Refurio Anachro
4,963 followers -
Higher maths is cool - come and see invisible worlds with me!
Higher maths is cool - come and see invisible worlds with me!
4,963 followers
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journeys in higher maths is the place where I collect the posts I wrote which I really care about. They're all popular maths introductions, many of them about topics for which I haven't seen any account in the pop-literature elsewhere.
I'm an amateur and not a professional, or decorated mathematician, and I write about what I'm learning at the time. Because I'm insatiably curious, because maths is beautiful, and more psychedelic than the whole 60's generation ever was, and all the while more real than reality!
Come and see how it can take a few iterations, help from generous professionals, and even taking the risk of total embarassment to get the unavoidable kinks straight. Or meet these generous folks in the comments. Any feedback welcome, especially questions!
You'll find the latest right on top so here's an older post featuring a popular topic, but with a peculiar slant.
Complex numbers explained in shocking facts:
https://plus.google.com/+RefurioAnachro/posts/gCDmGDj6KSz
Here someone 'recognized' journalistic qualities in my work! I didn't think of it like that, but attending was lots of fun, and a pleasure I intend to extend on occasion. There's also some homework left undone from that time...
Can anybody sneak into a math seminar?:
https://plus.google.com/+RefurioAnachro/posts/NH1GPUpKhH8
#collection of posts explaining topics from #higher #mathematics for a general audience.
I'm an amateur and not a professional, or decorated mathematician, and I write about what I'm learning at the time. Because I'm insatiably curious, because maths is beautiful, and more psychedelic than the whole 60's generation ever was, and all the while more real than reality!
Come and see how it can take a few iterations, help from generous professionals, and even taking the risk of total embarassment to get the unavoidable kinks straight. Or meet these generous folks in the comments. Any feedback welcome, especially questions!
You'll find the latest right on top so here's an older post featuring a popular topic, but with a peculiar slant.
Complex numbers explained in shocking facts:
https://plus.google.com/+RefurioAnachro/posts/gCDmGDj6KSz
Here someone 'recognized' journalistic qualities in my work! I didn't think of it like that, but attending was lots of fun, and a pleasure I intend to extend on occasion. There's also some homework left undone from that time...
Can anybody sneak into a math seminar?:
https://plus.google.com/+RefurioAnachro/posts/NH1GPUpKhH8
#collection of posts explaining topics from #higher #mathematics for a general audience.
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Minimal surfaces minimal style, made from paper strips!
+Alison Grace Martin has left a trail of these, mostly triaxially woven, topological (or rather conformal) exercises here on g+!
A Link to another place where I posted about this:
https://mastodon.cloud/@RefurioAnachro/100717988203473514
#triaxial #geometry #paperModel
+Alison Grace Martin has left a trail of these, mostly triaxially woven, topological (or rather conformal) exercises here on g+!
A Link to another place where I posted about this:
https://mastodon.cloud/@RefurioAnachro/100717988203473514
#triaxial #geometry #paperModel
Seeding weaving structures. ‘Discovering privileged topologies of molecular knots with self-assembling models’ Mattia Marenda, Enzo Orlandini and Cristian Micheletti, August 2018.
https://www.nature.com/articles/s41467-018-05413-z
https://www.nature.com/articles/s41467-018-05413-z
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> SYMPLECTIC GEOMETRY is the ultimate generalization of Hamiltonian mechanics! The basic idea of Hamiltonian mechanics is to write down an expression (called Hamiltonian) for a conserved quantity (like energy) as depending on an unknown function p(t) (e.g. position), and one related to its first derivative q(t) (say, momentum). You then demand that the Hamiltonian is stationary, that it doesn't change, which is cleverly formalized by setting its derivative to zero, and solve for p!
This is part 8 of a series on symplectic geometry I have started over here on mastodon:
https://mastodon.cloud/@RefurioAnachro/100589818866519298
I have wondered about this curious subject for a very long time, but only recently, when I stumbled into Nöther's theorem again, did I realize that I had enough background to get going!
Here's me, wondering if physics might be a sham, with some kind support by +Andrew Miloradovsky :
https://mastodon.cloud/@RefurioAnachro/100499490532058231
And here's another occasion, where similar thoughts of mine got spilled on +Lee McCullochJames 's lawn:
https://plus.google.com/+LeeMcCullochJames/posts/HWvYRXCiHy6
The series isn't done yet, and I will get back to it soon. Stay tuned! Tudelu!
#symplectic #geometry, and some #hamiltonian physics
This is part 8 of a series on symplectic geometry I have started over here on mastodon:
https://mastodon.cloud/@RefurioAnachro/100589818866519298
I have wondered about this curious subject for a very long time, but only recently, when I stumbled into Nöther's theorem again, did I realize that I had enough background to get going!
Here's me, wondering if physics might be a sham, with some kind support by +Andrew Miloradovsky :
https://mastodon.cloud/@RefurioAnachro/100499490532058231
And here's another occasion, where similar thoughts of mine got spilled on +Lee McCullochJames 's lawn:
https://plus.google.com/+LeeMcCullochJames/posts/HWvYRXCiHy6
The series isn't done yet, and I will get back to it soon. Stay tuned! Tudelu!
#symplectic #geometry, and some #hamiltonian physics
Refurio Anachro (@RefurioAnachro@mastodon.cloud)
mastodon.cloud
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If you haven't seen these classic and captivating public lectures on modern physics from the 60's (they're still very modern), the Stanford Institute for Theoretical Physics had them uploaded as a nice 7-part Playlist in 2015 here:
"Richard Feynman Messenger Lectures at Cornell"
https://www.youtube.com/playlist?list=PLS3_1JNX8dEh5YcO-Y05stU0u_T9nqIlF
"Richard Feynman Messenger Lectures at Cornell"
https://www.youtube.com/playlist?list=PLS3_1JNX8dEh5YcO-Y05stU0u_T9nqIlF
Public
9+10+11+12 = 13+14+15 = 2+4+ ... +12
My day will be the 19th, and there'll be a party on 28th. If you happen to be in Bonn on that date just pass me a note and I'll tell you how to find it. I'd be happy to welcome anyone with whom I had discussions here on g+!
My day will be the 19th, and there'll be a party on 28th. If you happen to be in Bonn on that date just pass me a note and I'll tell you how to find it. I'd be happy to welcome anyone with whom I had discussions here on g+!
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The ideal arch
> Let's define an ideal arch as one that doesn't have a tendency to fall apart sideways, outward or inward. This means no shear (sideways) stress between blocks, and that means the pressure force between blocks in contact is a normal force -- it acts along the line of the arch. That should sound familiar! For a hanging string, obviously the tension acts along the line of the string.
> […] the ideal arch shape is a catenary.
> In fact, Gaudi designed a church in Barcelona using a web of strings and weights to find correct shapes for the arches -- of course, the actual building would have a shape like the reflection in a horizontal mirror above the strings.
Woot Gaudi!
This stuff comes from lecture notes on mechanics in exquisite web quality (by Michael Fowler, the textbook being Landau and Lishitz' "Mechanics")! Its first and a bit of its second chapter carve out the catenary as solution to a few problems for which, if you think about it, or look a bit closer at the derivations, it is not obvious at all they have the same solution!
http://galileoandeinstein.physics.virginia.edu/7010/CM_01_Intro_Statics_Catenary_Arch.html
Hat tip to +`John Baez for the link!
https://en.wikipedia.org/wiki/Catenary
A sister post:
https://mastodon.cloud/@RefurioAnachro/100797813205818525
#catenary #architecture #mechanics
> Let's define an ideal arch as one that doesn't have a tendency to fall apart sideways, outward or inward. This means no shear (sideways) stress between blocks, and that means the pressure force between blocks in contact is a normal force -- it acts along the line of the arch. That should sound familiar! For a hanging string, obviously the tension acts along the line of the string.
> […] the ideal arch shape is a catenary.
> In fact, Gaudi designed a church in Barcelona using a web of strings and weights to find correct shapes for the arches -- of course, the actual building would have a shape like the reflection in a horizontal mirror above the strings.
Woot Gaudi!
This stuff comes from lecture notes on mechanics in exquisite web quality (by Michael Fowler, the textbook being Landau and Lishitz' "Mechanics")! Its first and a bit of its second chapter carve out the catenary as solution to a few problems for which, if you think about it, or look a bit closer at the derivations, it is not obvious at all they have the same solution!
http://galileoandeinstein.physics.virginia.edu/7010/CM_01_Intro_Statics_Catenary_Arch.html
Hat tip to +`John Baez for the link!
https://en.wikipedia.org/wiki/Catenary
A sister post:
https://mastodon.cloud/@RefurioAnachro/100797813205818525
#catenary #architecture #mechanics
9/27/18
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Before we get back to #symplectic geometry let's have some fun with alternate ways to do classical mechanics!
#altMechanics – I mentioned Lagrangian and Hamiltonian mechanics earlier. Lagrange's is often simpler, but it cannot handle cyclic coordinates. Meet Routhian mechanics! Routh found out that you can cherry-pick momenta or velocities as your generalized coordinates to your delight.
https://en.wikipedia.org/wiki/Routhian_mechanics
1/
The rest of this post can be found here:
https://mastodon.cloud/@RefurioAnachro/100680044084660691
#altMechanics – I mentioned Lagrangian and Hamiltonian mechanics earlier. Lagrange's is often simpler, but it cannot handle cyclic coordinates. Meet Routhian mechanics! Routh found out that you can cherry-pick momenta or velocities as your generalized coordinates to your delight.
https://en.wikipedia.org/wiki/Routhian_mechanics
1/
The rest of this post can be found here:
https://mastodon.cloud/@RefurioAnachro/100680044084660691
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Recent recording of a talk where his sister shares Memories.
"Being Feynman's Curious Sister" – Joan Feynman, filmed at "Feynman 100: A celebration of Richard Feynman's life & legacy on the occasion of his 100th birthday", May 11 2018.
https://www.youtube.com/watch?v=fuN8UzQCRWo
"Being Feynman's Curious Sister" – Joan Feynman, filmed at "Feynman 100: A celebration of Richard Feynman's life & legacy on the occasion of his 100th birthday", May 11 2018.
https://www.youtube.com/watch?v=fuN8UzQCRWo
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If you don't call the Yoneda Lemma a good friend of yours, go and read +John Cook 's nice and gentle introduction now! It's like the first hunk of a ski lift which might carry you all the way to n-Categories!
#categoryTheory
#categoryTheory
New post: Hom functors and a glimpse of the Yoneda lemma
https://www.johndcook.com/blog/2018/08/06/hom-functors/
https://www.johndcook.com/blog/2018/08/06/hom-functors/
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Maybe you know Tadashi Tokieda from +Numberphile, here's an hour long public talk he gave at Gresham College, published just a few days ago:
https://www.youtube.com/watch?v=j9SYMA8dhzY
"We want to see how mathematics breaks"
"Where incompatible regimes meet, nature has a tough decision to make"
#public #popMath #video #lecture
https://www.youtube.com/watch?v=j9SYMA8dhzY
"We want to see how mathematics breaks"
"Where incompatible regimes meet, nature has a tough decision to make"
#public #popMath #video #lecture
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