### Thomas Wilson

Shared publicly -http://xahlee.info/SpecialPlaneCurves_dir/Hypotrochoid_dir/hypotrochoid.html

http://en.wikipedia.org/wiki/Spirograph

Thomas Wilson

Works at Edward Jones Investments

Lives in Independence, MO

2,034 followers|577,707 views

AboutPostsPhotosVideos

A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle.

http://xahlee.info/SpecialPlaneCurves_dir/Hypotrochoid_dir/hypotrochoid.html

http://xahlee.info/SpecialPlaneCurves_dir/Hypotrochoid_dir/hypotrochoid.html

1

Yes the whole Spirograph toy (launched in 1965) is based on this:

http://en.wikipedia.org/wiki/Spirograph

http://en.wikipedia.org/wiki/Spirograph

Add a comment...

2

LOL i just shared that this morning cause it couldn't stop laughing watching it :D glad to see we have the same sense of humor :D

Add a comment...

3

Add a comment...

+Manjul Bhargava [1] is, in my mind (and many other peoples'), a top contender for a Fields medal later this year at the International Congress of Mathematicians in Seoul. A report on some recent work of his is here:

http://mattbakerblog.wordpress.com/2014/03/10/the-bsd-conjecture-is-true-for-most-elliptic-curves/

He has announced that the Birch and Swinnerton-Dyer conjecture [2] is true for at least (just under) 2/3 of all elliptic curves. This is an improvement of past results of his (and coauthors) in this direction (showing a 'positive proportion' satisfy BS-D), and a comment to the post indicates that this is expected to improve to 4/5 given some ongoing work by Chris Skinner and collaborators.

That this work is considered by many to be Fields medal-worthy is analogous to how Stephen Smale [3] and Michael Freedman [4] won the Fields medal (essentially) for their proofs of the Poincaré conjecture in dimensions 5 and above, and in dimension 4, respectively [5]; it wasn't the original big conjecture, but it shed light on the general problem and why proving it in dimension 3 (the 'real' Poincaré conjecture [6], eventually proved by Grisha Perelman [7]) was going to need completely different tools.

So what is the Birch and Swinnerton-Dyer conjecture? Essentially, it tells us something about the number of rational-number solutions to certain two-variable cubic equations in two variables, with rational coefficients, defining a so-called

However, if we look for solutions among the rational numbers a/b, with a and b whole numbers (and possibly b=0, corresponding to a 'point at infinity'!), then this is a lot harder, and then the problem falls into two cases: a finite number of solutions and infinitely many solutions. In the infinitely many solutions case, we can further distinguish the 'number' of solutions, in a manner of speaking, by the dimension, or

Now there is another way to calculate a 'rank' for an elliptic curve, which uses complex analysis, or more roughly, infinite products built from the elliptic curve. One defines a so-called

That these two numbers, the rank and the analytic rank, have anything to do with each other, especially since the second one wasn't even

So at last, what is the conjecture? Namely that the rank and analytic rank are equal, and in fact there is a conjectured formula for the rate at which the values of the L-function associated to the elliptic curve increase as one heads away from the point 1 in the complex plane. This is terrifically scary, involving the size of the Tate-Shafarevich group Ш (one of the few, if only, instances of Cyrillic used internationally by mathematicians), which is mentioned in the linked blog post, the number of solutions in the 'finite part' of the elliptic curve (for those who know group theory: the order of the torsion subgroup) and other quantities which are associated to each elliptic curve.

Now the really interesting thing is that we expect

y^2 + xy = x^3 − 26175960092705884096311701787701203903556438969515x + 51069381476131486489742177100373772089779103253890567848326,

due to +Noam Elkies, though there are examples with a rank at least 28, but with actual rank unknown. Interestingly, the 'finite part' of the elliptic curve (the

To summarise: what Bhargava has done (with his collaborators) is show that in at least 2/3 of all elliptic curves, the rank and the analytic rank coincide, showing the BSD conjecture for this many curves, with a view to extend this to 4/5 of all elliptic curves.

[1] http://en.wikipedia.org/wiki/Manjul_Bhargava

[2] http://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture

[3] http://en.wikipedia.org/wiki/Stephen_Smale

[4] http://en.wikipedia.org/wiki/Michael_Freedman

[5] http://en.wikipedia.org/wiki/Generalized_Poincar%C3%A9_conjecture

[6] http://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture

[7] http://en.wikipedia.org/wiki/Grigori_Perelman

[8] http://en.wikipedia.org/wiki/Mordell%27s_theorem

[9] http://jiggerwit.wordpress.com/2013/09/25/the-nsa-back-door-to-nist/

[10] http://en.wikipedia.org/wiki/Riemann_zeta_function

[11] http://en.wikipedia.org/wiki/Modularity_theorem

[12] http://en.wikipedia.org/wiki/Andrew_Wiles

[13] http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem

(Thanks to +Peter Woit for the link to Matt Baker's blog posting)

1

Add a comment...

The concept of epicycles stands as a cadaver of the Copernican Revolution, which killed it with a fantastic reduction of complexity and gains in efficiency and predictive power. As a consequence, epicycles now serve as standard metaphor for patching up a doomed paradigm.

But on another hand we've gained lots of perspective since the times of Copernicus and Newton. Epicycles can be viewed as precursors to Fourier theory. Newtonian Gravitation that concluded the Copernican Revolution has been superseded by Einstein's theory; and a very well known and long-advertised issue with the latter, is the difficulty of assembling it with quantum mechanics in a mathematically comprehensive whole - what's called*the unification problem in physics.*

Meanwhile, I believe it quite accurate to affirm that*Fourier Theory is to Quantum Mechanics like Arithmetic Addition to Accounting.*

Of course, astrophysics admits Fourier theory or related ideas to describe purely gravitational situations like orbital resonances or star vibrations and likely much more, but at the most elementary level, the negative status of the epicycles idea which could as the gif illustrates, positively serve as a pedagogical entry point to Fourier theory -- that negative status stands out as intriguingly correlated, when squinting, with how Gravitation resists marrying to QM -- QM*that's in turn completely dependent on Fourier theory.*

This makes me wonder if a more charitable treatment of epicycles than the traditional one dictated by history, should not be viewed as a plausible missing ingredient to the solution of the unification problem in physics.

But on another hand we've gained lots of perspective since the times of Copernicus and Newton. Epicycles can be viewed as precursors to Fourier theory. Newtonian Gravitation that concluded the Copernican Revolution has been superseded by Einstein's theory; and a very well known and long-advertised issue with the latter, is the difficulty of assembling it with quantum mechanics in a mathematically comprehensive whole - what's called

Meanwhile, I believe it quite accurate to affirm that

Of course, astrophysics admits Fourier theory or related ideas to describe purely gravitational situations like orbital resonances or star vibrations and likely much more, but at the most elementary level, the negative status of the epicycles idea which could as the gif illustrates, positively serve as a pedagogical entry point to Fourier theory -- that negative status stands out as intriguingly correlated, when squinting, with how Gravitation resists marrying to QM -- QM

This makes me wonder if a more charitable treatment of epicycles than the traditional one dictated by history, should not be viewed as a plausible missing ingredient to the solution of the unification problem in physics.

1

i never did understand why the unification problem in physics had to be sole dependent on the QM theory why can't it be solely dependent upon itself withing a fraction of the QM theory and yet still be independent on the Fourier theory itself seems more logical to say that it can be if re worked don't you think?

Add a comment...

Dots that are moving around in a circle! Connect them and you'll get a moving octahedron!

#octahedron

#octahedron

1

Add a comment...

Work

Employment

- Edward Jones InvestmentsFinancial Advisor, 2013 - present

Basic Information

Gender

Male

Relationship

Married

Story

Tagline

Science Fiction Author

Introduction

Since publishing my first two novels I have discovered that I enjoy writing books much more than I love reading them. I probably should have been an Engineer but life got in the way. I love that all of my crazy ideas that I come up with can be brought to life through the books that I write.

I Love to write books and read others books. I am a God fearing, family man with a 8 - 5 day job. I enjoy riding my motorcycle, and building models, along with spending as much time as possible raising my children with my wonderful wife.

I have written and E-Published two novels so far.

"Whisper" in January of 2011.

"No Rules Of Engagement" in September 2011.

Look for "Leviathan Deterrent" Sometime in 2013.

Currently the sequels to both books are being edited.

About to finish the rough draft of my fifth novel.

Aspiring authors or people who love History please follow my Blog at Thomaswilsonstoryteller dot blogspot dot com.

Bragging rights

Published E-Book Author as of 2011

Places

Currently

Independence, MO

Previously

Athol, Idaho - Fort Knox, KY

Links

Other profiles

Contributor to

- StorytellerPubs (current)
- Storyteller (current)
- yahoo.com (current)
- My StorytellerTDW Blog (current)