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#didyouknow 63 Earths can fit inside Uranus.

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PDF Book Link
https://gumroad.com/l/visualizingmaths-e-book

Blog Link
https://visualzingmathsandphysics.blogspot.in

1] How sin( ) is a measure of how much perpendicular two objects/forces are.

2] How cos( ) is a measure of how much parallel two objects/forces are.

3] How in complex numbers
i = rotation by 90 degrees
i^2= rotation by 180 degrees
i^3= rotation by 270 degrees.
i^4 = rotation by 360 degrees.

4] Transpose of a matrix = Rotation by 180 degrees around the diagonal.

5] e^i(angle) = rotation by that angle.

6] sin(30) = 1/2
because at 30 degree the effect of a force reduces to half over the other force/object (as against when the two forces/object are against at 90 degrees w.r.t each other)

7) A X B = |A| |B| sin(angle between A and B)
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visualizingmathsandphysics.blogspot.in
(1) Why sin(30) = 1/2 ?
(2) i ^ 2 = -1 = rotation by 180°
(3) Transpose [A] = Rotation by 180.
(4) Diagonal of a matrix = Its axis of rotation.
(5) Why A x B = ABsin( )??
(6) Why Log(A x B) = Log(A) + Log(B) ???
(7) What is the purpose of curl and divergence??
(8) Purpose of differential equations.
For (6$)
Link
https://gumroad.com/l/JXwPU
visualizingmathsandphysics.blogspot.in
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1] Sin( ) is a measure of how much perpendicular two objects/forces are.
2] Log(effect) = cause,....10^cause = effect.
3] Transpose of a Matrix = Rotation by 180 degrees.
4] i = rotation by 90 degrees,....i^2 = rotation by 180 degrees, i^3 =rotation by 270 degrees.
5] e^(i.any angle) = rotation anticlockwise by that angle.: e^(-i.any angle) =rotation clockwise by that angle.
6] Cos( ) is a measure of how much aligned two forces are.
7] Diagonal of a matrix is its axis of rotation.

Blog link
http://visualizingmathsandphysics.blogspot.in/

e-book link
https://gumroad.com/l/JXwPU
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e-book link
https://gumroad.com/l/JXwPU
blog link
visualizingmathsandphysics.blogspot.in
(1) Why sin(30) = 1/2 ?
(2) i ^ 2 = -1 = rotation by 180°
(3) Transpose [A] = Rotation by 180.
(4) Diagonal of a matrix = Its axis of rotation.
(5) Why A x B = ABsin( )??
(6) Why Log(A x B) = Log(A) + Log(B) ???
(7) What is the purpose of curl and divergence??
(8) Purpose of differential equations.
For (6$)
Link
https://gumroad.com/l/JXwPU
visualizingmathsandphysics.blogspot.in
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✨🇲️🇦️🇬️🇮️🇨️🇦️🇱️ 🇺️🇳️🇮️🇻️🇪️🇷️🇸️🇪️ - Lights at Wilson Arch

Today, Magical Universe is back to the new collaboration, this time it is Tony and Daphne Hallas that offer us a fantastic view of the Milky Way. Wilson Arch is also known as the Wilson Arch, a natural sandstone product located in southeast of Utaha, along US Route 191, just 24 miles south of Moab. It has a wingspan of 91 feet and a height of 46 feet. The elevation of the arch above sea level is about 6150 feet. Taking advantage of this natural wonder carved by the inclement weather, astrophotographer Tony Hallas has portrayed the Milky Way behind the famous arch.

Behind Wilson Arch stars dominate the sky, the visible gas in pink and the interstellar dust of the galaxy that shelters us offer a watercolor show that certainly does not leave the fans indifferent. Tony Hallas does the ..... Click on the image to read the full article.

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e-book link
https://gumroad.com/l/JXwPU
blog link
visualizingmathsandphysics.blogspot.in
(1) Why sin(30) = 1/2 ?
(2) i ^ 2 = -1 = rotation by 180°
(3) Transpose [A] = Rotation by 180.
(4) Diagonal of a matrix = Its axis of rotation.
(5) Why A x B = ABsin( )??
(6) Why Log(A x B) = Log(A) + Log(B) ???
(7) What is the purpose of curl and divergence??
(8) Purpose of differential equations.
For (6$)
Link
https://gumroad.com/l/JXwPU
visualizingmathsandphysics.blogspot.in
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1] Sin( ) is a measure of how much perpendicular two objects/forces are.
2] Log(effect) = cause,....10^cause = effect.
3] Transpose of a Matrix = Rotation by 180 degrees.
4] i = rotation by 90 degrees,....i^2 = rotation by 180 degrees, i^3 =rotation by 270 degrees.
5] e^(i.any angle) = rotation anticlockwise by that angle.: e^(-i.any angle) =rotation clockwise by that angle.
6] Cos( ) is a measure of how much aligned two forces are.
7] Diagonal of a matrix is its axis of rotation.

Blog link
http://visualizingmathsandphysics.blogspot.in/

e-book link
https://gumroad.com/l/JXwPU
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PDF BOOK LINK
https://gumroad.com/l/visualizingmath2book

Visualizing Math 2 deals with concepts like

1) How Fourier Transforms are the side-view of a wave.

2) Laplace Transforms are side-view + front view (Imaginary + real part)

3) How Z Transforms are nothing but the discrete cousin of Laplace and DFT of Fourier.

4) How the number 1 appears actually as a fraction 1/1 in Math which means full of full.

Thus sin(90) = 1/1 = full on influence at 90 deg

Thus Max probability = 1/1 = full of full sample space

Thus cos(0) = 1/1 = full on full influence at 0 deg (when parallel)

Unit Circle radius = 1/1 = magnitude doesn't decrease/increase

throughout the rotation. Else it would have been a ratio like 2/1 or 1/4 etc.

5) How Continous functions can be visualized as those functions which you can draw on a paper without lifting up the pencil.

6) How a function differentiable at a point means if you stand at that point,...

(1) You will experience a slope. Slope will exist.

(2) This slope however will not be infinite. (fully vertical)

(3) The slope will be either towards the left or the right but not both the directions.

(4) The slope will not wriggle like a snake (oscillate ) at that point.

7) How a hermitian matrix can be visualized as a any object which which exhitibits vertical symmetry. So even if it is rotated upside down about the central axis( diagonal of the matrix) you wont be able to tell the difference.



8) How probability can be visualized much more intuitively by multiplying it by 100 and thus converting it into a percentage.

Eg:- a probability of 0.2 can be converted to 0.2 x 100 = 20%



9) How probability density can be understood using an example of the Probability of finding a man after entering New-york v/s finding a man after entering a sparsely populated desert.



And so on.........



The book is still in works and subsequent updated will be sent to your mail id for free.

Binnoy
http://visualizingmathsandphysics.blogspot.in



A SEQUEL TO VISUALIZING MATH 1

The Book Visualizing Math 2 in word and pdf format is a sequel to Visualizing Math which is once again available on gumroad the link as

Visualizing Math 1 Link

https://gumroad.com/l/visualizingmaths-e-book

Visualizing Math 2 Link
https://gumroad.com/l/visualizingmath2book


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