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Chronicle of Walter of Guisborough
A canon regular of the Augustinian Guisborough Priory, Yorkshire, formerly known as The Chronicle of Walter of Hemingburgh, describes the period from 1066 to 1346. Before 1274 the Chronicle is based on other works. Thereafter, the Chronicle is original, and a remarkable source for the events of the time. This book provides a translation of the Chronicle from that date. The Latin source for our translation is the 1849 work edited by Hans Claude Hamilton. Hamilton, in his preface, says: 'In the present work we behold perhaps one of the finest samples of our early chronicles, both as regards the value of the events recorded, and the correctness with which they are detailed; Nor will the pleasing style of composition be lightly passed over by those capable of seeing reflected from it the tokens of a vigorous and cultivated mind, and a favourable specimen of the learning and taste of the age in which it was framed.'
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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).
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.
Chronicle of a Bourgeois of Valenciennes
Récits d’un bourgeois de Valenciennes aka The Chronicle of a Bourgeois of Valenciennes is a vivid 14th-century vernacular chronicle written by an anonymous urban chronicler from Valenciennes in the County of Hainaut. It survives in a manuscript that describes local and regional history from about 1253 to 1366, blending chronology, narrative episodes, and eyewitness-style accounts of political, military, and social events in medieval France, Flanders, and the Low Countries. The work begins with a chronological framework of events affecting Valenciennes and its region under rulers such as King Philip VI of France and the shifting allegiances of local nobility. It includes accounts of conflicts, sieges, diplomatic manoeuvres, and the impact of broader struggles like the Hundred Years’ War on urban life in Hainaut. Written from the perspective of a burgher (bourgeois) rather than a monastery or royal court, the chronicle offers a rare lay viewpoint on high politics and warfare, reflecting how merchants, townspeople, and civic institutions experienced the turbulence of the 13th and 14th centuries. Its narrative style combines straightforward reporting of events with moral and civic observations, making it a valuable source for readers interested in medieval urban society, regional politics, and the lived experience of war and governance in pre-modern Europe.
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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.