Course Outline Our topics: Algebra Geometry Functions and Graphs Trigonometry System of Linear Equations Proportion, Direct & Inverse Variation Analytic Geometry Statistics Calculus (Derivative and Integration) The A&W 3/9 lb. Burger | A&W Restaurants https://www.youtube.com/watch?v=EMNqJQaf08E https://www.cbc.ca/radio/undertheinfluence/how-failing-at-fractions-saved-the-quarter-pounder1.5979468 https://www.youtube.com/watch?v=YsEcpS-hyXw Contar (povo que não conta: https://www.bbc.com/portuguese/noticias/2016/01/160126_tribo_sem_numeros_mv) Contar por traços – impraticável: como contar a população de uma cidade? Necessidade de símbolos. Mathematics was invented or discovered? All start with Arithmetic (addition, subtraction,…) and Geometry(points, lines, shapes…). Babylonian geometry knew Pythagoras theorem long before Pythagoras. China dealt with decimal fractions 1500 years before Europe. The numbers we use are called Hindu-Arabic numerals they began in India about 3 centuries B.C. They were introduced to the west by Arab merchants about 12th century. Who started to concern about proofing were the Greeks. The Babylonians got their number system from the Sumerians https://en.wikipedia.org/wiki/Sumer , the first people in the world to develop a counting system. Developed 4,000 to 5,000 years ago, the Sumerian system was positional — the value of a symbol depended on its position relative to other symbols. (https://www.livescience.com/27853-who-invented-zero.html ) All geometry you know from high school came from there. Trigonometry (study of triangle) starts with the interest of how Earth moves around the Sun 300 B.C. "The Elements" is the most influential Mathematics text ever. Euclid based his geometry on that axiomatic method with deductive reasoning. Pythagoras Theorem = Book 1 Proposition 47 History of Algebra...in just 5 minutes https://www.youtube.com/watch?v=f97mGPgBL_Q Símbolos romanos: I, V, X, L, C, D, M – no ZERO (103 in Roman numerals is CIII. The number 99 is XCIX. You try adding CIII + XCIX. It’s absurd. https://www.vox.com/science-andhealth/2018/7/5/17500782/zero-number-math-explained ) ZERO concept came from India around fifth century AD. (https://www.livescience.com/27853-whoinvented-zero.html ) Cross-multiplication Which means X3 – X1/2 + X = 0 1º. através de palavras (retórica) 2º. Através de abreviações (exemplo Paciloi): cubo meno censo(Raiz quadrada) plus cosa(seria equivalente a xis) equale zero. X3 – X1/2 + X = 0 3º. Álgebra simbólica – como conhecemos agora. Descartes: He wanted to see if we can study Euclid’s geometry from an algebraic point of view. That is the Method. Fermat's Last Theorem Archimedes https://en.wikipedia.org/wiki/Archimedes Archimedes' other mathematical achievements include deriving an approximation of pi; defining and investigating the spiral that now bears his name; and devising a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics. Archimedes' achievements in this area include a proof of the principle of the lever,[10] the widespread use of the concept of center of gravity,[11] and the enunciation of the law of buoyancy.[12] He is also credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion. The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius, a votive crown for a temple had been made for King Hiero II of Syracuse, who had supplied the pure gold to be used; Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith.[30] Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density. In Vitruvius' account, Archimedes noticed while taking a bath that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the crown's volume. For practical purposes water is incompressible,[31] so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" (Greek: "εὕρηκα, heúrēka!, lit. 'I have found [it]!').[30] The test on the crown was conducted successfully, proving that silver had indeed been mixed in.[32] To do Calculus must a genius (Archimedes). The Calculus (collection of rules) not necessarily the others mentioned on the slide. The 3 areas of mathematics in antiquity: https://math.stackexchange.com/questions/280530/can-you-provide-me-historical-examples-of-puremathematics-becoming-useful