Unity and Duality Rudiments
Unity and Duality
The Relationship Between Fractal Geometry & Energy - https://www.wpi.edu/academics/departments/mathematical-sciences/research/fractal-geometry-energy
Geometry of the universe is expressed as fractals: Spirit is characterized by dilation - Unity expresses expansion in optimizing surface function: ..a small volume interfaces with a surrounding space over a large surface area. It is exemplified, says Mosco, by the fractal nature of tree leaves and roots, as well as the network of blood vessels and capillaries in our bodies.
Physics of the universe is expressed by matter: Matter is characterized pressure - Duality expresses constriction: “..in the classical situations, was the idea that many phenomena in nature are well described by say a ball or soap bubble. Many phenomena tend to surround the largest possible volume with the smallest possible surface because you’re trying to minimize some surface tension and this brings you ideally to the formation of a sphere, a ball.“
A black hole is a vortex in the fabric of space-time. It is therefore a geometrical phenomenon that expresses itself as gravitational force which is a physical phenomenon. A black hole is a two dimensional phenomenon which affects matter which is three dimensional.
The relation between the two sides of a right triangle,” says Mosco, “is a mysterious thing that has to do with what in mathematics is called duality.
Unity-duality relationship is expressed in the Pythagorean Theorem.
Pythagorean Theorem Demonstration - https://www.mathwarehouse.com/animated-gifs/geometry.php#righttris
How to get a wave from a circle?
sine-cosine-unit-circle-animation unit circle and the wave phenomenon
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
http://thenumerist.com/wp-content/uploads/2013/09/unit-circle-to-derive-Pythagorean-Identities-2.jpg
Pythagorean Identities: http://thenumerist.com/pythagorean-identities/
References:
Relationship between Pythagoras’ Theorem and the Fibonacci Sequence - Fibonacci Meets Pythagoras: https://www.researchgate.net/publication/261811825_Fibonacci_Meets_Pythagoras
When Fibonacci meets Pythagoras: https://brilliant.org/discussions/thread/when-fibonacci-meets-pythagoras/
Extra heuristics: Pythagorean Theorem and Unit Circles: https://www.youtube.com/watch?v=Wmz8itUVgPk
Unit Circle Formula - Demonstration of the Unit Circle Formula & Graph: https://www.mathwarehouse.com/unit-circle/graph-and-formula-unit-circle.php#gifs
The equivalent of the Pythagorean Theorem is cosH=cosA.cosB
A visual introduction to the dot product: https://medium.com/@robinlinderborg/a-visual-introduction-to-the-dot-product-3e7b65240c09
Right angled triangle diagram:
If a+b+c divides the product abc , then is (a,b,c) a Pythagorean Triple?: https://math.stackexchange.com/questions/2825945/if-abc-divides-the-product-abc-then-is-a-b-c-a-pythagorean-triple
Unit Circle Gifs - https://www.mathwarehouse.com/unit-circle/graph-and-formula-unit-circle.php
More here:
Best Animations -
https://bestanimations.com/Science/Math/Math.html
If a+b+c divides the product abc , then is (a,b,c) a Pythagorean Triple? - https://math.stackexchange.com/questions/2825945/if-abc-divides-the-product-abc-then-is-a-b-c-a-pythagorean-triple
How to get a
spiral from a circle? -
How to Fibonacci proportions from Pythagoras’ theorem?
Pythagorean Theorem in Circles - https://cetking.com/pythagorean-theorem-circles/
