Andrew D Hwang
@diffgeom.com
The online shop Differential Geometry: Original Math Designs, at www.diffgeom.com.
"Hwang" rhymes with "song" more or less, he/him: Freelance mathematician, mathematical artist (no machine learning), author, difficult to summarize. I block bots
"Hwang" rhymes with "song" more or less, he/him: Freelance mathematician, mathematical artist (no machine learning), author, difficult to summarize. I block bots
That suggests the visible explosion is initially all ejecta; the shock waves only become visible once the ejecta are subsonic, and are a lot smaller in radius than intuition might suggest...?
Corrections to my understanding are welcome!
[2/2]
Corrections to my understanding are welcome!
[2/2]
January 10, 2026 at 2:20 PM
That suggests the visible explosion is initially all ejecta; the shock waves only become visible once the ejecta are subsonic, and are a lot smaller in radius than intuition might suggest...?
Corrections to my understanding are welcome!
[2/2]
Corrections to my understanding are welcome!
[2/2]
(Caveat: mathematician, not scientist)
Long-time nit: In existing (still/animated) impact depictions, velocities look wrong to me: Impactor ~20-30 mi/s, but ejecta should be well below escape velocity (~4-5mi/s), and shock waves at speed of sound (in air, water, rock; ~0.2-1mi/s).
[1/2]
#SciArt
Long-time nit: In existing (still/animated) impact depictions, velocities look wrong to me: Impactor ~20-30 mi/s, but ejecta should be well below escape velocity (~4-5mi/s), and shock waves at speed of sound (in air, water, rock; ~0.2-1mi/s).
[1/2]
#SciArt
January 10, 2026 at 2:19 PM
(Caveat: mathematician, not scientist)
Long-time nit: In existing (still/animated) impact depictions, velocities look wrong to me: Impactor ~20-30 mi/s, but ejecta should be well below escape velocity (~4-5mi/s), and shock waves at speed of sound (in air, water, rock; ~0.2-1mi/s).
[1/2]
#SciArt
Long-time nit: In existing (still/animated) impact depictions, velocities look wrong to me: Impactor ~20-30 mi/s, but ejecta should be well below escape velocity (~4-5mi/s), and shock waves at speed of sound (in air, water, rock; ~0.2-1mi/s).
[1/2]
#SciArt
Same as for the 6yo, I'd ask probing questions to clarify what the symbol(s) "28" means to them. (And then what "36" means, and what "+" means.)
What happens next depends on the response(s) given.
For example, maybe we count out 28=2*10+8 pennies and 36=3*10+6 pennies and put them in one pile....
What happens next depends on the response(s) given.
For example, maybe we count out 28=2*10+8 pennies and 36=3*10+6 pennies and put them in one pile....
December 25, 2025 at 4:17 PM
Same as for the 6yo, I'd ask probing questions to clarify what the symbol(s) "28" means to them. (And then what "36" means, and what "+" means.)
What happens next depends on the response(s) given.
For example, maybe we count out 28=2*10+8 pennies and 36=3*10+6 pennies and put them in one pile....
What happens next depends on the response(s) given.
For example, maybe we count out 28=2*10+8 pennies and 36=3*10+6 pennies and put them in one pile....
"What's 28?" (Seriously.)
I had not heard of NumberBlocks, but did learn from a former colleague recently that some of their calculus students this fall did not know the difference between addition and multiplication.
What are numbers to a person like that? (Seriously.)
I had not heard of NumberBlocks, but did learn from a former colleague recently that some of their calculus students this fall did not know the difference between addition and multiplication.
What are numbers to a person like that? (Seriously.)
December 23, 2025 at 1:00 PM
"What's 28?" (Seriously.)
I had not heard of NumberBlocks, but did learn from a former colleague recently that some of their calculus students this fall did not know the difference between addition and multiplication.
What are numbers to a person like that? (Seriously.)
I had not heard of NumberBlocks, but did learn from a former colleague recently that some of their calculus students this fall did not know the difference between addition and multiplication.
What are numbers to a person like that? (Seriously.)
1. 😬 I might ought to apologize on behalf of all mathematicians
2. I do suggest she keep the book; working through it (with a classmate the summer after junior year, i.e., ~2 years after U of T uses it) was the first time I understood "dual vector spaces," "tensors," and "differential forms"
2. I do suggest she keep the book; working through it (with a classmate the summer after junior year, i.e., ~2 years after U of T uses it) was the first time I understood "dual vector spaces," "tensors," and "differential forms"
December 19, 2025 at 8:34 PM
1. 😬 I might ought to apologize on behalf of all mathematicians
2. I do suggest she keep the book; working through it (with a classmate the summer after junior year, i.e., ~2 years after U of T uses it) was the first time I understood "dual vector spaces," "tensors," and "differential forms"
2. I do suggest she keep the book; working through it (with a classmate the summer after junior year, i.e., ~2 years after U of T uses it) was the first time I understood "dual vector spaces," "tensors," and "differential forms"
Thank you; I do strive for promptness! :)
Most of the shipping process is outside my control, but just to note for passersby, orders placed in the next hour or so will go out today before first pick-up.
Most of the shipping process is outside my control, but just to note for passersby, orders placed in the next hour or so will go out today before first pick-up.
December 19, 2025 at 2:56 PM
Thank you; I do strive for promptness! :)
Most of the shipping process is outside my control, but just to note for passersby, orders placed in the next hour or so will go out today before first pick-up.
Most of the shipping process is outside my control, but just to note for passersby, orders placed in the next hour or so will go out today before first pick-up.
One never-ending surprise with these space curves is how their appearance changes with angle. Even the comparable band on the complex twisted cubic (t,t^2,t^3) looks non-rigid when it rotates about the "1-axis"! :)
December 19, 2025 at 2:44 PM
One never-ending surprise with these space curves is how their appearance changes with angle. Even the comparable band on the complex twisted cubic (t,t^2,t^3) looks non-rigid when it rotates about the "1-axis"! :)
This type of image would (seriously) make fine adult birthday cards.... 🤔
December 19, 2025 at 1:55 PM
This type of image would (seriously) make fine adult birthday cards.... 🤔
Reposted by Andrew D Hwang
#ArtAdventCalendar Day 18
"Lissajous 345", 2024
3D Lissajous figures and their 2D projections, created with code (no AI).
#MathArt #SciArt
"Lissajous 345", 2024
3D Lissajous figures and their 2D projections, created with code (no AI).
#MathArt #SciArt
December 18, 2025 at 9:04 PM
In the 90s as well, MAT 257 was a ... milestone ... in the specialist coursework. :)
Michael Spivak's thin, dense/rich (and to be honest, fraught) book "Calculus on Manifolds" was a common choice of text. Was that the book she used?
Sadly, the course-schedule stars never aligned me with 257....
Michael Spivak's thin, dense/rich (and to be honest, fraught) book "Calculus on Manifolds" was a common choice of text. Was that the book she used?
Sadly, the course-schedule stars never aligned me with 257....
December 19, 2025 at 1:39 PM
In the 90s as well, MAT 257 was a ... milestone ... in the specialist coursework. :)
Michael Spivak's thin, dense/rich (and to be honest, fraught) book "Calculus on Manifolds" was a common choice of text. Was that the book she used?
Sadly, the course-schedule stars never aligned me with 257....
Michael Spivak's thin, dense/rich (and to be honest, fraught) book "Calculus on Manifolds" was a common choice of text. Was that the book she used?
Sadly, the course-schedule stars never aligned me with 257....
Just so. :) @elkement.art and I separately have a thing for these shapely space curves!
December 18, 2025 at 8:49 PM
Just so. :) @elkement.art and I separately have a thing for these shapely space curves!
My oops; here is a link to the sticker pack page :)
www.diffgeom.com/product/viny...
From the Small World department, I taught at the U of T in the mid-to-late 90s, including MAT 267 (ODEs for math specialists) one semester.
The department had lively student cultures; I hope she's thriving!
www.diffgeom.com/product/viny...
From the Small World department, I taught at the U of T in the mid-to-late 90s, including MAT 267 (ODEs for math specialists) one semester.
The department had lively student cultures; I hope she's thriving!
www.diffgeom.com
December 18, 2025 at 12:16 AM
My oops; here is a link to the sticker pack page :)
www.diffgeom.com/product/viny...
From the Small World department, I taught at the U of T in the mid-to-late 90s, including MAT 267 (ODEs for math specialists) one semester.
The department had lively student cultures; I hope she's thriving!
www.diffgeom.com/product/viny...
From the Small World department, I taught at the U of T in the mid-to-late 90s, including MAT 267 (ODEs for math specialists) one semester.
The department had lively student cultures; I hope she's thriving!