# Fourier Transform Geometry

**How is the Fourier Transform related to Sound Wave Geometry?**

Link to potential geometry post

Link to all circle posts

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https://en.wikipedia.org/wiki/Calculus

https://en.wikipedia.org/wiki/Unit_circle

https://en.wikipedia.org/wiki/Trigonometric_functions

https://en.wikipedia.org/wiki/List_of_triangle_topics

https://en.wikipedia.org/wiki/Solution_of_triangles

https://en.wikipedia.org/wiki/Trigonometry

https://en.wikipedia.org/wiki/Spherical_trigonometry

https://en.wikipedia.org/wiki/Generalized_trigonometry

https://en.wikipedia.org/wiki/Trigonometric_series

https://en.wikipedia.org/wiki/Fourier_analysis

https://en.wikipedia.org/wiki/Fourier_series

https://en.wikipedia.org/wiki/Time%E2%80%93frequency_analysis

https://en.wikipedia.org/wiki/Fourier_transform

https://en.wikipedia.org/wiki/Harmonic_analysis

https://en.wikipedia.org/wiki/Discrete_Fourier_transform

https://en.wikipedia.org/wiki/List_of_Fourier-related_transforms

https://en.wikipedia.org/wiki/Discrete_wavelet_transform

https://en.wikipedia.org/wiki/Quantum_Fourier_transform

https://en.wikipedia.org/wiki/DFT_matrix

https://en.wikipedia.org/wiki/Fourier_operator

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https://en.wikipedia.org/wiki/Extended_real_number_line

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**https://en.wikipedia.org/wiki/Projectively_extended_real_line**

In real analysis, the **projectively extended real line** (also called the one-point compactification of the real line), is the extension of the number line by a point denoted ∞.

The added point is called the point at infinity, because it is considered as a neighbour of both ends of the real line. More precisely, the point at infinity is the limit of every sequence of real numbers whose absolute values are increasing and unbounded.

The projectively extended real line may be identified with the projective line over the reals in which three points have been assigned specific values (e.g. 0, 1 and ∞). The projectively extended real line must not be confused with the extended real number line, in which +∞ and −∞ are distinct.

**https://en.wikipedia.org/wiki/Wheel_theory**

**Wheels** are a type of algebra where division is always defined. In particular, division by zero is meaningful. The real numbers can be extended to a wheel, as can any commutative ring.

**https://en.wikipedia.org/wiki/Division_by_zero**

**The function y = 1/x. **

**As x approaches 0 from the right, y approaches infinity. **

**As x approaches 0 from the left, y approaches negative infinity.**

https://en.wikipedia.org/wiki/Asymptote

https://en.wikipedia.org/wiki/Penrose_diagram

https://www.google.com/search?hl=en&site=webhp&q=fourier+nonintersecting+curve

https://www.google.com/search?hl=en&site=webhp&q=fourier+noise

https://www.google.com/search?hl=en&site=webhp&q=fourier+smoothness

https://www.google.com/search?hl=en&site=webhp&q=fourier+linear

### Quantum Information: An Overview

By Gregg Jaeger

https://en.wikipedia.org/wiki/Indeterminate_form#Expressions_that_are_not_indeterminate_forms

The indeterminate forms typically considered in the literature are denoted 0/0, ∞/∞, 0 × ∞, ∞ − ∞, 0^{0}, 1^{∞} and ∞^{0}.

https://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_power_of_zero

https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule

vhttps://en.wikipedia.org/wiki/Spherical_harmonics

https://en.wikipedia.org/wiki/Circulant_graph

https://en.wikipedia.org/wiki/Circulant_matrix

https://en.wikipedia.org/wiki/Affine_transformation

https://en.wikipedia.org/wiki/Point_reflection#Reflection_through_the_origin

https://en.wikipedia.org/wiki/Automatic_control

https://en.wikipedia.org/wiki/Numerical_methods_in_fluid_mechanics

**https://en.wikipedia.org/wiki/Nine-point_circle**

**CONSIDER THE PYTHAGOREAN THEOREM**

**A GENERALIZATION TO ALL POINTS IN SPACETIME**

**EVENTS IN TRIPLETS**

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Embed brian greene World Science Festival clip

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link to and quote betterexplained.com

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### Terence McKenna – How It Began

https://en.wikipedia.org/wiki/Poncelet_point

research unit circle and right triangles …

https://www.google.com/search?site=&source=hp&q=unit+circle+special+right+triangles

https://www.google.com/search?q=unit+circle+and+right+triangles

https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Historic_shorthands

https://en.wikipedia.org/wiki/Small-angle_approximation

https://en.wikipedia.org/wiki/Multidimensional_transform

https://en.wikipedia.org/wiki/Uniqueness_quantification

**— move the below to potential geometry post**

https://en.wikipedia.org/wiki/L%C3%A9n%C3%A1rt_sphere

https://en.wikipedia.org/wiki/Electromagnetic_radiation

https://en.wikipedia.org/wiki/Circle_graph

https://en.wikipedia.org/wiki/Representation_theory

https://en.wikipedia.org/wiki/Spherical_basis

https://en.wikipedia.org/wiki/Chord_(geometry)

https://en.wikipedia.org/wiki/Cubic_harmonic

https://en.wikipedia.org/wiki/Cylindrical_harmonics

https://en.wikipedia.org/wiki/Conic_section

https://en.wikipedia.org/wiki/Vector_spherical_harmonics

https://en.wikipedia.org/wiki/Spin-weighted_spherical_harmonics

Traversable acausal retrograde domains in spacetime

http://iopscience.iop.org/article/10.1088/1361-6382/aa6549

https://www.researchgate.net/figure/275017053_fig9_Fig-9-A-representation-of-a-multi-layered-organization-structure-of-the-human-brain

https://physics.stackexchange.com/questions/194713/definition-of-event-horizon-gravity-around-blackholes

https://jila.colorado.edu/~ajsh/insidebh/penrose.html

.https://www.wired.com/2014/11/check-universe-exist/

https://www.wired.com/2014/11/check-universe-exist/#slide-3

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