iiinova — where your digital self keeps evolving

James Cleveland-Tran @jclevelandtran.com · 19/08/2026

At least that’s consistent with the very first op-ed guy:

From the Wikipedia page for Op-Eds:

When Swope took over as main editor in 1920, he opted to
designate a page from editorial staff as "a catchall for book reviews,
society boilerplate, and obituaries" Swope explained:

"It occurred to me that nothing is more interesting than
opinion when opinion is interesting, so I devised a method
of cleaning off the page opposite the editorial, which
became the most important in America ... and thereon I
decided to print opinions, ignoring facts."

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James Cleveland-Tran @jclevelandtran.com · 10/08/2026

Some mathematical photos from my most recent trip to Scandanavia.

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James Cleveland-Tran @jclevelandtran.com · 11/05/2026

Not always compelled to try but this one spoke to me:

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James Cleveland-Tran @jclevelandtran.com · 22/04/2026

This quote reminds me of this graph I once drew for my students:

Horizontal axis: “length of student response”
Vertical axis: “likelihood of being 100% correct”
The graph is hill-shaped.

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James Cleveland-Tran @jclevelandtran.com · 17/11/2025

How I just found the eggs in the fridge. (#howmany?)

A twenty-four carton of eggs, 4x6, with most of the eggs missing. Remaining eggs go diagonally inwards from the corners.

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James Cleveland-Tran @jclevelandtran.com · 13/11/2025

I'm still iffy about probabilities involving infinite spaces, but my diagram to think about it is this, and I think the white space is greater than the red space (if you keep going), which would make concave more likely?

A triangle on a grid. In a cone out from each vertex is a white space. Fanning out from each side is a red space. The interior of the triangle is white.

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James Cleveland-Tran @jclevelandtran.com · 06/11/2025

Here’s my write-up for n=even

Because n is the median, the middle two numbers must be n. To the left are some numbers, n/2 - 1 of them. To the right, n/2 - 2 numbers, then the max.

Because we want to maximize the max, we want to minimize all those numbers to the right. Therefore they all equal n.

We also want to minimize the numbers on the left. Because there are fewer of them than there are Ns, we can set them all to the min, called a, while keeping n the unique mode.

a + n = max
Because range =n

(n/2 - 1)a + max + (n/2)*n = n^2
by mean = n

an/2 -a +a +n +(n^2)/2 = n^2

Some more algebra

a = n - 2

So Max = n - 2 + n = 2n - 2

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James Cleveland-Tran @jclevelandtran.com · 15/10/2025

I recently worked on a fun problem involved the Pokémon TCG. Here's a post about the problem and my thought process/solution. jclevelandtran.com/2025/10/15/s...

In the Pokémon TCG Pocket app, I would earn 10 points for winning a match and lose 7 points when losing a match. However, you also get a win streak bonus – the second win in a row gets a bonus of 3 points, the third gets 6, the fourth 9, and the fifth (and all subsequent) gets 12. Assuming I have a win rate of 50% (which I did at the time), what’s my expected value for playing n games? (How many games would I expect to play to earn x points?)

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James Cleveland-Tran @jclevelandtran.com · 14/10/2025

We did a fun problem today. Suppose you have this Pairwise Matrix. (How to read: each cell shows how many points the row player gets against the column player. So in a match of A vs B, A gets 54 points and B gets 51, so A wins.) Can you seed an 8-player bracket such that A will win? What about C?

Photo of data table which can also be found here: https://docs.google.com/spreadsheets/d/1pflkRhCslWUs1MfpabUb0lhLer6Or7UVFaap1EsHwVs/edit?gid=0#gid=0

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James Cleveland-Tran @jclevelandtran.com · 11/10/2025

The traditional fifth anniversary gift is wood, so Dũng got me a board game that is 100% wood - even the box.

The game Hexapolis, in a wooden hex box with stacks of wooden hex pieces.

Our finished game state, with Dũng’s piece on a tall 4 tower surrounded by walls, with various other connected hexes. Dũng crossed arms visible in the background.

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James Cleveland-Tran @jclevelandtran.com · 19/08/2025

Oh man, this is such a good math burn (though you need to know about the critiques of Newton's calculus for it to land.)

Except from Wikipedia on the Jefferson Method.

"This pathology led to widespread mockery of Jefferson's method when it was learned Jefferson's method could "round" New York's apportionment of 40.5 up to 42, with Senator Mahlon Dickerson saying the extra seat must come from the "ghosts of departed representatives."

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James Cleveland-Tran @jclevelandtran.com · 17/08/2025

I appreciate that this menu is in fractions.

A menu with things like "Additional sauce, 3/4." "Tavern Knots, 9 1/2"

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James Cleveland-Tran @jclevelandtran.com · 09/08/2025

Some lovely #mathart at the Milwaukee Domes, including the structure itself. #mathphoto

Three foxes made of small triangles. The triangles become spread out as you approach the tail, giving a sense of speed

A tower with tiles stacked, each turned from the one below in a golden ratio-esque manner

A spiral of maple blocks that reminds me of those potatoes you can get, although wider in the middle

The roof of one of the domes from the inside. A pentagon inside a circle, with concentric circles around it, and arms spiraling out from that main circle both clockwise and counterclockwise, overlapping to make smaller triangles

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James Cleveland-Tran @jclevelandtran.com · 08/08/2025

Picked up this fun mathy Venn diagram card game while on ky trip. Reminds me of Eleusis (@mathhombre). Can you guess the rules for each ring? (Note: we’re playing on the train in the middle of nowhere North Dakota, which is relevant for the red clue)

A Venn diagram of three colors. Yellow is “word”, Blue is “attribute”, Red is “context”

Yellow contains moon, pretzel, bell, museum, chalkboard, brick, field
Blue contains moon, igloo, yoyo, pretzel, bell, pasta, pancake
Res contains pancake, pasta, pretzel, bell, museum, field, brick, chalkboard, saw, robot, candle, microscope
None contains gargoyle

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James Cleveland-Tran @jclevelandtran.com · 29/07/2025

More hotel bathrooms need to have shower instructions like this. Very useful. Although the good decision here is undercut by several other bad decisions in the design, such as having the towel rack be inside the shower.

Sign on hotel bathroom mirror with shower handle instructions. In the reflection can also be seen the towel rack inside the shower.

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James Cleveland-Tran @jclevelandtran.com · 10/07/2025

I’m sure it’s not actually the first productive thing I’ve done this summer, but it might be.

Image of the shelf I put up im the kitchen with 6 pots and pans hanging from it

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James Cleveland-Tran @jclevelandtran.com · 05/07/2025

A found (fictional) Talking Math with Kids scene from a book I just read. One reason I was happy with it, besides the rarity of such scenes in fiction, is that Ben (the adult) is not particularly good at maths, but he is good at encouraging children’s passions, and that’s sufficient. #tmwyk #tmwopk

An excerpt from “It Takes Two to Tumble” by Cat Sebastian

"There's a gooseberry custard tart on the sideboard, but
something went terribly wrong when Mrs. Morris sliced it,"
Ben said to no one in particular. "She cut it into eight slices."

Out of the corner of his eye he saw Jamie watch him intently. Jamie knew this as the preamble to one of his favorite games. "That's fine by me," Jamie said. "Peg won't get any if she launches those peas at me, which leaves two slices each for the rest of us."

"Quite right, but she isn't going to launch peas or anything else." Out of the corner of his eye, he saw Peggy rest her spoon on her plate.

"One and three-fifths of a slice for each of us," Jamie said promptly.

"But what if I decide to allocate the pie according to weight? That seems only fair. I'd say I'm about twelve stone, and so is your father." The mere estimation of what the captain might have beneath his clothes by way of sinew and muscle was enough to make Ben's cheeks heat. "You and Peggy are maybe four stone apiece and Ned's about seven."

"That's about a tenth of the pie each for me and Peg."

"Ah, but I don't have tenths, I have eighths."

Jamie made an impatient sound. "Remove a quarter of an eighth and you'll have a tenth."

"Which is grossly unfair because I don't even care for gooseberry tart and I don't see why I ought to have twice as much—"

"Three times as much," Jamie corrected.

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James Cleveland-Tran @jclevelandtran.com · 07/03/2025

My students pointed out that my bug got thinner and thinner as it went around the triangle. I guess it was quite a workout!

A diagram of a triangle with a hand-drawn bug at various points around it. The bug gets thinner as it goes counterclockwise from the lower left corner, point A.

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James Cleveland-Tran @jclevelandtran.com · 07/03/2025

My calculus class doesn’t love the interval notations using parentheses, nor the one using inequalities, so we decided to use hearts instead. It’s kinda like two parentheses! #iTeachMath #MTBoS

Photo of the whiteboard with the below written:
Increasing: (-infinity, 0) U (1, infinity)
Decreasing: (0, 1)
Inflection point:
x= 0.75
Interval(s) where function
Concave Up
(0.75,inf) but in a heart
Concave Down
(-inf, 0.75) but in a heart

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James Cleveland-Tran @jclevelandtran.com · 04/03/2025

The correct way to eat a slice of pizza (per my husband): (1) Fold as normal. (2) Eat about half of the slice. (3) Unfold and then refold orthogonally. (4) Eat the rest as you would a taco or hot dog.

A slice of pizza folded normally (that is, with the fold down the length of the slice)

The half-slice is now folded so that the fold goes down the width of the slice.

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James Cleveland-Tran @jclevelandtran.com · 11/02/2025

That field guide to sabotage has some good pages. For example, this one could be thought of as a guide to Posting.

Simple Sabotage Field Manual
3. MOTIVATING THE SABOTEUR
To incite the citizen to the active practice of simple sabotage and to keep him prac-
ticing that sabotage over sustained periods is a special problem.
Simple sabotage is often an act which the citizen performs according to his own
initiative and inclination. Acts of destruction do not bring him any personal gain and
may be completely foreign to his habitually conservationist attitude toward materials
and tools. Purposeful stupidity is contrary to human nature. He frequently needs
pressure, stimulation or assurance, and information and suggestions regarding feasi-
ble methods of simple sabotage.
(1) Personal Motives
(a) The ordinary citizen very probably has no immediate personal motive for com-
mitting simple sabotage. Instead, he must be made to anticipate indirect personal
gain, such as might come with enemy evacuation or destruction of the ruling govern-
ment group. Gains should be stated as specifically as possible for the area addressed:
simple sabotage will hasten the day when Commissioner X and his deputies Y and Z
will be thrown out, when particularly obnoxious decrees and restrictions will be abol-
ished, when food will arrive, and so on. Abstract verbalizations about personal liberty,
freedom of the press, and so on, will not be convincing in most parts of the world. In
many areas they will not even be comprehensible.
(b) Since the effect of his own acts is limited, the saboteur may become discouraged
unless he feels that he is a member of a large, though unseen, group of saboteurs
operating against the enemy or the government of his own country and elsewhere.
This can be conveyed indirectly: suggestions which he reads and hears can include
observations that a particular technique has been successful in this or that district.
Even if the technique is not applicable to his surroundings, another's success will
encourage him to attempt similar acts. It also can be conveyed directly: statements
praising the effectiveness of simple sabotage can be contrived which will be pub-
lished by white radio, freedom stations, and the subversive press. Estimates of the
proportion of the population engaged in sabotage can be disseminated. Instances of
successful sabotage already are being broadcast by white radio and freedom stations,
and this should be continued and expanded where compatible with security.
(c) More important than (a) or (b) would be to create a situation in which the citi-
zen-saboteur acquires a sense of responsibility and begins to educate others in sim-
ple sabotage.

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James Cleveland-Tran @jclevelandtran.com · 05/02/2025

Doing my Tangent Line Art project in calculus today, one student had the idea to use a circle as the domain/range restriction, which led to cool things like this. #MTBoS #iTeachMath #mathArt

A circle of radius 3 centered at the origin. The function y=0.1x^2-1/x is contained within, as well as 120 tangent lines to that function in various colors.

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James Cleveland-Tran @jclevelandtran.com · 12/01/2025

Today's Nancy is pretty #mathComic while also representing how I feel after giving what I think are fairly thorough and foolproof instructions to students www.gocomics.com/nancy/2025/0...

Today's Nancy comic by Olivia Jaimes.
Panel 1: Nancy holds a pizza cutter over a pizza, Aunt Fritzi says: "No funny business when you cut up the pizza, Nancy"
Panel 2: Fritzi saying "Be symmetrical"
Panel 3: Fritzi saying "Make the pieces the same shape"
Panel 4: Fritzi saying "And make sure that Sluggo's slice takes up just as much room on the table as yours does"
Panel 5: Sluggo frowning in front of the bottom half of the pizza, while to the side Nancy has fork in hand ready to eat the top half

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James Cleveland-Tran @jclevelandtran.com · 10/01/2025

Feel like this graph accurately describes my experience grading exams, and I need to make sure my students know. #MTBoS #iTeachMath #EduSky

A graph of "likelihood of being 100% correct" vs "length of student response" which is in an upsidedown parabola shape

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James Cleveland-Tran @jclevelandtran.com · 09/01/2025

Excited to get multiple colors of masks to match my multiple colors of shoes.

Six left shoes in a row with KN95 masks sitting in their openings: red, yellow, green, blue, purple, black

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James Cleveland-Tran @jclevelandtran.com · 29/12/2024

I'm amused by these blocks my nephew got advertising the Pythagorean Theorem.

A box of Magic Tower blocks with a 3-4-5 triangle on the side

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James Cleveland-Tran @jclevelandtran.com · 27/12/2024

Passed this cool decoration while walking just now

LED figure of a toy soldier but I guess it uses mirrors or something because it looks like it has depth even though it is flat

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James Cleveland-Tran @jclevelandtran.com · 21/11/2024

I modified the definite integral one and it was quite fun! There was a bidding war for the exponential, but it wound up being the cubic in the winning ARoC.

Average Rate of Change Auction Catalog

Lot 1: a=-2, f(x)=4ln(x) - x + 2
Lot 2: f(x)=x^3-3x^2+4, b=2
Lot 3: b=4, f(x)=e^x
Lot 4: 1.5b, Absolute value
Lot 5: a=-3, f(x)=2cos(x)
Lot 6: b=3, value ± 1
Lot 7: b=6, f(x) = -2x + 4
Lot 8: a = -5, f(x) = -x^2 + 4
Lot 9: a=1, -a
Lot 10: b=5, f(x) = ceil(0.5x)

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James Cleveland-Tran @jclevelandtran.com · 31/10/2024

This furniture design at the NYPL feels like they are just asking people to throw out books.

Identical library bins, except one says “trash” and the other says”book drop”

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James Cleveland-Tran @jclevelandtran.com · 29/09/2024

It is ironic that, directly below the exhibit about ocean plastic pollution at the Griffin Museum of Science and Industry, is the exhibit where you can make useless junk out of plastic.

Mold-o-rama machine at the Museum of Science and Industry

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James Cleveland-Tran @jclevelandtran.com · 29/09/2024

I found this to be very useful exiting the subway in Chicago. Get on it, NYC.

Compass rose at the top of the subway entrance in Chicago

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James Cleveland-Tran @jclevelandtran.com · 27/09/2024

Feels appropriate to have a geometry session in a room with these lights. #nctmchi24

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James Cleveland-Tran @jclevelandtran.com · 27/09/2024

My mind was blown in this session about ambiguous patterns. We were working on a visual pattern at our tables, and then had to go talk to people from other tables. Then we discovered that we had different incomplete patterns at each table! Creating a need to collab w/ incomplete info #nctmchi24

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James Cleveland-Tran @jclevelandtran.com · 18/04/2024

On one of my discords we made a “keeping it 86” emoji.

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James Cleveland-Tran @jclevelandtran.com · 05/02/2024

Sorting geometry class into new groups today based on the quadrilateral anagram congruencies.

List of congruent statements
TIME ITEM
EMIT MITE
EMIT ITEM
ITEM MITE
TIME EMIT
TIME MITE
MANE NAME
MANE AMEN
NAME AMEN
ARTS TSAR
RATS STAR
RATS TARS
STAR TARS
LEIS ISLE
AGED EGAD
CODE DECO

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James Cleveland-Tran @jclevelandtran.com · 14/07/2023

I honestly thought the second one was just a joke for the purpose of the ad, but I just saw someone in the hear 2023 wearing a mask like that on be subway.

MTA mask wearing PsA; second figure has mask over nose but not mouth

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