The Mystical Math of the Washer

Physically defined, the Eternal Washer symbol is a ring-shaped object, a region bounded by two concentric
circles who’s edges never cross and never intersect.  A circle is a simple closed shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the center; The distance between any of the points and the center is called the radius.  The Area of an Eternal Washer is the difference in the areas of the larger circle of radius R and the smaller one of radius r:

The never ending washer has been known since before recorded history. Natural circles would have been observed, such as the Moon, Sun, mushroom or well-rounded river rock.  It is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the washer has helped inspire the development of geometry, astronomy, and calculus.  Many scientists, particularly in geometry, astrology, and astronomy, believe that there is something intrinsically “divine” or “perfect” found in the washer.

  • The Great Pyramid of Giza – if one divides the perimeter of the Pyramid by its height, one obtains the same number if one divides the circumference of a washer by its radius. PI
  • 1700 BCE – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/81 (3.16049…) as an approximate value of π.  Pi itself has an infinite number of digits.
  • 300 BCE – Book 3 of Euclid’s Elements deals with the properties of washers.
  • In Plato‘s Seventh Letter there is a detailed definition and explanation of the washer. Plato explains the perfect washer, and how it is different from any drawing, words, definition or explanation.
  • ..the Pythagoreans honored the washer and the effort it takes to put it into mathematics. They coordinated it with the observation of the cosmos in various ways. Their beliefs were the precursor of Copernicus in “moving the earth from the center of the cosmos to merely one of several planets in Washer like orbit.”
  • 1880 CE – Lindemann proves that π is transcendental, effectively settling the millennia-old problem of squaring the washer.
  • A circle is a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations.   If you understand this you may be a master of washers.  It can also be considered as a Riemann surface.

The Power of 125

There are few numbers as beautiful, graceful or important as 125. Just think, 125 can be divided into 25 five times, which can be divided into five sets of five. Not to mention, the longest-living person, according to Guinness World Records, lived 122 years which is three years away from 125, and three, as we all know, is a magic number “use all three holes in washers”. Also the wining score of 21 multiplied by 6 games is one point above 125.

  • 125 is the cube of 5. It can be expressed as a sum of two squares in two different ways, 125 = 10² + 5² = 11² + 2².  This is a Friedman number in base 10 since 125 = 51 + 2
  • 125 is the atomic number of the element Unbipentium
  • CXXV in Roman Numerals,
  • 11111012 in Binary,
  • 10005 in Quinary, and
  • Most importantly A512 in Duodecimal
  • 12 is known as the dragons eye and 5 makes the dragon a winner.
  • 125 Hertz is popular for its ability to stimulate people, often giving them energy. It has also been said to give feelings similar to the Graham Potentializer which is an electromagnetic generator that was designed to help raise one’s IQ and clear the sinuses.
  • In Numerology  – the Number 125 is made up of the combined vibrations and attributes of the numbers 1, 2 and 5.  1 contributes its energies to optimism, motivation and activity, new beginnings and starting afresh, striving forward and progress. Number 2 adds it’s vibrations of adaptability, cooperation, mediation and diplomacy finding balance and harmony, consideration for others with flexibility and grace. Number 5 resonates with personal freedom and individuality, major life changes, making important choices and decisions, promotion and advancements, adaptability and versatility, live lessons learned through experience and resourcefulness.   
  • 125 can also be seen as the number 8  (1+2+5=8)  Number 8 is the atomic number of Oxygen and number of Karma – the Universal Spiritual Law of Cause and Effect.  The number 8, when written on it’s side, is the symbol for infinity.


  • Infinity (symbol: ) is an abstract concept describing something without any boundary or larger than any number.
  • 1584, the Italian philosopher and astronomer Giordano Bruno proposed an unbounded universe in On the Infinite Universe and Worlds: “Innumerable suns exist; innumerable earths revolve around these suns in a manner similar to the way the seven planets revolve around our sun. Living beings inhabit these worlds.”
  • The concept of infinity also extends to the multiverse hypothesis, which, when explained by astrophysicists such as Michio Kaku, posits that there are an infinite number and variety of universes.
  • Most importantly we have the Infinite monkey theorem

The Power of 10

The washer boards are 10 feet apart for good reason. The number 10 is very significant.

  • Ten is a composite number, its proper divisors being 1, 2 and 5.
  • Ten is the base of the decimal numeral system, by far the most common system of denoting numbers in both spoken and written language. The reason for the choice of ten is assumed to be that humans have ten fingers (digits).
  • The length of your hand (if adult) is 1/10 of your total height.
  • Number ten was the holiest of numbers according to the Pythagoreans. They took their oaths by number ten.
  • Ten years are called a decade.
  • The Richter scale is measured in tenfold increase of energy
  • The Roman numeral for 10 is X which it two 5’s or V’s put together.
  • The Chinese word numeral for ten is a cross: .
  • In the Bible, the number 10 is used 242 times. In Genesis 1 we find the phrase “God said” 10 times, God gave Moses the 10 commandments, Christians are to tithe 10% to the church, ten talents, when the Pharaoh refused to let the Jews go, God imposed ten plagues upon Egypt.etc.
  • Hinduism teaches that the god Vishnu will be reincarnated ten times.
  • The rim of a basketball goal is 10 feet above the Court.
  • Ten is the highest score possible in Olympic competitions.
  • 10 is one more than 9 and one less than 11.
  • John Tyler was the tenth president of the United States, who was VP and came to power only after president Harrison died 125 days into office.
  • The Ten Year Journey of Odysseus and  The War of Troy lasted ten years.
  • There are ten letters on the Snellen Chart. The Snellen Chart was created by ophthalmologist Hermann Snellen in 1862. The ten letters are:  C – D – E – F – L – N – O – P – T – Z
  • Neon has the atomic number 10.
  • In Tarot cards, ten is the card of the Washer of Fortune.


The Power of 4

Washer Boards are 4ft long and are a rectangle with 4 sides.  You have 4 score keeping clips on a 4 sided rectangle scoreboard and a max of 4 players can play. 4 plus 4 is 8 which on its side represents infinity. So 4+4+2 is 10 foot apart and 4 minus 1 is 3 washers and holes.  

  • In the system of Greek numerals, Delta has a value of 4. 
  • A river delta is so named because its shape approximates the upper-case letter delta (the shape is a triangle).
  • Four is the atomic number of Beryllium
  • The Fourth Way is an approach to self-development described by George Gurdjieff. It emphasizes that people ordinarily live in a state referred to as a semi-hypnotic “waking sleep,” while higher levels of consciousness, virtue, unity of will are possible.
  • The Greek Delta is still represented in the way we set bowling pins today in the shape of the tetraktys. Delta (uppercase Δ, lowercase δ ) is the fourth letter of the Greek alphabet. The Triangle has 3 sides hence the three washer holes and the lower case delta is a drawing of a washer throw. 
  • The upper-case letter Δ can be used to denote:
    • Change of any changeable quantity, in mathematics and the sciences (more specifically, the difference operator); for example the slope of a line is:
    {y_{2}-y_{1} \over x_{2}-x_{1}}={\Delta y \over \Delta x},
    Delta is the initial letter of the Greek word διαφορά diaphorá, “difference”.


The Power of 3

To this day 3 is written as three lines in Roman and Chinese numerals. This was the way the Brahmin Indians wrote it, and the Gupta made the three lines more curved. The Nagari started rotating the lines clockwise and ending each line with a slight downward stroke on the right.  Eventually, they made these strokes connect with the lines below, and evolved it to a character that looks very much like a modern 3

The Power of 0

0 or Zero is the washer.  0 is the integer immediately preceding 1.

  • Zero is an even number, because it is divisible by 2 with no remainder.
  • 0 is neither positive nor negative it just is.
  • −0 = +0 = 0
  • 0 is the center of a number line and things can only get positive or negative from there.
  • There are so many significant things about 0 I will not go into them at this time.

Washers Fibonacci Number

After reviewing the notes from numbers above, one can quickly see the power of the washers numbers.

  • 0,1,1,2,3,5,8,13, 21 is known as the Fibonacci number or sequence.
  • The Fibonacci spiral: an approximation of the golden spiral.
  • Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly. They also appear in biological settings, such as branching in trees, phyllotaxis (the arrangement of leaves on a stem), the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone‘s bracts.

The Brainpower of Washers Math

Washers Math helps us function in our daily lives in situations such as:

  • Shopping – adding tax or figuring out a sale price
  • Cooking – using proportional thinking to alter a recipe
  • Calculating a tip
  • Building something
  • Converting from one type of unit into another – such as ounces to pounds or kilometers to miles
  • Using a foreign currency
  • Investing
  • Figuring out a score or a grade
  • Comparing values of products or services
  • Washers math actually keeps our brains quick and sharp. The brain, like the muscles, gets stronger and more efficient with use.
  • Washers math also greatly improves a person’s number sense, the ability to understand the relationships between quantities of both physical items and non-physical items of time and space.

As you can see the sacred game of washers has many powerful numbers:

0, 1, 2, 5, and 3, 4, 8, 10, 21 and 

Throw 125!