"We live in a left brain world." -Charles J. Timmins - CJT@SixFigureCareerMastery.com.
Left Brain / Right Brain theory - a vast oversimplification of how our minds tend to work.
The left brain watches a horse race at the track. The left brain has $100.00 on a hot tip. The horse's name is Blue Lightning. The odds on Blue Lightning are Six to One. If Blue Lightning wins, the left brain gets $600.00 for an investment of $100.00. At 8:03 pm and 12 seconds on December 18th, 2010, Blue Lightning comes in dead last in a field of eight horses. The left brain thinks, "Loser! I am such a loser for betting $100.00 on a horse that came in dead last!"
The right brain watches a horse race at the track. "What a race, all those horses finished the race at about the same time." But the right brain does not have a voice that talks, it just experiences everything and moves on.
Sunday, December 19, 2010
Friday, November 12, 2010
Tectonic Toys (R)
The sacred geometry of the ancients acts as the basis for the structure of much of western art. Harmony and beauty are often achieved through understanding certain geometric and mathematical principles in classical art and architecture. Such rules of proportion and composition are embodied in the five basic forms of solid geometry - the tetrahedron, the cube, the octahedron, the icosahedron and the dodecahedron. See the contact page of www.tectonictoys.com for descriptions of these unique geometric forms.
The popular book by Dan Brown, The Da Vinci Code, in chapter twenty has a good description of one particular number that can be found throughout the universe. This number is PHI (pronounced fee) and if you were to round this irrational number into a shorter rational one, its value is 1.618. The Ancient Greeks knew this number and used it to design buildings such as the Parthenon. 1.618 is known as the divine proportion. This divine proportion can be found in the fundamental measurements of the human body. For example, the height of an average person divided by the height of this person's navel, from the ground, gives us the divine proportion of 1.618(or there abouts). The divine proportion has also been referred to as the golden section. The molecular blueprint found in every cell of our bodies, DNA, has the golden section at the core of its structure. The divine proportion is found everywhere in nature. As Dan Brown states in The Da Vinci Code, "1.618 is the most beautiful number in the universe".
Pythagoras (pronounced "Pee/tha/GOR/as") thought that all numbers were beautiful, which is understandable because he was a mathematician (of the 6th century BC). He was the first to develop the proof that the square of the legs of a right triangle is equal to the square of the right triangle's hypotenuse. Pythagoras was especially impressed with the beauty of whole numbers and the harmony that can be found in the universe. There were some numbers that Pythagoras did not like as much as the whole numbers. He could not understand them. These numbers are called irrational numbers. If you take a perfect square with four right angles and draw a diagonal from one corner to the other, you get an irrational number: the square root of two. Pythagoras did not like this number because he could not find two whole numbers in the form of a fraction to represent this number.
This was in conflict with his world view. Pythagoras liked things neat and tidy. Put in other words, he could not find an exact number that when multiplied by itself equals two. He could get close, but he was a mathematician and mathematicians like exactness. For practical purposes, the square root of two when rounded to a convenient decimal place, equals the value of 1.414.
Pythagoras liked geometry and he especially liked the regular solids. These regular solids are shapes made with equilateral triangles, squares and pentagons. Every edge of each of these shapes are equal, just like whole numbers. On a number line, it takes exactly the number one to get from one whole number to the next when counting. The faces of the regular solids are all equal and congruent to each other. It was from this kind of thinking that we get the notion that one man, one person is one vote. This is a very democratic idea. All men, that is people, are created equal. This is the idea that is the basis for democracy and how a free society may hope to govern itself. Its important to note that the Ancient Greeks had this democratic idea apply only to men who are considered citizens. In order to be considered a citizen and to be able to vote, a man must own land and have wealth. The Greek version of democracy was "all citizens are created equal".
Back to the five shapes. For short, lets use Tectonics nomenclature. The Tetra is made with four equilateral triangles. The Kube is made with six squares. The Okta is made with eight equilateral triangles. The Iko is made with twenty equilateral triangles. The Dodeka is made with twelve pentagons. Pythagoras loved these shapes because they were mathematically perfect. When one builds four equilateral triangles and joins the edges in order to enclose a space, if one is careful in the initial construction, a near perfect form is made - a Tetra. There are no overlaps or extra material to trim off to get everything to align. This is true with all of these regular solids. Another important idea about the regular solids is that all five of these forms have a special relationship to the sphere. Just as a sphere has a radius and an exact volume that it encloses, a sphere has, as part of its structure the five shapes. For any sphere, there can be derived the five regular solids with an exact mathematical relationship to such a sphere.
Let me put this in simpler terms to make it more comprehensible. Just as any circle has a circumference and a radius, there is an equilateral triangle of an exact size that can be inscribed in this circle. Every circle has an inscribed inner equilateral triangle and also an outer equilateral triangle. The inner equilateral triangle touches the circle with each of it three vertices at exact points and divide the circumference of this circle into thirds. The outer equilateral triangle touches the circle at the midpoints of the sides of the triangle at third points of the circumference also. This process can continue with the square, the pentagon, the hexagon and so forth. Just as the circle has special corresponding equilateral triangles of a definite size and proportion, the sphere has regular solids with an equivalent correspondence. For any Sphere, there is an inner Tetra that will fit in it and touch it at just four points that correspond to the vertices of the Tetra. For any Sphere there is a outer Tetra whose faces touch the sphere at their exact center points.
The sacred geometry of the ancients acts as the basis for the structure of much of western art. Harmony and beauty are often achieved through understanding certain geometric and mathematical principles in classical art and architecture. Such rules of proportion and composition are embodied in the five basic forms of solid geometry - the tetrahedron, the cube, the octahedron, the icosahedron and the dodecahedron. See the contact page of www.tectonictoys.com for descriptions of these unique geometric forms.
The popular book by Dan Brown, The Da Vinci Code, in chapter twenty has a good description of one particular number that can be found throughout the universe. This number is PHI (pronounced fee) and if you were to round this irrational number into a shorter rational one, its value is 1.618. The Ancient Greeks knew this number and used it to design buildings such as the Parthenon. 1.618 is known as the divine proportion. This divine proportion can be found in the fundamental measurements of the human body. For example, the height of an average person divided by the height of this person's navel, from the ground, gives us the divine proportion of 1.618(or there abouts). The divine proportion has also been referred to as the golden section. The molecular blueprint found in every cell of our bodies, DNA, has the golden section at the core of its structure. The divine proportion is found everywhere in nature. As Dan Brown states in The Da Vinci Code, "1.618 is the most beautiful number in the universe".
Pythagoras (pronounced "Pee/tha/GOR/as") thought that all numbers were beautiful, which is understandable because he was a mathematician (of the 6th century BC). He was the first to develop the proof that the square of the legs of a right triangle is equal to the square of the right triangle's hypotenuse. Pythagoras was especially impressed with the beauty of whole numbers and the harmony that can be found in the universe. There were some numbers that Pythagoras did not like as much as the whole numbers. He could not understand them. These numbers are called irrational numbers. If you take a perfect square with four right angles and draw a diagonal from one corner to the other, you get an irrational number: the square root of two. Pythagoras did not like this number because he could not find two whole numbers in the form of a fraction to represent this number.
This was in conflict with his world view. Pythagoras liked things neat and tidy. Put in other words, he could not find an exact number that when multiplied by itself equals two. He could get close, but he was a mathematician and mathematicians like exactness. For practical purposes, the square root of two when rounded to a convenient decimal place, equals the value of 1.414.
Pythagoras liked geometry and he especially liked the regular solids. These regular solids are shapes made with equilateral triangles, squares and pentagons. Every edge of each of these shapes are equal, just like whole numbers. On a number line, it takes exactly the number one to get from one whole number to the next when counting. The faces of the regular solids are all equal and congruent to each other. It was from this kind of thinking that we get the notion that one man, one person is one vote. This is a very democratic idea. All men, that is people, are created equal. This is the idea that is the basis for democracy and how a free society may hope to govern itself. Its important to note that the Ancient Greeks had this democratic idea apply only to men who are considered citizens. In order to be considered a citizen and to be able to vote, a man must own land and have wealth. The Greek version of democracy was "all citizens are created equal".
Back to the five shapes. For short, lets use Tectonics nomenclature. The Tetra is made with four equilateral triangles. The Kube is made with six squares. The Okta is made with eight equilateral triangles. The Iko is made with twenty equilateral triangles. The Dodeka is made with twelve pentagons. Pythagoras loved these shapes because they were mathematically perfect. When one builds four equilateral triangles and joins the edges in order to enclose a space, if one is careful in the initial construction, a near perfect form is made - a Tetra. There are no overlaps or extra material to trim off to get everything to align. This is true with all of these regular solids. Another important idea about the regular solids is that all five of these forms have a special relationship to the sphere. Just as a sphere has a radius and an exact volume that it encloses, a sphere has, as part of its structure the five shapes. For any sphere, there can be derived the five regular solids with an exact mathematical relationship to such a sphere.
Let me put this in simpler terms to make it more comprehensible. Just as any circle has a circumference and a radius, there is an equilateral triangle of an exact size that can be inscribed in this circle. Every circle has an inscribed inner equilateral triangle and also an outer equilateral triangle. The inner equilateral triangle touches the circle with each of it three vertices at exact points and divide the circumference of this circle into thirds. The outer equilateral triangle touches the circle at the midpoints of the sides of the triangle at third points of the circumference also. This process can continue with the square, the pentagon, the hexagon and so forth. Just as the circle has special corresponding equilateral triangles of a definite size and proportion, the sphere has regular solids with an equivalent correspondence. For any Sphere, there is an inner Tetra that will fit in it and touch it at just four points that correspond to the vertices of the Tetra. For any Sphere there is a outer Tetra whose faces touch the sphere at their exact center points.
Saturday, July 3, 2010
TectonicToys(R) Poem
TECTONICS™ – The Folding Plate Frame System
Commune with the ancient shapers of Western thought!
As Socrates, Plato and others had classically taught:
The World was all round, a beautiful sphere,
Music governed by Math that they did hear
Originally, the Prime Mover did give birth
To a Universe of Fire, Water, Air and Earth.
Ideal realms of pure thought revealed naked,
The five regular solids that were discovered
The ancient Greeks deemed sacred.
It may be true, these shapes are cool,
Learn from the best - the Athens School.
It was 2600 years ago today,
That Pythagoras with geometry would play,
Get into his head and do the same,
And build these universal forms by name.
Five Forms - Erroneous Elements - Tectonic Form Name
1) Tetrahedron - Fire - Tetra
2) Octahedron - Air - Okta
3) Cube - Earth - Kube
4) Icosahedron - Water - Iko
5) Dodecahedron - Universe - Dodeka
Tectonic Toys® is a quick and flexible way to build the five basic forms
and countless others that have never seen the light of day! To build with
this frame system allows one to discover, to invent and to explore forms
ancient and new more quickly and easily than ever before.
Tectonic Toys® is a registered trademark of DLC Architecture, LLC.
This frame system is patent pending with the United States Patent and Trademark Office.
Commune with the ancient shapers of Western thought!
As Socrates, Plato and others had classically taught:
The World was all round, a beautiful sphere,
Music governed by Math that they did hear
Originally, the Prime Mover did give birth
To a Universe of Fire, Water, Air and Earth.
Ideal realms of pure thought revealed naked,
The five regular solids that were discovered
The ancient Greeks deemed sacred.
It may be true, these shapes are cool,
Learn from the best - the Athens School.
It was 2600 years ago today,
That Pythagoras with geometry would play,
Get into his head and do the same,
And build these universal forms by name.
Five Forms - Erroneous Elements - Tectonic Form Name
1) Tetrahedron - Fire - Tetra
2) Octahedron - Air - Okta
3) Cube - Earth - Kube
4) Icosahedron - Water - Iko
5) Dodecahedron - Universe - Dodeka
Tectonic Toys® is a quick and flexible way to build the five basic forms
and countless others that have never seen the light of day! To build with
this frame system allows one to discover, to invent and to explore forms
ancient and new more quickly and easily than ever before.
Tectonic Toys® is a registered trademark of DLC Architecture, LLC.
This frame system is patent pending with the United States Patent and Trademark Office.
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