Golden ratio relationships appear in the Name of G-d in the Hebrew Bible. In Gematria, the most holy name of God, referred to as the Tetragrammaton, embodies some very interesting Golden Ratio relationships. Gematria is a system of assigning numerical value to a word or phrase. It is likely that the term derives from the order of the Greek alphabet, gamma being the third … [Read more...]
Phi in the Bible
Although perhaps not immediately obvious, phi and the golden section also appear in the Bible. Also see the Theology page. The Ark of the Covenant is uses Fibonacci numbers, approximating a Golden Rectangle In Exodus 25:10, God commands Moses to build the Ark of the Covenant, in which to hold His Covenant with the Israelites, the Ten Commandments, saying, "Have them … [Read more...]
Theology
Is there meaning hidden in Phi, the symbol for the Golden Number? The use of the Greek letter Phi Phi to represent the golden number 1.618 ... is generally said to acknowledge Phidias, a 5th century B.C. sculptor and mathematician of ancient Greece, who studied phi and created sculptures for the Parthenon and Olympus. The message from scripture of all the major monotheistic … [Read more...]
Phi Mandalas
Phi-based geometric shapes produce interesting mandala designs. A mandala is a geometric design, often symbolic of the universe and used in Eastern religions as an aid to meditation. Phi-based geometric shapes can be used to create some interesting phi mandalas, embodying the phi proportion found throughout creation and iterating into the infinitely large and the infinitely … [Read more...]
Penrose Tiling and Phi
Tiling in 5-fold symmetry was thought impossible! Areas can be filled completely and symmetrically with tiles of 3, 4 and 6 sides, but it was long believed that it was impossible to fill an area with 5-fold symmetry, as shown below: 3 sides 4 sides 5 sides leaves gaps 6 sides The solution was found in Phi, the Golden … [Read more...]
Squaring the Circle with Phi
Squaring the Circle comes within four decimal places using the Golden Ratio. Even before the foundations of the Great Pyramids were laid men have tried to "square the circle." That is, in a finite number of steps, construct a square and a circle that are precisely equal in area using only the most primitive instruments; namely, an unmarked compass & straightedge. Some of … [Read more...]
The DOR
A new fundamental geometric shape with a relationship to Phi. Here's a challenge to "all the real mathematicians in the back row," as my college professor often said: Picture the classic solids of geometry, each sitting inside a cube that encloses it on all sides. What is the ratio of surface area of this tangent cube to the surface area of the solid, and which solid … [Read more...]
Phi Formula Geometric Construction
Phi is most often calculated using by taking the square root of 5 plus 1 and divided the sum by 2: √5 + 1 2 This mathematical expression can be expressed geometrically as shown below: Three circle construction: Put three circles with a diameter of 1 (AB and DE) side by side and construct a triangle that connects the bottoms of the outside circles (AC) and the top and … [Read more...]
Quasi-crystals and the Golden Ratio
Quasi-crystals represent a newly discovered state of matter. Most crystals in nature, such as those in sugar, salt or diamonds, are symmetrical and all have the same orientation throughout the entire crystal. Quasicrystals represent a new state of matter that was not expected to be found, with some properties of crystals and others of non-crystalline matter, such as … [Read more...]
Orthogons and the Golden Auron
The Golden Section is an Orthogon called the Auron. The golden section can be constructed from a square with a compass and ruler: This is the most commonly known of twelve orthogons which can be constructed using this technique. Among orthogons, the golden section is known as the auron, coming from the root "aur," meaning gold. Orthogons provide a system of … [Read more...]
