Text this colour links to Pages. Text this colour links to Family Trees. Place the mouse over images to see a larger image. Click on paintings to see the painter's Biography Page. Mouse over links for a preview. Move the mouse off the painting or link to close the popup.
Mathematics is in General Things.
Culture, General Things, Mathematics, Numbers
Culture, General Things, Mathematics, Real Numbers
Real Numbers can be either Algebraic Numbers or Transcendental Number.
Culture, General Things, Mathematics, Real Numbers, 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 + ....
Culture, General Things, Mathematics, Real Numbers, Transcendental Number, e
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.
Become a Member via our 'Buy Me a Coffee' page to read complete text.
Culture, General Things, Mathematics, Real Numbers, Transcendental Number, e, Natural Logarithm of 2
All About History Books
The 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." Available at Amazon in eBook and Paperback.
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 + ....
Culture, General Things, Mathematics, Real Numbers, Transcendental Number, e, PI
PI is the ratio of diameter and circumference of a circle. It is a Transcendental Number.
Culture, General Things, Mathematics, Series
Culture, General Things, Mathematics, Fibonacci Series
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.