Math symbols A tour of the scientific calculator Significance of symbols • Icons – The original icons • Thought control • Hilbert – meaningless symbols which acquire some substitute of meaning only through metamathematics. (23) Origin of = • Robert Recorde (c. 1510 – 1558) was a Welsh physician and mathematician. He introduced the "equals" sign (=) in 1557. • The 'equals' symbol '=' appears in Recorde's book The Whetstone of Witte published in 1557. He justifies using two parallel line segments:• ... bicause noe 2 thynges can be moare equalle . • The symbol = was not immediately popular. The symbol || was used by some and ae ( or oe), from the word 'aequalis' meaning equal, was widely used into the 1700s. = Not on all calculators. algebraic vs reverse Polish algabraic: 1+2= RPN: 1 (enter) 2+ on the calculator = really means do the operation = what does equals mean? 1. not the same as 2. not identical with 3. not similar 4. perhaps: equal in some sphere of sense 1.within the limits of the situation, the the two ideas are equal 1.the same number Equality • Equality may refer to: • Social concepts – Egalitarianism, the belief that all/some people ought to be treated equally – Equality before the law – Equal opportunity – Equality of outcome or equality of condition – Gender equality – Racial equality (disambiguation) – Social equality • Mathematics and computing – Congruence (geometry) – Equality (mathematics) – Equality (relational operator), a common operator used in programming languages • • • • • • • • • • • • • • • • • • • • Equal (Wolfram MathWorld) Two quantities are said to be equal if they are, in some well-defined sense, equivalent. Equality of quantities a and b is written a=b. Equal is implemented in Mathematica as ... Approximately Equal (Wolfram MathWorld) If two quantities A and B are approximately equal, this is written A approx B. Equal-Area Projection (Wolfram MathWorld) A map projection in which areas on a sphere, and the areas of any features contained on it, are mapped to the plane in such a way that two are related by a constant scaling ... Equal Detour Point (Wolfram MathWorld) The center of an inner Soddy circle. It has equivalent triangle center functions alpha = 1+(2Delta)/(a(b+c-a)) (1) alpha = sec(1/2A)cos(1/2B)cos(1/2C)+1, (2) where Delta is ... Equal Parallelians Point (Wolfram MathWorld) Through a point K in the plane of a triangle DeltaABC, draw parallelians through a point as illustrated above. Then there exist four points K for which ... Equality (Wolfram MathWorld) A mathematical statement of the equivalence of two quantities. The equality "A is equal to B" is written A=B. Cylindrical Equal-Area Projection (Wolfram MathWorld) The map projection having transformation equations x = (lambda-lambda_0)cosphi_s (1) y = sinphisecphi_s (2) for the normal aspect, where lambda is the longitude, lambda_0 is ... Equalizer (Wolfram MathWorld) An equalizer of a pair of maps f,g:X->Y in a category is a map e:E->X such that 1. f degreese=g degreese, where degrees denotes composition. 2. For any other map e^':E^'->X ... Behrmann Cylindrical Equal-Area ... (Wolfram MathWorld) The Behrmann cylindrical equal-area projection is a cylindrical equal-area projection with a standard parallel of phi_s=30 degrees. Lambert Cylindrical Equal-Area ... (Wolfram MathWorld) The Lambert cylindrical equal-area projection is a cylindrical equal-area projection with standard parallel phi_s=0 degrees. = • Equal – Equal vs the same • Underlying value system – Calories vs mass – Mass vs value – The value system of numbers • Abstract – Removed from other values = • Calculator: do the operation – RPN: NO EQUALS • Computer: – J=1,N – J=J+1 • Function – Y=sin x2 = • Is it really true? – Are the 2 sides of the equation the same? – 7 + 3 = 10 • Which do you prefer? – Best case: one party perfers 7 and 3; the other prefers 10 – 1+1=2 • What if this is a religious equation? • What if there is only a unique 1? • Is the left side the same as the right? – In the calculator, it is asymmetric Ideas conveyed by the symbol • Lines are the same length • Parallel • Horizontal like a balance Tzad Hashaveh שווה שווה equal length of the lines parallel related to equal a sameness that is not identiy the balance =? • Never! • If it were true, there would be no reason to tell you. What about Homocystein Hereditary thrombophilia: When to send the tests