Word Gems
exploring selfrealization, sacred personhood, and full humanity
Editor’s collection of notes:
Mathematics
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please click on each linkicon
PreAlgebra
Arithmetic and Algebra, differences
Arithmetic, word origin
Decimals
Decimals, no "oneths" place
Decimals, Percents, Fractions
Fraction
Fraction Equivalent
Fraction, Negative
Fraction, Numerator and Denominator
Fraction, Proper and Improper
Numbers: Cardinal, Ordinal, Nominal
Number Line
Number, Negative
Number vs. Numeral
Number, Mixed
Number, Whole
Order of Operations: PEMDAS
Period
Place Value
Property, Associative: Addition, Multiplication
Property, Commutative: Addition, Multiplication
Property, Distributive: Multiplication over Addition, Subtraction
Property, Equality: Addition, Subtraction, Multiplication, Division
Property, Equality: Reflexive
Property, Equality: Substitution
Property, Equality: Symmetry
Property, Equality: Transitive
Property, Identity: Addition, Subtraction, Multiplication, Division
Ratios, Rates, Proportions
Algebra
Algebra: definition
Inequalities
Equation, Linear
Equation, OneStep
Equation, TwoStep
Equation, ThreeStep
Equation, MultiStep
Equation, Variables on both sides
Equation with parentheses
Expressions
Expressions, Evaluating
Fractions
Statements
Terms
Geometry
Trigonometry
Calculus
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a project in process during 2022  2030
‘his whole affection given to purer speculations, not to vulgar needs of life; to studies of beauty and grandeur’
“La Mort dArchimède,” Death Of Archimedes,
painted in oil, 1815, by Thomas Degeorge
lost in thought, the greatest mind of the ancient world, put to the sword by a brash soldier with a bruised ego
Plutarch, writing c.100 AD, writes of the death of the Greek scientist and mathematician, Archimedes, during the Roman siege of Syracuse, Sicily, 212 BC.
The Roman general, like the Allies hoping to capture German rocket scientists, had given strict orders that the famed inventor of war machines not be harmed. However, an insolent soldier, commanding Archimedes to follow, became enraged when the 75 yearold genius, lost in thought over a math problem, refused to leave his work; and so the legionnaire killed him on the spot.
Archimedes Thoughtful
by Domenico Fetti, 1620
in pursuit of the beautiful
Plutarch comments that Archimedes, despite successfully engineering various advanced weaponry, had come to a point in his life of “repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit.” Instead, he had now given himself to the pursuit of knowledge for its own sake, a quest for the “beauty” found in nature, a desire to witness a “grandeur” expressed in science and mathematics.
All thinking, all highminded people, of every culture and age of history, yearn with Archimedes for a better world, one without war machines, violence, and oppression. And we would seek for the beautiful, for truth, for the mind of God. In the “real world,” in Summerland, this is exactly how maturing persons conduct themselves; those who do not have some “unfinished homework to complete” in the Dark Realms before they can join civilized society.
The quest for the beautiful is no optional sideroute. Without this focus, as discussed elsewhere, we will not survive “the terror of living forever.” Our world, more and more, is marching toward greater expressions of incivility, oppression, and totalitarianism. Nothing has changed since the days of Archimedes, there’s been no real progress of the egoled human spirit since that time.
We can’t change the world with its endless pendulum swing of evil’s “rise and fall,” but we don’t need to be part of it; we have to live in it for now, but our spirits can enjoy a detachment. We can seek for, and make note of, beauty, as we find it, in our studies and observations of the natural world; as did Archimedes.

