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Asterism 

noun1. ASTRONOMY

a prominent pattern or group of stars, typically having a popular name but smaller than a constellation.

2. a group of three asterisks (⁂) drawing attention to following text.

Also used as Therefore in mathematics. 

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The Rule of Three in Mathematics

rule-of-three-calculator-150x150The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c, such that, ( a / b = c / x), (i.e., a: b :: c: x ) you can calculate the unknown number. The Rule of Three Calculator uses the Rule of Three method to calculate the unknown value immediately based on the proportion between two numbers and the third number.

The working of the Rule of Three Calculator can be expressed as follows:

Rule of Three Calculator

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Math is racist: How data is driving inequality


By Aimee Rawlins September 06, 2016 17:24PM ED

These “WMDs,” as she calls them, have three key features: They are opaque, scalable and unfair.

It’s no surprise that inequality in the U.S. is on the rise. But what you might not know is that math is partly to blame.

In a new book, “Weapons of Math Destruction,” Cathy O’Neil details all the ways that math is essentially being used for evil (my word, not hers).

From targeted advertising and insurance to education and policing, O’Neil looks at how algorithms and big data are targeting the poor, reinforcing racism and amplifying inequality.
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brainteaser – 4 squares to 3 squares

4 squares with 12-toothpicks
4 squares with 12-toothpicks
4 squares with 12-toothpicks

Here is a brainteaser involving 12 toothpicks that’s melting the grey matter of the entire internet. Can you beat it? The challenge is to turn this four-square pattern into just three squares. The rules? You can only move one toothpick at a time in any manner wish, but you cannot break or modify the toothpicks.

Answer below:

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Euler’s Formula

Euler’s Formula says: for any convex polyhedron (which includes the five Platonic Solids) the Number of Faces plus the Number of Vertices (corner points) minus the Number of Edges always equals 2
 It is written: F + V – E = 2

cube
cube

Try it on the cube:

A cube has 6 Faces, 8 Vertices, and 12 Edges,

so:

6 + 8 – 12 = 2

Source: http://www.mathsisfun.com/geometry/platonic-solids-why-five.html

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Hindu-Arabic numerals

finger numerals
Muslim caculation systems
Muslim caculation systems

The Indian numerals discussed in our article Indian numerals form the basis of the European number systems which are now widely used. However they were not transmitted directly from India to Europe but rather came first to the Arabic/Islamic peoples and from them to Europe.

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The Three Laws of Energy

thermodynamics
by Gordon Ettie

“Energy is not lost or destroyed, it is merely transferred from one party to the next.” – Sir Isaac Newton

thermodynamics
thermodynamics

In a discussion of energy the basic understanding revolves around the fact that there are three laws.  These are simple laws dealing with energy and can be defined as follows:

First Law

Energy can neither be created nor destroyed.  This means that you can’t make energy out of nothing— the total amount of energy in the universe is a constant. (Please note that this applies to a closed system – the Earth is not a closed system, the Earth receives energy all the time from the Sun).

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Pythagorean cube – seven

cube seven points
cube seven points
cube seven points

Pythagorean teaching – From this comes the great occult axiom: “The center is the father of the directions, the dimensions, and the distances.”

This cube represents six points with man in the middle.

Seven Planetary Spheres

Ancient Greeks taught that souls come to the earth from, and return to the Milky Way via seven planetary spheres – those being Saturn, Jupiter, Mars the Sun, Venus, Mercury and the Moon. In the image above we see the stars and signs of the zodiac at the top, Saturn through Mercury down the back of the chair, the Moon in the sky and Earth in his hands.

The logic of this order doesn’t appear to make sense until you look at an image which shows the spheres mapped onto the seven points (including the center) of a hexagram. Note how the sun (symbolized by a point in a circle) is at the center of this diagram and how the planets are divided with the outer ones being ‘above’ the sun.

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the story of tidbit – narrated by Kasey Wells

Published on Mar 17, 2015

http://thestoryoftidbit.weebly.com/

the story of tidbit was written to be a THEORY OF EVERYTHING and a MODERN CREATION MYTH in one… a visual adventure searching the origins of the UNIVERSE and the essence of GOD.

the story of tidbit follows the inception and evolution of polarized MATTER and LIFE as they are perpetually propelled around and through the magnetic fields and neutral positions that bind/intertwine them.

Scoped by scientific and spiritual principles the story of tidbit recognizes the infinite value of neutral both atomically and philosophically.

Dedicated to THE PURSUIT OF TRUTH, EQUALITY, and ACHIEVING NEUTRALITY.

 

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Classifications and Combinations of Functions

The modern notion of a function is derived from the efforts of many seventeenth- and eighteenth-century mathematicians. Of particular note was Leonhard Euler, to whom we are indebted for the function notation y = f(x). By the end of the eighteenth century, mathematicians and scientists had concluded that many real-world phenomena could be represented by mathematical models taken from a collection of functions called elementary functions.

Elementary functions fall into three categories.

  1. Algebraic functions (polynomial, radical, rational)
  2. Trigonometric functions (sine, cosine, tangent, and so on)
  3. Exponential and logarithmic functions

Source: Essential Calculus – Early Transcendental Functions by Ron Larson

 

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Three types of Translations

reflection

 Rotation = Turn!

 rotation-2d

  • “Rotation” means turning around a center:
  • The distance from the center to any point on the shape stays the same.
  • Every point makes a circle around the center.

Reflection = Flip!

reflection 

 

 

  • Reflection about the X axis
  • Reflection about the Y axis
  • Reflection about the origin (Inverse functions)

Translation = Slide!

reflect-graph

  • Every point of the shape must move:
  • the same distance
  • in the same direction.

 

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Algebraic Limits and Continuity

DEFINITION:

A function f is continuous at x = a if:

1)     f(a) exists, (The output at a exists.)

2)     The limit as x approaches a of f(x) exists, (The limit as "x approaches a" exists.)

3)     The limit is the same as the output.

A function is continuous over an interval if it is continuous at each point in that interval.


Continuity and 2 sided limits

If  is continuous at  x=a then, 

continuity