Bill Shillito
@solidangles.bsky.social
Math instructor at Oglethorpe University. Views my own. Talk to me about anything combinatorial game theory related!
He/him. Pronounced SHILL-lit-toe.
Websites: https://www.solidangl.es, https://1dividedby0.com
He/him. Pronounced SHILL-lit-toe.
Websites: https://www.solidangl.es, https://1dividedby0.com
Question for anyone who's taught multivariable calculus (without line/surface integrals — just up through multiple integrals).
If you were to choose a "capstone" topic that ties multiple topics together, what would you choose?
Teaching the Calculus sequence again soon and trying to plan ahead.
If you were to choose a "capstone" topic that ties multiple topics together, what would you choose?
Teaching the Calculus sequence again soon and trying to plan ahead.
February 13, 2026 at 2:36 PM
Question for anyone who's taught multivariable calculus (without line/surface integrals — just up through multiple integrals).
If you were to choose a "capstone" topic that ties multiple topics together, what would you choose?
Teaching the Calculus sequence again soon and trying to plan ahead.
If you were to choose a "capstone" topic that ties multiple topics together, what would you choose?
Teaching the Calculus sequence again soon and trying to plan ahead.
WOOHOO! Our sandwiches paper has been published! 🥳
...in celebration, I'm going to claim that tonight's lasagna was a sandwich. 🥪
...in celebration, I'm going to claim that tonight's lasagna was a sandwich. 🥪
My newest paper about defining sandwiches is out!
@drew-lewis.com @sbagley.bsky.social @annemho.bsky.social Mary, Jessica, Bill, @matthematics.com Kate, Sarah
www.tandfonline.com/doi/full/10....
@drew-lewis.com @sbagley.bsky.social @annemho.bsky.social Mary, Jessica, Bill, @matthematics.com Kate, Sarah
www.tandfonline.com/doi/full/10....
Humanizing Defining in Mathematics with Sandwiches
This paper discusses multiple versions of an activity in which participants create, discuss, and analyze possible definitions of the term “sandwich.” This activity has helped us humanize mathematic...
www.tandfonline.com
January 23, 2026 at 1:49 AM
WOOHOO! Our sandwiches paper has been published! 🥳
...in celebration, I'm going to claim that tonight's lasagna was a sandwich. 🥪
...in celebration, I'm going to claim that tonight's lasagna was a sandwich. 🥪
Teaching logic tomorrow ... with Clue!
January 21, 2026 at 3:38 AM
Teaching logic tomorrow ... with Clue!
It’s ironic that the people who seem to be able to benefit the most from AI tools are the ones who don’t actually need them.
I'm gonna keep banging this drum:
AI is a useful tool for an expert, it can provide shortcuts and efficiencies in the same way as many other tech tools do.
AI is a massive problem for anyone inexpert, because it makes stuff up. If you lack expertise you just can't tell how good the output is.
AI is a useful tool for an expert, it can provide shortcuts and efficiencies in the same way as many other tech tools do.
AI is a massive problem for anyone inexpert, because it makes stuff up. If you lack expertise you just can't tell how good the output is.
January 15, 2026 at 8:17 PM
It’s ironic that the people who seem to be able to benefit the most from AI tools are the ones who don’t actually need them.
As my contribution to sharing subtraction strategies, here's how I do subtraction nowadays, using negative numbers!
Made this up on the fly way back when I first started tutoring because I couldn't remember how to do multiple borrowing anymore and I never liked the lie of "you can't take 3 from 2".
Made this up on the fly way back when I first started tutoring because I couldn't remember how to do multiple borrowing anymore and I never liked the lie of "you can't take 3 from 2".
January 2, 2026 at 7:06 PM
As my contribution to sharing subtraction strategies, here's how I do subtraction nowadays, using negative numbers!
Made this up on the fly way back when I first started tutoring because I couldn't remember how to do multiple borrowing anymore and I never liked the lie of "you can't take 3 from 2".
Made this up on the fly way back when I first started tutoring because I couldn't remember how to do multiple borrowing anymore and I never liked the lie of "you can't take 3 from 2".
Deviled eggs for New Year's Eve!
January 1, 2026 at 4:41 AM
Deviled eggs for New Year's Eve!
Reposted by Bill Shillito
We are aware of an ongoing situation concerning our GitHub organization and Discord server (both of which have been deleted) and are working on resolving this as soon as possible.
In the meantime we have setup discord.gg/fGG4TFSdKh as a new home on Discord for our community, come join us there!
In the meantime we have setup discord.gg/fGG4TFSdKh as a new home on Discord for our community, come join us there!
Join the Manim Discord Server!
Check out the Manim community on Discord – hang out with 95 other members and enjoy free voice and text chat.
discord.gg
December 26, 2025 at 8:22 AM
We are aware of an ongoing situation concerning our GitHub organization and Discord server (both of which have been deleted) and are working on resolving this as soon as possible.
In the meantime we have setup discord.gg/fGG4TFSdKh as a new home on Discord for our community, come join us there!
In the meantime we have setup discord.gg/fGG4TFSdKh as a new home on Discord for our community, come join us there!
Had a dream last night… except the main thing of the dream was that I stayed in bed until like 4 PM.
There were other things going on too, but I think someone is trying to tell me to get more sleep. 😂
There were other things going on too, but I think someone is trying to tell me to get more sleep. 😂
December 23, 2025 at 3:45 PM
Had a dream last night… except the main thing of the dream was that I stayed in bed until like 4 PM.
There were other things going on too, but I think someone is trying to tell me to get more sleep. 😂
There were other things going on too, but I think someone is trying to tell me to get more sleep. 😂
Reposted by Bill Shillito
🙂↔️🫸 Calculus II exam
😎👉 Series finale
😎👉 Series finale
December 22, 2025 at 2:43 PM
🙂↔️🫸 Calculus II exam
😎👉 Series finale
😎👉 Series finale
Most underrated video game villain.
December 22, 2025 at 12:15 AM
Most underrated video game villain.
Reposted by Bill Shillito
For today’s Advanced Topics test I wrote my own
@joeldavidhamkins.bsky.social -style question 😁
#iteachmath #MathSky
@joeldavidhamkins.bsky.social -style question 😁
#iteachmath #MathSky
December 15, 2025 at 3:03 PM
For today’s Advanced Topics test I wrote my own
@joeldavidhamkins.bsky.social -style question 😁
#iteachmath #MathSky
@joeldavidhamkins.bsky.social -style question 😁
#iteachmath #MathSky
Anyone have any idea where I can find a direct reference to the following quote? Especially in its original script? I want to verify the translation.
"Anantam api sankhyaatmakam iti budhyate. / Through numbers, even the infinite can be understood." — Madhava of Sangamagrama
"Anantam api sankhyaatmakam iti budhyate. / Through numbers, even the infinite can be understood." — Madhava of Sangamagrama
December 9, 2025 at 5:42 PM
Anyone have any idea where I can find a direct reference to the following quote? Especially in its original script? I want to verify the translation.
"Anantam api sankhyaatmakam iti budhyate. / Through numbers, even the infinite can be understood." — Madhava of Sangamagrama
"Anantam api sankhyaatmakam iti budhyate. / Through numbers, even the infinite can be understood." — Madhava of Sangamagrama
Students who take AP Statistics are 3x more likely to be able to tell the difference between correlation and causation.
December 7, 2025 at 2:55 AM
Students who take AP Statistics are 3x more likely to be able to tell the difference between correlation and causation.
November 18, 2025 at 7:33 PM
Reposted by Bill Shillito
You kids and your six trig functions. Back in my day we had only one, and we used it for everything.
sin(θ)
sin(π/2 - θ)
sin(θ)/sin(π/2 - θ)
1/sin(θ)
1/sin(π/2 - θ)
sin(π/2 - θ)/sin(θ)
sin(θ)
sin(π/2 - θ)
sin(θ)/sin(π/2 - θ)
1/sin(θ)
1/sin(π/2 - θ)
sin(π/2 - θ)/sin(θ)
November 7, 2025 at 12:15 AM
You kids and your six trig functions. Back in my day we had only one, and we used it for everything.
sin(θ)
sin(π/2 - θ)
sin(θ)/sin(π/2 - θ)
1/sin(θ)
1/sin(π/2 - θ)
sin(π/2 - θ)/sin(θ)
sin(θ)
sin(π/2 - θ)
sin(θ)/sin(π/2 - θ)
1/sin(θ)
1/sin(π/2 - θ)
sin(π/2 - θ)/sin(θ)
If you'd never seen the definitions for the dot product and the cross product, how might you have invented them for yourself?
Who took two vectors, thought "I wonder how I multiply these", and came up with ... those?
I've been toying with this since yesterday and would love to hear other thoughts.
Who took two vectors, thought "I wonder how I multiply these", and came up with ... those?
I've been toying with this since yesterday and would love to hear other thoughts.
November 7, 2025 at 1:05 PM
If you'd never seen the definitions for the dot product and the cross product, how might you have invented them for yourself?
Who took two vectors, thought "I wonder how I multiply these", and came up with ... those?
I've been toying with this since yesterday and would love to hear other thoughts.
Who took two vectors, thought "I wonder how I multiply these", and came up with ... those?
I've been toying with this since yesterday and would love to hear other thoughts.
Hey @desmos.com, any plans to have Desmos be able to choose between the math convention and the physics convention for θ and φ as a quick toggle?
I've taught both math majors and physics majors, and it would be nice to allow them to choose the convention that their field uses. 🙂
I've taught both math majors and physics majors, and it would be nice to allow them to choose the convention that their field uses. 🙂
November 5, 2025 at 8:22 PM
Hey @desmos.com, any plans to have Desmos be able to choose between the math convention and the physics convention for θ and φ as a quick toggle?
I've taught both math majors and physics majors, and it would be nice to allow them to choose the convention that their field uses. 🙂
I've taught both math majors and physics majors, and it would be nice to allow them to choose the convention that their field uses. 🙂
How to graph y = cosh x:
TI-84 CE:
1. Press [Y=].
2. Press [2nd] [0] (CATALOG).
3. Press [PRGM] (C) to skip to the C functions.
4. Scroll down until you find cosh( and press [ENTER].
5. Type the rest of the expression and press [GRAPH].
@desmos.com:
1. Type y = cosh x.
TI-84 CE:
1. Press [Y=].
2. Press [2nd] [0] (CATALOG).
3. Press [PRGM] (C) to skip to the C functions.
4. Scroll down until you find cosh( and press [ENTER].
5. Type the rest of the expression and press [GRAPH].
@desmos.com:
1. Type y = cosh x.
October 29, 2025 at 11:53 PM
How to graph y = cosh x:
TI-84 CE:
1. Press [Y=].
2. Press [2nd] [0] (CATALOG).
3. Press [PRGM] (C) to skip to the C functions.
4. Scroll down until you find cosh( and press [ENTER].
5. Type the rest of the expression and press [GRAPH].
@desmos.com:
1. Type y = cosh x.
TI-84 CE:
1. Press [Y=].
2. Press [2nd] [0] (CATALOG).
3. Press [PRGM] (C) to skip to the C functions.
4. Scroll down until you find cosh( and press [ENTER].
5. Type the rest of the expression and press [GRAPH].
@desmos.com:
1. Type y = cosh x.
There's a part of math history that mystifies me.
We used to have a whole bunch of interesting named curves — cissoid, tractrix, strophoid, involute, pedal curve, and so on.
Now they've mostly been relegated to quaint examples in math textbooks.
Why were these relevant? And what happened to them?
We used to have a whole bunch of interesting named curves — cissoid, tractrix, strophoid, involute, pedal curve, and so on.
Now they've mostly been relegated to quaint examples in math textbooks.
Why were these relevant? And what happened to them?
October 24, 2025 at 11:45 PM
There's a part of math history that mystifies me.
We used to have a whole bunch of interesting named curves — cissoid, tractrix, strophoid, involute, pedal curve, and so on.
Now they've mostly been relegated to quaint examples in math textbooks.
Why were these relevant? And what happened to them?
We used to have a whole bunch of interesting named curves — cissoid, tractrix, strophoid, involute, pedal curve, and so on.
Now they've mostly been relegated to quaint examples in math textbooks.
Why were these relevant? And what happened to them?
Question for anyone that teaches Calculus I. (Been asking this in a few chats.)
What's the point of having students learn about the normal line? What's it good for specifically? (And "they'll see normals again in Calculus III" doesn't count.)
What's the point of having students learn about the normal line? What's it good for specifically? (And "they'll see normals again in Calculus III" doesn't count.)
October 24, 2025 at 1:04 PM
Question for anyone that teaches Calculus I. (Been asking this in a few chats.)
What's the point of having students learn about the normal line? What's it good for specifically? (And "they'll see normals again in Calculus III" doesn't count.)
What's the point of having students learn about the normal line? What's it good for specifically? (And "they'll see normals again in Calculus III" doesn't count.)
This was the exact moment I learned it's called "maths" across the pond.
October 21, 2025 at 12:00 AM
This was the exact moment I learned it's called "maths" across the pond.
Ah yes, the four basic operations: addition, subtraction, checkmark, and multiplication.
October 11, 2025 at 9:07 PM
Ah yes, the four basic operations: addition, subtraction, checkmark, and multiplication.
Cool thing I just realized about f-means!
If deg(f) < deg(g), then the f-mean of a data set is less than the g-mean.
So since f(x)=log x has "degree" 0 and g(x)=x has degree 1, the geometric mean is less than the arithmetic mean.
(I always forget which way it goes — now I'll always remember!)
If deg(f) < deg(g), then the f-mean of a data set is less than the g-mean.
So since f(x)=log x has "degree" 0 and g(x)=x has degree 1, the geometric mean is less than the arithmetic mean.
(I always forget which way it goes — now I'll always remember!)
October 10, 2025 at 2:40 AM
Cool thing I just realized about f-means!
If deg(f) < deg(g), then the f-mean of a data set is less than the g-mean.
So since f(x)=log x has "degree" 0 and g(x)=x has degree 1, the geometric mean is less than the arithmetic mean.
(I always forget which way it goes — now I'll always remember!)
If deg(f) < deg(g), then the f-mean of a data set is less than the g-mean.
So since f(x)=log x has "degree" 0 and g(x)=x has degree 1, the geometric mean is less than the arithmetic mean.
(I always forget which way it goes — now I'll always remember!)
I've been thinking a lot about means recently!
Probably some combination of (1) teaching our data analysis unit in our STEM 101 course at Oglethorpe and (2) all of @howiehua.bsky.social's great posts surrounding Mean Girls Day.
I'd like to show how some of these various means are related.
🧵 [0]
Probably some combination of (1) teaching our data analysis unit in our STEM 101 course at Oglethorpe and (2) all of @howiehua.bsky.social's great posts surrounding Mean Girls Day.
I'd like to show how some of these various means are related.
🧵 [0]
October 9, 2025 at 2:23 AM
I've been thinking a lot about means recently!
Probably some combination of (1) teaching our data analysis unit in our STEM 101 course at Oglethorpe and (2) all of @howiehua.bsky.social's great posts surrounding Mean Girls Day.
I'd like to show how some of these various means are related.
🧵 [0]
Probably some combination of (1) teaching our data analysis unit in our STEM 101 course at Oglethorpe and (2) all of @howiehua.bsky.social's great posts surrounding Mean Girls Day.
I'd like to show how some of these various means are related.
🧵 [0]
Welp, looks like my Erdős number is still infinity. 🙃
(My journal submission based on my dissertation research got outright rejected.)
(My journal submission based on my dissertation research got outright rejected.)
October 2, 2025 at 1:29 PM
Welp, looks like my Erdős number is still infinity. 🙃
(My journal submission based on my dissertation research got outright rejected.)
(My journal submission based on my dissertation research got outright rejected.)