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Do you have a g+ collection with mathy stuff? You're very welcome to share it here! Or reshare a post from it, if you also take care to link your g+ collection, so people can find more posts like it.

Or any other g+ community or other people's g+ collections, if related to math, they are all welcome here. We all want to know! Don't be shy, share!

In case you're looking for responses on a particular subject or result of yours, please consider posting to one of the many communities listed below, instead.

I'd like to use the opportunity to thank everyone who posted here, engaged with a post, or reads here, in short: You. And also to all the nice people who collect or talk about math stuff, and especially those who come up with cool posts we all like reading so much: Thank you!

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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)

PDF Book Link

Blog Link
7 Photos - View album

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There is a lot more happening with and around the Coq proof assistant than +Julien Narboux​​​​​​' community currently reflects. Let's take it as a good sign! More room for starters! Share your first experiences there and I hereby promise to try and help you over a few hurdles!

You may have seen me post a link to +Arnaud Spiwack​​​​​'s collection about Coq:

That was just before I found this community. I wouldn't be surprised if Arnaud has more to tell, so keep looking out, even if I grew unhappy making a fuss about it. Cheers!

As usual you'll find a representative post below the fold, click through the blue category link to find the community.

#coq #proofAssistant #community

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+Sean Walker​​​ makes animations like this cool snub dodecahedron folding over to a mustbea-stellated whatisit-hedron one in processing, and curates teasers to his work in this wonderful collection:

They all have a mathematical background and many show classical ideas in fresh colors. Go now and enjoy! Cool stuff, Sean!

#collection of cool #math #animation #gif's
The prickly Inversion of a Snub Dodecahedron

It tumbled away and awkwardly came to an unseemly rest. A naked pile of shards unintentionally revealed. All the untidy truths had punctured through the affected membrane of calm, revealed in sharp edges and wicked points. This is it, do you see?

This is an animation from 2015. Polyhedrons occupied most of my attention once I got my legs with 3D Processing techniques. I'll revisit them in Blender at some point I imagine.


#processing #mathart #dodecahedron #polyhedron
Animated Photo

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Look at this nice #collection about #rings! It has introductory material, links to blog posts, and lectures waiting for you:

The varied outlooks and starting points invite you to get in touch with #ringTheory, and learn what is known about #fields along! Cool stuff, +Aaron Johnson​, thank you!

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I revived my old collection All Things Math today, after being away for nearly a year. In this blog, I present some news, interesting problems, fascinating articles, topics that I am working on, and other mathematical findings that would be enjoyable to a general audience. Check it out here!

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+Aaron Johnson​​​​ is currently sifting for stuff to appear in his very interesting "GRAPH THEORY" collection:

I like your short intros and cool finds Aaron! Folks, have a look and click follow!

#graph #theory #collection
Spectral graph theory
In mathematics, spectral graph theory is the study of properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated to the graph, such as its adjacency matrix or Laplacian matrix.

An undirected graph has a symmetric adjacency matrix and therefore has real eigenvalues (the multiset of which is called the graph's spectrum) and a complete set of orthonormal eigenvectors.

While the adjacency matrix depends on the vertex labeling, its spectrum is a graph invariant.

Spectral graph theory is also concerned with graph parameters that are defined via multiplicities of eigenvalues of matrices associated to the graph, such as the Colin de Verdière number.

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+Rob Jongschaap is a reliable source for science news, and usually includes a relevant excerpt from the post. That's very convenient! He's also very organized and his "Math" collection is well curated:

There's so much stuff out there, and this nice stream can help you keep up!

#collection with #annotated #math posts

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The "R programming for data analysis" community is about the statistics package 'R'. It is very much alive and in addition to simple intros like +Igor Misechko​​​​​​'s nice one below, you get announcements and q&a, all in high quality.

It's a great resource and will get you in touch with R users and experts if you want to learn more about statistics an data analysis.

#R #statistics #software #community
Explanation how analyse data from google account.

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Here's a representative post from +Aaron Johnson​'s cool collection on Knot Theory. It's well curated with pictures, explanations and links. Even the occasional link-dropping posts are quite informative. Quality stuff you shouldn't miss!

#knot #collection 
Writhing Number
The writhing number measures the global geometry of a
closed space curve or knot.

In knot theory, there are several competing notions of the quantity writhe, or Wr. In one sense, it is purely a property of an oriented link diagram and assumes integer values. In another sense, it is a quantity that describes the amount of "coiling" of a mathematical knot (or any closed, simple curve) in three-dimensional space and assumes real numbers as values. In both cases, writhe is a geometric quantity, meaning that while deforming a curve (or diagram) in such a way that does not change its topology, one may still change its writhe

Normal holonomy and writhing number of polygonal knots

Computing the Writhing Number of a Polygonal Knot

On White's formula - University of Edinburgh

Properties of ideal composite knots
Here we describe the properties of ideal forms of composite knots — knots obtained by the sequential tying of two or more independent knots (called factor knots) on the same string. We find that the writhe (related to the handedness of crossing points) of composite knots is the sum of that of the ideal forms of the factor knots. By comparing ideal composite knots with simulated configurations of knotted, thermally fluctuating DNA, we conclude that the additivity of writhe applies also to randomly distorted configurations of composite knots and their corresponding factor knots. We show that composite knots with several factor knots may possess distinct structural isomers that can be interconverted only by loosening the knot.
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