as n-dimensional manifolds ( both Euclidean and non-Euclidean ), Hermann Grassmann's theory of extensions, William Rowan Hamilton's Hamiltonians, Sophus Lie's theory of transformation groups, and Cantor's set theory.

According to Carnap's " Logicist Foundations of Mathematics ", Russell wanted a theory that could plausibly be said to derive all of mathematics from purely logical axioms.

According to Steinhaus, while he was strolling through the gardens he was surprised to over hear the term " Lebesgue measure " ( Lebesgue integration was at the time still a fairly new idea in mathematics ) and walked over to investigate.

According to ScienceWatch, UVic is nationally ranked first in geoscience, second in space science and education, and third in engineering and mathematics for the period of 2000 – 2004.

According to Lakoff, even mathematics is subjective to the human species and its cultures: thus " any question of math's being inherent in physical reality is moot, since there is no way to know whether or not it is.

According to Parentalia, he was " initiated " in the principles of mathematics by Dr William Holder, who married Wren's elder sister Susan ( or Susanna ) in 1643.

According to general semantics, language, natural or otherwise ( including the language called ' mathematics ') can be used to describe the taste of an orange, but one cannot give the taste of the orange using language alone.

According to general semantics, the content of all knowledge is structure, so that language ( in general ) and science and mathematics ( in particular ) can provide people with a structural ' map ' of empirical facts, but there can be no ' identity ', only structural similarity, between the language ( map ) and the empirical facts as lived through and observed by people as humans-in-environments ( including doctrinal and linguistic environments ).

According to Lewis ( 1918 ), the " principle of these diagrams is that classes set ( mathematics ) | set s be represented by regions in such relation to one another that all the possible logical relations of these classes can be indicated in the same diagram.

According to the mathematics of drift, when comparing divergent populations, most of the single-nucleotide differences can be assumed to have accumulated at the same rate as individuals with mutations are born.

According to Elvin, Chinese knowledge of science, mathematics, and engineering in the 14th century was far more advanced than anywhere else in the world.

According to Porterfield, " There he improved his mathematics, struggled with Latin, listened to music that stirred him ( opera and oratorios, light ' classics ' of the day ), and learned, for the first time, of two poets — Tennyson and Browning — whose work would soon become an integral part of his intellectual equipment.

According to McLarty ( 2005 ), this diagrammatic approach to contemporary mathematics largely stems from Mac Lane ( 1948 ).

According to his great-great-grandson, d ' Alembert received him rather poorly, and to get rid of him gave him a thick mathematics book, saying to come back when he had read it.

According to the Department of Education 2011 breakdown of A-level results, John Mason were the sixth best in the UK for performance in mathematics, with 38 % of students getting A * grade.

According to Kapoor, she was a good student and received first-class honours in all subjects except mathematics.

According to one of the classic texts of Confucianism, Zhou Li ( 周禮 / 周礼 ), Archery and charioteering were part of the " six arts " (, including rites, music, calligraphy and mathematics ) of the Zhou Dynasty ( 1122 – 256 BCE ).

According to Shamir, he read mathematics and law at Novosibirsk University.

According to Sol Garfunkel, the cake-cutting problem had been one of the most important open problems in 20th century mathematics, when the most important variant of the problem was finally solved with the Brams-Taylor procedure by Steven Brams and Alan Taylor in 1995.

According to a Pennsylvania Department of Education study released in January 2009, 25 % of Pleasant Valley High School graduates required remediation in mathematics and or reading before they were prepared to take college level courses in the Pennsylvania State System of Higher Education or community colleges.

According to a Pennsylvania Department of Education study released in January 2009, 25 % of Pleasant Valley High School graduates required remediation in mathematics and or reading before they were prepared to take college level courses in the Pennsylvania State System of Higher Education or community colleges.

According to some sources, the emir himself was behind Muhammad's fall, as well as Al-Mutarrif's death in 895.

According to the plans, the Third Army, under general Radko Dimitriev, was deployed east of and behind the First, and was covered by the cavalry division hiding it from the Turkish view.

According to tradition, a Praetorian named Gratus found him hiding behind a curtain and suddenly declared him princeps.

According to National Football League history, it legalized the forward pass from anywhere behind the line of scrimmage on February 25, 1933.

According to a poll conducted in 1947, Robinson was the second most popular man in the country, behind Bing Crosby.

According to Vasilyev, Khazar populations remained behind in Transoxiana under Pecheneg and Oghuz suzerainty, possibly remaining in contact with the main body of their people.

According to Knuth, literate programming provides for higher-quality programs, since it forces programmers to explicitly state the thoughts behind the program, making poorly thought-out design decisions more obvious.

According to Eichenwald, preceding the investigation Whitacre was scammed by a group in Nigeria in an advance fee fraud, and suggests that Whitacre's losses in the scam may have been the initial reason behind his embezzlement activity at ADM.

According to Metcalfe, the rationale behind the sale of networking cards was that ( 1 ) the cost of the network was directly proportional to the number of cards installed, but ( 2 ) the value of the network was proportional to the square of the number of users.

According to Amnesty International, the number of kidnappings has decreased in recent years but the human rights organization estimates that FARC and ELN guerrillas continue to be behind hundreds of cases.

According to the Apogee website the original storyline was the following: After the fall of Hitler, the true powers behind him have drawn into seclusion, planning their next strategy for world domination.

According to Oxford County Sheriff deputy Matt Baker, King was hit from behind and some witnesses said the driver was not speeding, reckless, or drinking.

According to Clark, again posting on the TrekBBS, dissatisfaction over the finale episode is the driving factor behind the continuation novels / relaunch including a story arc that suggests that Trip's death in the finale was not as it seemed.

According to a survey by Forbes magazine, Istanbul, Turkey's financial capital, had a total of 28 billionaires as of March 2010 ( down from 34 in 2008 ), ranking 4th in the world behind New York City ( 60 billionaires ), Moscow ( 50 billionaires ), and London ( 32 billionaires ).

According to the 2011 census, the total population of the United Kingdom is around 63, 100, 000 — the third-largest in the European Union ( behind Germany and metropolitan France ) and the 22nd-largest in the world.

According to him, lacrosse was where he learned to protect himself from hard checks: " In those days you could be hit from behind in lacrosse, as well as cross-checked, so you had to learn how to roll body checks for self-protection.

According to Forbes Magazine, the Redskins are the second most valuable franchise in the NFL, behind the Dallas Cowboys, and were valued at approximately $ 1. 55 billion as of 2009.

According to Hill and Worthington, dykes in the far north and south may have different dates, and though they may be connected with Offa's Dyke, there is as yet no compelling evidence behind this.

According to the tradition used in Virgil's Aeneid, Segesta was founded jointly by the territorial king Acestes ( who was son of the local river Crinisus by a Dardanian woman named Segesta or Egesta ) and by those of Aeneas ' folk who wished to remain behind with Acestes to found the city of Acesta.

According to Swazi royalist tradition, these chiefdoms came to be classified in the Dlamini kingdom as the Emakhandzambile category of clans (" those found ahead ", e. g. the Gamedze ), meaning that they were on the land prior to Dlamini immigration and conquest, as opposed to the Bomdzabuko (" true Swazi ") who accompanied the Dlamini kings, and the Emafikemuva (" those who came behind ") who joined the kingdom later.

According to Susan McClary ( 2000, p. 1285 ) the discipline of " music lags behind the other arts ; it picks up ideas from other media just when they have become outmoded.

According to New Scientist, " The oil industry seems to be behind the move.

According to the Memoirs of Li Zongren, the supervisory unit shot at waves of fleeing Chinese soldiers from behind.

According to Moore, the concept behind the series was initially a " Justice League of Victorian England " but quickly grew into an opportunity to merge several works of fiction into one world.