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The History of William Marshal was commissioned by his son shortly after William’s death in 1219 to celebrate the Marshal’s remarkable life; it is an authentic, contemporary voice. The manuscript was discovered in 1861 by French historian Paul Meyer. Meyer published the manuscript in its original Anglo-French in 1891 in two books. This book is a line by line translation of the first of Meyer’s books; lines 1-10152. Book 1 of the History begins in 1139 and ends in 1194. It describes the events of the Anarchy, the role of William’s father John, John’s marriages, William’s childhood, his role as a hostage at the siege of Newbury, his injury and imprisonment in Poitou where he met Eleanor of Aquitaine and his life as a knight errant. It continues with the accusation against him of an improper relationship with Margaret, wife of Henry the Young King, his exile, and return, the death of Henry the Young King, the rebellion of Richard, the future King Richard I, war with France, the death of King Henry II, and the capture of King Richard, and the rebellion of John, the future King John. It ends with the release of King Richard and the death of John Marshal.
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Mathematics is in General Things.
Real Numbers can be either Algebraic Numbers or Transcendental Number.
Transcendental Number are numbers which are non-algebraic. They transcend Algebraic Numbers hence the name.
Real Numbers can be either Algebraic Numbers or Transcendental Number.
Natural Logarithm of 2. Is the logarithm of 2 to the base of e. It is usually written as ln2. It is a Transcendental Number.
The Alternating Harmonic Series: SUM(1,INFINITY) ( (-1)**(N+1) ) / N = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + ....
Or Binary Rising Constant Factorial: SUM(1,INFINITY) 1 / ( ( 2**N ) *N) = 1/2 + 1/8 + 1/24 + 1/64 + 1/160 + 1/384 + 1/896 + ....
Or SUM(0,INFINITY) 1 / ( ( 2N + 1 ) * ( 2N + 2 ) ) = 1 / ( 4N**2 + 6N + 2 ) = 1/2 + 1/12 + 1/30 + 1/56 + 1/90 + 1/132 + 1/182 + 1/240 + ....
e. Euler's Number is 2.718254. It is usually written as 'e'. It is a Transcendental Number.
Euler's Number is the number to which compounding, as in compount interest, converges.
For example, if interest is paid at 100% then after one year £1 becomes £2.
If the interest is charged at 50% twice then the interest will be ( 1 * 1.5 ) * 1.5 = 1.5**2 = 2.25
If the interest is charged at 25% four times then the interest will be ( ( ( ( 1 * 1.25 ) * 1.25 ) * 1.25 ) * 1.25 )= 1.25**4 = 2.44
If the interest is charged at 8.33% twelve times then the interest will be 1.0833**12 = 2.612
If the interest is charged at 4.2% twenty-four times year then the interest will be ( 1.042**4 ) = 2.67
If the interest is charged at 0.1% one thousand times then the interest will be ( 1.001**1000 ) = 2.72
If the interest is charged at an infinite number of times then the interest will be ( 1.00/∞ )**∞ = 2.718254... which is Euler's number.
Euler's Number is the sum of the infinite series ( 1 / n! ) ie 1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 + 1/720 + 1/5040 .... = 2.718281828.
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Natural Logarithm of 2. Is the logarithm of 2 to the base of e. It is usually written as ln2. It is a Transcendental Number.
The Alternating Harmonic Series: SUM(1,INFINITY) ( (-1)**(N+1) ) / N = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + ....
Or Binary Rising Constant Factorial: SUM(1,INFINITY) 1 / ( ( 2**N ) *N) = 1/2 + 1/8 + 1/24 + 1/64 + 1/160 + 1/384 + 1/896 + ....
Or SUM(0,INFINITY) 1 / ( ( 2N + 1 ) * ( 2N + 2 ) ) = 1 / ( 4N**2 + 6N + 2 ) = 1/2 + 1/12 + 1/30 + 1/56 + 1/90 + 1/132 + 1/182 + 1/240 + ....
Abbot John Whethamstede’s Chronicle of the Abbey of St Albans
Abbot John Whethamstede's Register aka Chronicle of his second term at the Abbey of St Albans, 1451-1461, is a remarkable text that describes his first-hand experience of the beginning of the Wars of the Roses including the First and Second Battles of St Albans, 1455 and 1461, respectively, their cause, and their consequences, not least on the Abbey itself. His text also includes Loveday, Blore Heath, Northampton, the Act of Accord, Wakefield, and Towton, and ends with the Coronation of King Edward IV. In addition to the events of the Wars of the Roses, Abbot John, or his scribes who wrote the Chronicle, include details in the life of the Abbey such as charters, letters, land exchanges, visits by legates, and disputes, which provide a rich insight into the day-to-day life of the Abbey, and the challenges faced by its Abbot.
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PI is the ratio of diameter and circumference of a circle. It is a Transcendental Number.
Fibonacci Series. The series that starts with 0 and 1. Some mathematicians suggest it starts with 1 and 1. The next term in the series is the sum of its previous two terms: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.