Let's see: Let a and b be real, where a and b are nonzero. Suppose a = b. So if a = b, by multiplying both sides of equality by a we have: a 2 = ab Subtracting b 2 from both sides of equality we have: a 2 -b 2 = ab-b 2 We know (factoring) that a 2 - b 2 = (a + b) (ab). So: (a + b) (ab) = ab-b 2 Putting b on the right side we have: (a + b) (ab) = b (ab) Dividing both sides by (ab) we have: a + b = b As at the beginning we said that a = b, so instead of a I can put b: b + b = b So 2b = b.

Andrei Andreyevich Markov was born on June 14, 1856 in Ryazan, Russia. He died on July 20, 1922 in Petrograd (now St. Petersburg), Russia. He graduated from the University of St. Petersburg (1878), where he became a professor in 1886. Markov's early work was mainly on number theory and analysis, continuous fractions, integral limits, approximation theory, and series convergence.
Gaspard Monge, Frenchman, the son of a poor businessman, under the influence of a lieutenant colonel, attended classes at the Mezière Military School where he would later teach. Of great capacity, he was one of the mathematicians of the French Revolution, contributing many articles to the "Memories of the Academy of Sciences".
Alexis Claude Clairaut was born on May 7, 1713 in Paris (France) and died on May 17, 1765, also in Paris. The son of a French mathematician from whom he received his training, he became one of the earliest and most celebrated mathematicians in history. He studied calculus at the age of 10, published his first mathematical work at 13, and wrote a mathematical treatise at 18.
Karl Theodor Wilhelm Weierstrass was born in Germany, from a liberal Catholic family. Weierstrass did not like music but did very well in his studies. Encouraged by his father, he went to Bonn University to study law. Then he became adept at drinking and fencing instead of law and mathematics, leaving without graduating.
Georg Simon Ohm was born on March 16, 1789 in Bavaria (Germany), and died on July 6, 1854 in Munich. Physicist and mathematician, Ohm was a math teacher in Cologne and Nuremberg. Between 1825 and 1827, he developed the first mathematical theory of electrical conduction in circuits, based on the study of Fourier heat conduction and fabricating metal wires of different lengths and diameters used in his studies of electrical conduction.
Arquitas de Tarento was born in 428 BC in Tarento, a Greek colonial city in southern Italy, and died in 365 BC. He was a Greek mathematician, astronomer, musician and politician. Legitimate representative of the Pythagorean school and of Platonic character, was one of those responsible for fundamental changes in mathematics of the fifth century BC.
Robert Record was an English mathematician, son of Thomas Record and Rose Jones. He was born in 1510 in Tenby, Wales (England), and died in 1558 in London. He is well known for creating the equal sign (=) in the year 1557. The equality symbol has not always been the parallel traits we are so used to.
Marin Mersenne was born on September 8, 1588 in Oize-Maine, France. He died on September 1, 1648 in Paris, France. He is best known for his work of clarification and correspondence between eminent philosophers and scientists, and for his work in Number Theory. Mersenne attended Mans College after which, and from 1604, spent five years at the Jesuit College of La Fleche.
In 2000, the Clay Mathematics Institute announced that it would pay the \$ 1 million prize to every mathematician who could solve some of the so-called "millennium problems." These are seven problems created over the centuries that had never been solved. After ten years, Russian Grigori Perelman solved one of them, the “Poincaré Conjecture”, a series of abstract calculations involving three-dimensional spheres.
Seki Takakazu, also known as Seki Kōwa, was born in March 1642 in Fujioka (Japan), and died on October 24, 1708 in Edo (now Tokyo), Japan. He was born into a family of samurai warriors. However, very young, he was adopted by a noble family named Seki Gorozayemon. The name by which he is now known derives from the family that adopted him.
An enuple is an ordered sequence of n elements. It is also known as n-tuple, n-tuple or simply tuple. When n = 2, we can call the sequence double. For example, (1,2) is a double. Already the sequence (-2, 1) is another double. Therefore, what differs an enuple from a set is that: - An enuple can contain an object more than once.
These are integers of the form M p = 2 p -1. If M p is a prime number, so is p. They are named after their most distinguished scholar, Marin Mersenne. The first are the null mersenne (M 0 = 0) and the unitary (M 1 = 1). There are prime and non-prime mersennes, but cousins ​​are the most studied.
The French author Alphonse Rebière, in his 1889 Mathématiques et mathématiciens, tells that Tsar Ivan IV of Russia, nicknamed "the Terrible," once posed a problem to a geometer in his court. It was a matter of determining how many bricks would be required to construct a regular building, the dimensions of which were indicated.
"Pay attention: in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the collars. That is: a 2 = b 2 + c 2. Is that clear?" The teacher drops the chalk and turns to the class: "for this is the statement of the Pythagorean theorem. Now let's move on to the demonstration." As the teacher turns back to the blackboard, some students look at each other: "And who was this Pythagoras?
Many people, when writing the number 7, still put a small dash in the middle of the number. Officially, this little trace does not exist, as we can see on computer keyboards or calculators. But what is the origin of this custom? To better understand the different spellings of number 7, it should be remembered that our system originates from the Indo-Arabic system.
Two 20-year-old members of the University of Sheffield Mathematical Society (UK), in partnership with the Debenhams store, devised a formula for decorating the perfect Christmas tree, ending bare branches or garish decorations and calculating the required amount of balls, ribbons, lights and the size of the star at the top.
We know that a hexagonal number is one that can be represented in the form of a hexagon, such as the number 6: However, there are also centralized hexagonal numbers, which can be arranged in hexagonal form, starting with a dot. in the middle. Examples: How to Quantify People at Public Events Index Next >> Rubin's Vase
There are several proverbs that involve the number two. Examples: "A bird is better than two flying". "Warned man is worth two." "Kill two birds with one stone". "One take better than two I will give you." "Two profits don't fit in one bag." "Between the two come the devil and choose."
This number, multiplied by 1, 2, 3, 4, 5, 6, 8, or 9, results in another number whose digits are in the same order as the original. But if the result is 7 digits instead of 6, just add the first to the last number to get the sequence again. See: 142857 x 5 = 714285 142857 x 8 = 1142856, summing the extremes (1 + 6) = 7 -> 714285 Best of all, you don't need to get 142857, you can get any 6-digit number in this sequence, that they all have this property.
Have a person mark any given calendar month in a 3-by-3 “square” containing 9 days. See an example of a calendar choice below for August 2005. August 2005 Sun Mon Tue Wed Thu Fri Sat 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Then ask her to tell you the smallest date on the square, and say that with that date alone you will find out the sum of all the chosen dates.