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
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.)
Reposted by Bill Shillito
What this thread doesn't mention: the English language contains the numerals lakh and crore for a significant percentage of its native speakers.
en.wikipedia.org/wiki/Indian_...
en.wikipedia.org/wiki/Indian_...
September 25, 2025 at 5:48 AM
What this thread doesn't mention: the English language contains the numerals lakh and crore for a significant percentage of its native speakers.
en.wikipedia.org/wiki/Indian_...
en.wikipedia.org/wiki/Indian_...
Hot take:
The English language is not base ten.
It's base thousand.
Sure, we write numbers using the Hindu-Arabic digits 0 through 9, but the way our language is structured groups numbers in powers of a thousand.
If anything, we're sub-base ten.
(1/5)
The English language is not base ten.
It's base thousand.
Sure, we write numbers using the Hindu-Arabic digits 0 through 9, but the way our language is structured groups numbers in powers of a thousand.
If anything, we're sub-base ten.
(1/5)
September 25, 2025 at 2:21 AM
Hot take:
The English language is not base ten.
It's base thousand.
Sure, we write numbers using the Hindu-Arabic digits 0 through 9, but the way our language is structured groups numbers in powers of a thousand.
If anything, we're sub-base ten.
(1/5)
The English language is not base ten.
It's base thousand.
Sure, we write numbers using the Hindu-Arabic digits 0 through 9, but the way our language is structured groups numbers in powers of a thousand.
If anything, we're sub-base ten.
(1/5)
Holding class discussions on readings is HARD.
English teachers, how do y'all even do it?
I'm honestly struggling. 😕
English teachers, how do y'all even do it?
I'm honestly struggling. 😕
September 11, 2025 at 2:30 AM
Holding class discussions on readings is HARD.
English teachers, how do y'all even do it?
I'm honestly struggling. 😕
English teachers, how do y'all even do it?
I'm honestly struggling. 😕
Student: “Babylonian numerals are kinda confusing… 60 is such a weird and unintuitive base.”
Me: “Yeah I know right? Oh hey by the way, what time does this class end?”
Student: “At 11:30.”
Me: *waits*
Multiple students: “…OHHHHHHHHHH”
#MathSky
Me: “Yeah I know right? Oh hey by the way, what time does this class end?”
Student: “At 11:30.”
Me: *waits*
Multiple students: “…OHHHHHHHHHH”
#MathSky
September 5, 2025 at 4:57 PM
Student: “Babylonian numerals are kinda confusing… 60 is such a weird and unintuitive base.”
Me: “Yeah I know right? Oh hey by the way, what time does this class end?”
Student: “At 11:30.”
Me: *waits*
Multiple students: “…OHHHHHHHHHH”
#MathSky
Me: “Yeah I know right? Oh hey by the way, what time does this class end?”
Student: “At 11:30.”
Me: *waits*
Multiple students: “…OHHHHHHHHHH”
#MathSky
Today's lesson in COR 314!
Students learned how to count in Iñupiaq and write numbers using the Kaktovik numerals (as well as convert between base ten and base twenty). 🧮
Lots of discussion about how the way we're used to thinking isn't the only way to do things! 🙂
Students learned how to count in Iñupiaq and write numbers using the Kaktovik numerals (as well as convert between base ten and base twenty). 🧮
Lots of discussion about how the way we're used to thinking isn't the only way to do things! 🙂
September 3, 2025 at 5:10 PM
Today's lesson in COR 314!
Students learned how to count in Iñupiaq and write numbers using the Kaktovik numerals (as well as convert between base ten and base twenty). 🧮
Lots of discussion about how the way we're used to thinking isn't the only way to do things! 🙂
Students learned how to count in Iñupiaq and write numbers using the Kaktovik numerals (as well as convert between base ten and base twenty). 🧮
Lots of discussion about how the way we're used to thinking isn't the only way to do things! 🙂
Anyone else moving to more in-class assessments this semester due to AI concerns and not particularly thrilled about it, but not feeling like they have much of another choice? 😕
August 17, 2025 at 8:24 PM
Anyone else moving to more in-class assessments this semester due to AI concerns and not particularly thrilled about it, but not feeling like they have much of another choice? 😕
Reposted by Bill Shillito
August 14, 2025 at 4:32 PM
Me: After I graduate I’m gonna write my own textbook! And start a new video series! And program a game! And go to the gym! And cook more often! And…
Also me: I dun wanna get up it’s not noon yet
Also me: I dun wanna get up it’s not noon yet
August 14, 2025 at 12:52 AM
Me: After I graduate I’m gonna write my own textbook! And start a new video series! And program a game! And go to the gym! And cook more often! And…
Also me: I dun wanna get up it’s not noon yet
Also me: I dun wanna get up it’s not noon yet
Anyone have ideas for games (especially combinatorial ones) that inherently involve taxicab geometry? Not just games that happen to take place on a square lattice but where taxicab distance is actually an important part of playing the game?
August 9, 2025 at 3:06 AM
Anyone have ideas for games (especially combinatorial ones) that inherently involve taxicab geometry? Not just games that happen to take place on a square lattice but where taxicab distance is actually an important part of playing the game?
Who’s going to be at #MAAthfest next week? Let’s meet up!
July 29, 2025 at 8:29 PM
Who’s going to be at #MAAthfest next week? Let’s meet up!
My dissertation is officially uploaded, so I finally feel like I can say I have my PhD! 🥳
scholarworks.gsu.edu/entities/pub...
It's been exhausting going to school while working full time at Oglethorpe... But looking forward to doing my own projects again, like video-making and textbook-writing!
scholarworks.gsu.edu/entities/pub...
It's been exhausting going to school while working full time at Oglethorpe... But looking forward to doing my own projects again, like video-making and textbook-writing!
Using Combinatorial Game Theory to Introduce the Concept of Mathematical Proof in a Mathematics for Liberal Arts Course
This dissertation investigates students' development of the notion of mathematical proof in a Mathematics for Liberal Arts course through the lens of Combinatorial Game Theory. There has been extensiv...
scholarworks.gsu.edu
July 25, 2025 at 2:02 PM
My dissertation is officially uploaded, so I finally feel like I can say I have my PhD! 🥳
scholarworks.gsu.edu/entities/pub...
It's been exhausting going to school while working full time at Oglethorpe... But looking forward to doing my own projects again, like video-making and textbook-writing!
scholarworks.gsu.edu/entities/pub...
It's been exhausting going to school while working full time at Oglethorpe... But looking forward to doing my own projects again, like video-making and textbook-writing!
Something seems off about the Euler characteristic of this hush puppy.
March 1, 2025 at 12:14 AM
Something seems off about the Euler characteristic of this hush puppy.