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
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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.
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