William of Worcester's Chronicle of England
William of Worcester, born around 1415, and died around 1482 was secretary to John Fastolf, the renowned soldier of the Hundred Years War, during which time he collected documents, letters, and wrote a record of events. Following their return to England in 1440 William was witness to major events. Twice in his chronicle he uses the first person: 1. when writing about the murder of Thomas, 7th Baron Scales, in 1460, he writes '… and I saw him lying naked in the cemetery near the porch of the church of St. Mary Overie in Southwark …' and 2. describing King Edward IV's entry into London in 1461 he writes '… proclaimed that all the people themselves were to recognize and acknowledge Edward as king. I was present and heard this, and immediately went down with them into the city'. William’s Chronicle is rich in detail. It is the source of much information about the Wars of the Roses, including the term 'Diabolical Marriage' to describe the marriage of Queen Elizabeth Woodville’s brother John’s marriage to Katherine, Dowager Duchess of Norfolk, he aged twenty, she sixty-five or more, and the story about a paper crown being placed in mockery on the severed head of Richard, 3rd Duke of York.
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Algebraic Numbers is in Real Numbers.
Real Numbers can be either Algebraic Numbers or Transcendental Number.
Irrational Number. An Irrational Number is a number that cannot be expressed as a Fraction.
Constructable Numbers are numbers that can be derived using a straight edge and a compass.
The Golden Ratio, also known as the Golden Mean and Golden Section, is 1.618033... It is the solution to the equation x^2 - x - 1 = 0, or ( a + b ) / a = a / b.
The Golden Ratio is usually represented by the Greek Letter phi φ.
The Fibaonacci Series converges on the Golden Ratio.
The formula ( 1 + SQRT(5) ) / 2 is the Golden Ratio.
Square Root of 2, or 2^(1/2) being the length of the diagonal of a square with sides of length 1. It is 1.4142135623...
99/70 = 1.4142857 approximates to the Square Root of 2.
Non-Constructable Numbers are the solution to algebraic equations with a cube root of higher eg 2^(1/3).
Chronicle of Geoffrey le Baker of Swinbroke
Baker was a secular clerk from Swinbroke, now Swinbrook, an Oxfordshire village two miles east of Burford. His Chronicle describes the events of the period 1303-1356: Gaveston, Bannockburn, Boroughbridge, the murder of King Edward II, the Scottish Wars, Sluys, Crécy, the Black Death, Winchelsea and Poitiers. To quote Herbert Bruce 'it possesses a vigorous and characteristic style, and its value for particular events between 1303 and 1356 has been recognised by its editor and by subsequent writers'. The book provides remarkable detail about the events it describes. Baker's text has been augmented with hundreds of notes, including extracts from other contemporary chronicles, such as the Annales Londonienses, Annales Paulini, Murimuth, Lanercost, Avesbury, Guisborough and Froissart to enrich the reader's understanding. The translation takes as its source the 'Chronicon Galfridi le Baker de Swynebroke' published in 1889, edited by Edward Maunde Thompson.
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Fractions are an Integer divided by an Integer eg 1/2, 5/13, 241/98.
Rational Number. A Rational Number is a number that can be expressed as a Fraction of two Integers. Integers are Fractions with a divisor of 1.
Irrational Number. An Irrational Number is a number that cannot be expressed as a Fraction.
Integers aka whole numbers. Fractions with a divisor of 1.
Rational Number. A Rational Number is a number that can be expressed as a Fraction of two Integers. Integers are Fractions with a divisor of 1.
Prime Number. A Prime Number is an Integer that is only divisible by 1 and itself with the Remainder ie. 1, 2, 3, 5, 7, 11, 13, 17, 19, ...
Fermat Prime. A Prime Number that is a solution to 2^2^N + 1 eg 3, 5, 17, 65537, 4294967297, 18446744073709551617
2 ^ 2 ^ 0 + 1 = 3
2 ^ 2 ^ 1 + 1 = 5
2 ^ 2 ^ 2 + 1 = 17
With the exeception of the first and second terms Germat Primes always end in 7.
Mersenne Prime. A Mersenne Prime is a prime number that is one less than a power of two. Mersenne Primes do not include all numbers that are one less than a power of two eg 16 - 1 = 15 which is divisible by 1, 3 and 5.