If a linear system has n equations and n unknowns, it can be: a) possible and determined if D = det A 0; in which case the solution is unique. Example: m = n = 3 Then the system is possible and determined by having a unique solution. b) possible and undetermined, if D = D x1 = D x2 = D x3 =… = D xn = 0, for n = 2. If n 3, this condition is valid only if there are no equations with respectively proportional unknown coefficients and non-proportional independent terms.
Ada Byron King, the Countess of Lovelace, was one of the few women in the history of data processing. Born in London on December 10, 1815. His baptismal name was Augusta Ada King, Lady Lovelace for posterity. His father was Lord Byron, a very famous poet, and his mother was Anne Isabelle Milbanke, from whom he acquired a love of mathematics.
He was a Portuguese mathematician and university professor. Born on April 1, 1901, in Rua dos Fidalgos, in Vila Viçosa, in a modest dependence of the Chagas Convent, where some servants of the house of Bragança were housed, Bento de Jesus Caraça was the son of rural workers. He lived the first five years of his life in the Casa Branca estate, in the parish of Montoito, where he learned to read and write with a worker, José Percheiro.
We start with the following equality: -24 = -24 We write the number -24 in two different ways: 16 - 40 = 36 - 60 The numbers 16, 40, 36 and 60 can be written as follows: 4x4 - 2x4x5 = 6x6 - 2x6x5 We can add 25 on both sides of the equation without changing it: 4x4 - 2x4x5 + 5x5 = 6x6 - 2x6x5 + 5x5 Now we see that on both the left and the right side we have a squared binomial (the first squared term minus twice the product of the two terms plus the square of the second) (4 - 5) 2 = (6 - 5) 2 Eliminating the square on both sides of the equation gives: 4 - 5 = 6 - 5 Finally, by adding 5 on both sides, we get the result: 4 = 6 Obviously this demonstration has an error because we all know that 4 is not equal to 6 (or does anyone have any questions?
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.
Sueli dos Santos The content of this work was developed by the academic Sueli dos Santos of the Pedagogy course modality Degree for the Early Years of Elementary School Open and Distance Education Institute of the Federal University of Mato Grosso, to complete the area of Mathematics .
Monia Andreia Tomieiro BUENO Abstract The greatness of the Inca civilization was not only evident in its engineering techniques, but also in the way in which this civilization organized its state, creating, for that, a string system - the kipus - for alphanumeric registration, used in the 15th and 16th centuries to encode their information and solve numerical problems.
The use of digital multimedia as methodological support in the didactic process of mathematical education
Prof. Ms. Eduardo Vianna Gaudio UFES / UNIVILA Vitória / ES Until the 1990s, the vast majority of mathematics teachers used as methodological support in the preparation of their teaching activities, basically the textbook. The largest source of information, from the advent of digital multimedia, has been virtualized.
Annius Mantius Torquato Severinus Boethius, also known as Anitius Manlius Torquatus Severinus Boethius, was born in Rome from about 430 BC to 800 BC. He was from a noble family, studied in the Greek East, unknown in Athens or Alexandria. He was a statesman and philosopher, translator, commentator, and author of books on mathematics, music, theology, and Roman man of state (consul and senator), considered the chief mathematical author of ancient Rome.
Henry Briggs was an English mathematician, born in February 1561, and died on January 26, 1630. He was the man most responsible for scientists accepting the logarithms. Briggs was educated at Cambridge University and was the first professor of geometry at Gresham College, London.
Augustin Louis Cauchy was born August 21, 1789, and died May 23, 1857. It was a French mathematician and physicist who proved (1811) that the angles of a convex polyhedron are determined by their faces (the flat surfaces that form a geometric solid). Numerous terms in mathematics have his name, for example, Cauchy's integral theorem in complex function theory and Cauchy-Kovalevskaya, the existing theorem for solving partial differential equations.
William Kingdon Clifford, an English mathematician and philosopher, was born in the town of Exeter on May 4, 1845. He died at a young age of 33 on March 3, 1879 in the Autonomous Region of Madeira. In addition to being a mathematician, he was a gymnast, writer of children's stories (such as The Little People Collection) and a renowned reciter, winning numerous awards.
Gabriel Cramer was born on July 31, 1704 in Geneva (now Switzerland), and died on January 4, 1752 in Bagnols-sur-Cèze, France. Cramer worked on analysis and determinants. He became a mathematics teacher at Geneva and wrote in physics work, also in geometry and history of mathematics.
Galileo was an Italian physicist, mathematician, astronomer and philosopher who played a unique role in the scientific revolution. Born on February 15, 1564 in the city of Pisa, Italy. His most cited work and one of the most revolutionary for the time in which he lived is the proposition of the Heliocentric theory, which describes a model of the universe where the sun is the still center, not the earth as was believed at the time.
Leonhard Euler, was born on April 15, 1707, and died on September 18, 1783. He was the most prolific mathematician in history. His 866 books and articles represent approximately one-third of his entire body of research in mathematics, physical theories, and mechanical engineering published between 1726 and 1800.
Colin Maclaurin was born in February 1698 in Kilmodan, Scotland, and died on June 14, 1746 in Edinburgh, Scotland. He was born in Kilmodan where his father was the parish minister. The village (population 387 in 1904) is on the Ruel river and the church is in Glendauel. He was a student in Glasgow. He became professor of mathematics at Marischal College, Aberdeen, from 1717 to 1725 and then at the University of Edinburgh from 1725 to 1745.
Manoel Jairo Bezerra was a well-known Brazilian mathematics teacher. He was born in 1920 in the city of Macau, Rio Grande do Norte, where he spent his childhood. He taught mathematics, his passion, between 1939 and 1996. He wrote 53 books and held important positions in public institutions. He was one of the pioneers of distance mathematics.
Johannes Kepler was born on December 27, 1571, in the south of present-day Germany, which at that time belonged to the Holy Roman Empire, in a town called Weil der Stadt, Swabian region. He was the son of Heinrich Kepler, a soldier, and his wife Katharina, whose maiden name was Guldenmann. His paternal grandfather, Sebald Kepler, was mayor of the city, despite being Protestant (Lutheran) in a Catholic city.
Lélio Gama lived most of his life in Rio de Janeiro. He was Full Professor of Mathematical and Higher Analysis at Univ. Federal District (1935-38) and the University of Brazil (1939). Received the title of member of the Brazilian Academy of Sciences. It had its professional beginning in 1929, with Astronomy.
Archimedes was born in Syracuse, Sicily in 287 BC, and was educated in Alexandria, Egypt. It was devoted to mathematics, more especially to geometry. Very young still began to distinguish itself for its scientific works. Returning to Syracuse, he devoted himself to the study of geometry and mechanics, discovering principles and making applications that immortalized him.
Johann Carl Friedrich Gauss was born in Brunswick, Germany. From humble family but with the encouragement of his mother obtained brilliance in his career. Studying in his hometown, one day when the teacher told the students to add numbers from 1 to 100, Gauss immediately found the answer - 5050 - seemingly without calculation.