If you disregard the very simplest cases, there is in all of mathematics not a single infinite series whose sum has been rigorously determined. In other words, the most important parts of mathematics stand without a foundation.
Abel, Niels H. (Quoted in G F Simmons, Calculus Gems)
Welcome to the blog Math1089 – Mathematics for All.
The root of the term mathematics is in the Greek word Mathema (μάθημα), which was used quite generally in early writings to indicate any subject of instruction or study.
A baker’s dozen is a group of 13.
Johann Rahn introduced the division symbol, known as the obelus, in 1659. This symbol took the form of a horizontal line with a dot above and below it (÷) and was featured in his book Teutsche Algebra.
282589933 – 1 is the largest prime number with 24862048 digits known until October 2023.
The Chaos Theory explores the behavior of dynamic systems that are highly sensitive to initial conditions, like the famous butterfly effect.
There are 17 standard-form types of quadratic surfaces (quadrics).
National Mathematics Day is observed in India on the 22nd of December, commemorating the birth anniversary of the renowned Indian mathematician, Srinivasa Ramanujan.
The first four pairs of digits following the decimal point of 1/97 are powers of three:
1/97 = 0.01030927….
Conway’s constant is an algebraic number of degree 71.
The percentage of y relative to x is equal to the percentage of x relative to y. In other words,
x% of y = y% of x.
The Bermuda Triangle, located in the western part of the North Atlantic Ocean, is infamous for its mysterious disappearances of ships and aircraft. Although many theories surround these disappearances, scientists attribute them to natural causes rather than any supernatural triangle-related phenomenon.
The sum of the reciprocals of the factors of any perfect number is equal to 2.
81 is the only two-digit number that is the square of the sum of its digits: 81 = (8 + 1)2.
A barrel that holds 63 gallons is called a hogshead.
The most prestigious award in mathematics is the Fields Medal, established in 1936 and awarded every four years (except around World War II) to up to four individuals. It is considered the mathematical equivalent of the Nobel Prize.
There are 179 even days in one year.
The number 5040 has unique properties that is , this number is the sum of 42 primes that is 42 consecutive primes and that is
23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 +163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229
One way to convert words to numbers is to let A = 1, B = 2, C = 3, . . . , Z = 26; and then compute the sum. Using this “alphabet code,” the word PRIME is prime.
If we consider the shadow of any object, the length of the shadow is equal to the height of the object when the angle of elevation is 45°.
The cube of 18 and the fourth power of 18 together use each digit exactly once: 183 = 5832 and 184 = 104976.
The term algebra comes from the Arabic word al-jabr, meaning the reunion of broken parts.
2 related items are often called a pair, and words like dual, duel, couple, twin, and double emphasize the significance of the number two.
There is a designated day, called Pi Day, that we celebrate on 14 March (3.14, excluding the year). Math enthusiasts around the world celebrate Pi Day on March 14th (3/14) in honour of the mathematical constant π (pi), which represents the ratio of a circle’s circumference to its diameter.
Do Pythagorean triples relate to Fibonacci numbers? Surprisingly yes. Consider any four consecutive Fibonacci numbers, say 2, 3, 5, 8. The product of the outer numbers is 2 × 8 = 16; twice the product of the inner numbers is 2 × 3 × 5 = 30; the sum of the squares of the inner numbers is 32 + 52 = 34, and they form a Pythagorean triplet!
Buy 2 get 1 free is a very common discount format with an approximate discount amount 33.3333% on each item.
A centenarian is a person who has reached the age of 100 years.
The Königsberg Bridge Problem led to the development of graph theory when Euler showed that it was impossible to walk through the city of Königsberg, crossing each bridge once and only once.
157 is the smallest three-digit prime that produces five other primes by changing only its first digit: 257, 457, 557, 757, and 857.
A magic square is a grid of numbers where the sums of the numbers in each row, column, and diagonal are the same. Magic square of order 2×2 cannot be constructed.
Any integer, however large, can be expressed by using only three 2’s. In fact, we have
The following identity is one which relates what some refer to as the famous five numbers, e, π, i, 1, and 0.
eiπ + 1 = 0
61 (sixty-one) is the largest prime whose name spelled out in English has no repeated letters.
A googol (10100) contains 101 digits. The search engine Google’s play on the term reflects the company’s mission to organize the immense amount of information available on the web.
ASCII characters (the long-established way to represent characters on a computer) are numbered from 0 to 127.
139 is the smallest prime that contains one prime digit, one composite digit, and one digit that is neither prime nor composite.
916 gold, also known as 22 Karat gold, is a widely preferred choice for jewellery in India. It contains 91.6% pure gold and 8.4% other alloys. 24-carat gold will have a hallmark 999, meaning it contains 99.9% pure gold.
There are exactly 103 geometrical forms of magic knight’s tour of the chessboard.
The hour and second hands of an analog clock align exactly 719 times every twelve hours.
Concentric circles are a set of circles with same centre, but have different radii. A common example is in the ripples of a pond when something hits the surface of the water. But we also see concentric circles in the layers of an onion and the rings of trees that form as it grows and ages.
A circle is associated to each triangle, known as the nine point circle, passing through
- The midpoint of each side of the triangle;
- The foot of each altitude;
- The midpoint of the line segment from each vertex of the triangle to the orthocentre (where the three altitudes meet; these line segments lie on their respective altitudes).
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