iiinova — where your digital self keeps evolving

Mark Trushkowsky @marktrushkowsky.bsky.social · 08/09/2026

A little something I like to revisit this time of year. When I read this in 1998, I had no idea bell hooks was welcoming me to the adult basic education class I found myself teaching in 2001, in a community where I felt whole and where I belonged, two feelings that were novel to me at the time.

"The academy is not paradise. But learning is a place where paradise can be created. The classroom, with all its limitations, remains a location of possibility. In that field of possibility we have the opportunity to labor for freedom, to demand of ourselves and our comrades, an openness of mind and heart that allows us to face reality even as we collectively imagine ways to move beyond boundaries, to transgress. This is education as the practice of freedom."

bell hooks, Teaching to Transgress

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Mark Trushkowsky @marktrushkowsky.bsky.social · 06/09/2026

Gorgeous sashiko stitching (hitomezashi & moyōzashi) at the Minnesota State Fair.

An indigo blue jacket embroidered with intricate white geometric stitching, displaying a first-place blue ribbon from the Minnesota State Fair.

A close-up view of dark indigo jacket with intricate hand-stitched patterns in white thread, including geometric flowers and swirling water-like designs.

A large framed fabric panel with two dozen of square sections, each demonstrating a unique geometric pattern made of white stitching on dark cloth.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 05/09/2026

Even more amazing quilts from the Minnesota State Fair. 3/3

A patchwork quilt with hidden details arranged into a landscape of a bright yellow sun rising over red, orange and green rolling hills, with a blue river.

A close-up art quilt with a green tree frog with red feet, large orange eyes, and black Buddy Holly glasses with colored circles, against a light yellow background.

A geometric triangular pattern in muted shades of olive green, mustard yellow, gray, and cream.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 05/09/2026

More beautiful quilts from the Minnesota State Fair. 2/3

A rainbow quilt with an optical illusion design of a curving tunnel, using geometric patchwork blocks fading into a bright yellow center against a dark frame.

A multi-colored quilt featuring a grid of bright rectangular blocks.

A quilt made of repeating star, triangle, and square patterns, created with rainbow-colored fabrics framed by bright white fabric.

A rainbow quilt featuring a central black flower with colorful fabric ribbons spiralling out against a textured gray background.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 05/09/2026

Beautiful quilts from this year’s Minnesota State Fair 1/3

A dark quilt with a vibrant diamond pattern with sharp contrasting, bright yellow, orange, red, and blue patterned fabrics.

A colorful modern quilt made of mismatched fabric rectangles in a vibrant grid pattern. A blue award ribbon hangs in the upper right.

A quilt with a diamond pattern made of blue and off-white fabric triangles that convey a sense of movement.

A brilliant geometric quilt made of light aqua, dark teal, navy blue, and white fabrics in a repeating diamond design.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 08/06/2026

Learned a new word today. Last week I led some folks in an exploration of probability w/ a game of roller derby, where you roll 2 dice and look at the sum. Looking at our results—w/ its messy but triangular distribution & that tower of 7s—I’m calling it a Punktlandung. #ANNMath #MTBoS #ITeachMath

A hand-drawn tally chart tracking the sums of rolling two dice from 2 to 12. The tallies form a rough, messy triangular distribution, with a massive column for the number 7 that tower over the rest of the numbers, shooting completely out of the top of the grid.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 07/06/2026

Super excited about the new instructional routine I recently learned that develops data literacy, spatial reasoning, estimation skills, and a conceptual understanding of part-to-whole relationships - Paper Plate Circle Graphs! adultnumeracynetwork.org/Instructiona... #ANNMath #MTBOS #ITeachMath

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Mark Trushkowsky @marktrushkowsky.bsky.social · 07/06/2026

3/n Step 3: We cut out our bars, taped them into one long bar, taped the ends to form a circle and then used it to estimate a circle graph. Like every good Gather/Show/Tell data cycle, I uncovered some surprises, I answered a few of my questions, and I raised new questions. #ANNMath #MTBoS

a rough estimate of a circle graph. The red section (countries with 0-9.9% of the workforce in labor unions, based on the countries on the labels of our clothing) is roughly 30% of the graph. The green section (10-19.9%) about 42%. The orange section (20-29.9%), a sliver at about 2%. The blue (40-49.9%), a little more than a quarter at 25%.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 07/06/2026

2/n Step 2: Use group data to make another graph that has fewer categories. I used a Statista page that gave the % share of the workforce from various countries who are members of labor unions (as of 2020). I did it based on the countries (19) and then using the number of post-its (50).

A bar graph with two bars for each category.

0 to 9.9% (Red) - one bar is 7 rows tall (7 out of 19) and the other bar is 15 rows tall (15 out of 50).

10-19.9% (Green) - one bar is 8 high (8 out of 19) and the other is 21 high (21 out of 50)

20-29.9% (Orange) - each bar is one row high (1/19 and 1/50)

30-39.9% - No bars (0/19 and 0/50)

40-49.9% (Blue) - 2/19 and 13/50

Next to the graph is a list of countries with the percentage of workforce in unions: Honduras (2.6%), China (44.2%), Thailand (3.3%), Vietnam - (49.62%), Jordan - ?, India (19.8%), Pakistan (4.7%), Bangladesh (11.9%), Madagascar (7.2%), Mauritius (27.7%), Cambodia (9.6%), Korea (12.4%), US (10.3%), Sri Lanka (10.1%), Indonesia (13%), Mexico (13.2%), Guatemala (3.1%), Germany (16.3%), Nicaragua (5.3%)

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Mark Trushkowsky @marktrushkowsky.bsky.social · 07/06/2026

1/n Got to do Countries In Our Closet data activity from @terc-stem.bsky.social EMPower book, Many Points Make A Point. Step 1: Create a graph showing the countries where our clothing was made. What do you notice? What do you wonder? #ANNMath #MTBoS #ITeachMath #statisticalliteracy #data

A graph with columns of post-its stacked over various country names.
Honduras - 5 post-its
China - 6
Thailand - 4
Vietnam - 7
Jordan - 1
India - 3
Pakistan - 1
Bangladesh - 3
Madagascar - 1
Mauritius - 1
Cambodia - 1
Korea - 1
USA - 4
Sri Lanka - 4
Indonesia - 2
Mexico - 2
Guatemala - 1
Germany - 2
Nicaragua - 1

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Mark Trushkowsky @marktrushkowsky.bsky.social · 07/06/2026

It was too bad the the game was called, but what a sky.

Dark swirling storm clouds over a softball field

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Mark Trushkowsky @marktrushkowsky.bsky.social · 07/06/2026

Say hello to some of my little friends…

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Mark Trushkowsky @marktrushkowsky.bsky.social · 07/06/2026

I know you are @triangleman.bsky.social, but I saw all these irregular pentagonal columns outside the MN Aurora game and thought of all you’ve given me to think about over the years. Thank you!

Waist high, irregular pentagonal column made of stone

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Mark Trushkowsky @marktrushkowsky.bsky.social · 18/04/2026

Once again, a simple set-up yielded many questions and ribbit holes… ahem, rabbit holes, to explore. Super fun Community of Adult Math Instructors (CAMI) meeting on this swapping frogs problem! nyccami.org/ribbit/ #ANNMath #ITeachMath #MTBoS #AdultEdu

What do you notice? What do you wonder?

On the top row, there are two pink frogs facing right and two blue frogs facing left, with a single space between them. The frog pairs are facing towards each other.

On the bottom, there are two blue frogs on the left, still facing left, and two pink frogs facing right, with a single space between them. The frog pairs are facing away from each other.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 19/02/2026

At Instructional Routines Club, someone commented that one of the benefits of virtual manipulatives is that you can cut/decompose them. I used that idea to represent my reasoning behind one of my equations. #ANNMath #Iteachmath #MTBoS

At the top is a pictorial equation: a pink triangle and small green triangle on the left side of the equals sign and a red trapezoid on the right side.

Below are five steps, linked by arrows. Step one has all three shapes from the equation. Step two has the green triangle placed over the red trapezoid, covering a portion of it. Step three has the pink triangle place over the red trapezoid as well. A triangular piece of the pink triangle is sticking out above the area of the red trapezoid. The only part of the red trapezoid still visible is a red triangle. Step four has the pink triangular piece slide over to be above the visible triangular piece of the red trapezoid. Step five shows that the access pink triangle exactly covers the remaining red triangle. This shows that the areas of the pink triangle and the small green triangle together are equal to the area of the red trapezoid.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 19/02/2026

I started making equations using only the shapes to show different relationships between the pieces. #ANNMath #Iteachmath #MTBoS

1. One pink triangle equals 2 small green triangles
2. One red trapezoid equals 3 small green triangles
3. One red trapezoid and one small green triangle equals one large green triangle equals to pink triangles equals four small green triangles
4. One pink triangle and one small green triangle equals one red trapezoid

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Mark Trushkowsky @marktrushkowsky.bsky.social · 19/02/2026

It was a virtual meeting, and some of us used Polypad to noodle with the shapes. Inspired by a colleague, I started making wordless visual representations of my reasoning. #ANNMath #Iteachmath #MTBoS

A trapezoid divided up into 12 congruent triangles. 3 of the triangles are red, together forming a smaller trapezoid within the larger trapezoid. The remaining 9 triangles are green.

3/12 of the triangles in the larger trapezoid are red.

An equation. On the left side of the equal sign, a larger trapezoid is composed of three smaller orange trapezoids and 3 small triangles. On the right side are four trapezoids. Three are the same as the smaller orange ones on the left side of the equation. One of them is composed of the three small yellow triangles, arranged to show they have the same area as each orange trapezoid.

My colleague created this representation for showing that the red trapezoid 1/4 the area of the original shape. Her goal was to get there without finding the 3/12 and then reducing. I had a similar approach, but loved how clearly her model conveyed our thinking without words.

The original trapezoid rearranged as three large triangles.
The triangle on the left is pink. The middle triangle is green. The triangle on the right is broken up into 4 smaller, congruent triangles. Three of those are red and one is green.

The goal was to show that the red trapezoid can be seen as 3/4 of 1/3.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 19/02/2026

We did a fraction talk at @adultnumeracy.bsky.social Instructional Routine Club today. #ANNMath #Iteachmath #MTBoS

$Text: What fraction of this shape is red? How do you know? How else do you know? Image: a trapezoid composed of 5 different pattern blocks. Two pink right triangles are arranged to create an equilateral triangle that can be seen as one-third of the area of the trapezoid. A large green triangle in the middle of the trapezoid has the same area as the pink. A third triangle is composed of a red trapezoid and a smaller green triangle. The red trapezoid and small green triangle together have the same area as the pink triangles and as the large green triangle.$

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Mark Trushkowsky @marktrushkowsky.bsky.social · 14/02/2026

Some friends and I were wondering if these dystopian days will bring about the end of asking each other, “how are you doing?” and it brought me back to these nurturing & sustaining questions, gifted by @teachnexttmb.bsky.social as a better way.

A screenshot of a thread with the following questions:

On the water front -
Are you having enough to drink today? Do you need anything to wash and clean? Can I help replenish any tears you've shed? Are you staying fluid these days? Are your waters calm, still, deep, turbulent, rushing, frozen, evaporated...?

Through the fire -
Where is the sun for you? Are you in enough light? How can I help you stay warm? What's burning for you? Do you need any fuel? What spark are you carrying? Is your blaze to high? Do you need rekindling? What's the smoke?

From the earth -
How grounded are you feeling? What is nourishing your soil? Where are you rich? Are you getting vitamins/minerals? Can I help you stand more firmly? Are you eating your veggies? When was your last rest? Do you need to lay down?

In the air -
Have you taken a breath? What's inspiring you? Have you felt the wind/breeze? What's in your wings/sails? Can I help you stay afloat? What do you need to fly? What whisper would you like to hear?

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Mark Trushkowsky @marktrushkowsky.bsky.social · 03/02/2026

“Hold on, hold on, my dear ones, here comes the dawn.”

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Mark Trushkowsky @marktrushkowsky.bsky.social · 03/02/2026

“Oh in the great unraveling, I love you.”

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Mark Trushkowsky @marktrushkowsky.bsky.social · 03/02/2026

Communal singing led by a Justice Choir tonight at the site of Alex Pretti’s final moments. In case you need a good cry, like I did. “Only through heartbreak did I learn to shake, And the strength And the depth Of my heart.”

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Mark Trushkowsky @marktrushkowsky.bsky.social · 27/01/2026

"DHS’s overbroad mandate and unchecked powers have turned it into a tinderbox, now ignited by a president willing to trample on the constitutional limits of presidential power.” (ACLU 8/11/2020) DHS is a 24 y.o. experiment that has failed. It's time to dismantle it. www.aclu.org/news/immigra...

A photograph of an aloe plant that is older than the U.S. Department of Homeland Security.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 27/01/2026

There are over 230 million people living within 100 miles of the U.S. border. We want ICE out of our city, but we don't want them to just move to yours. Moving ICE isn't justice. Ending ICE is.

A map of the United States that shows all of the cities within a 100-mile of the border. Text reads: Nearly 2 out of 3 people live within the 100-mile border zone.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 24/01/2026

There are an estimated 14 million undocumented people living in US. There are an estimated 95,000 undocumented people living in the Minneapolis/St Paul metro area. Less than 1% of the US undocumented population (approximately 0.7%) lives in the Minneapolis/St Paul area. Why is ICE really here?

A circle graph showing the the percentage of undocumented residents in the United States estimated to live in the Minneapolis/St Paul metro area: 0.7%

Sources:

- 14 million undocumented people estimated to be in the United States. (https://www.pewresearch.org/race-and-ethnicity/2025/08/21/u-s-unauthorized-immigrant-population-reached-a-record-14-million-in-2023/)

- The Minneapolis/St Paul metro area is estimated to have 95,000 undocumented people. (https://www.pewresearch.org/short-reads/2024/07/22/what-we-know-about-unauthorized-immigrants-living-in-the-us/).

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Mark Trushkowsky @marktrushkowsky.bsky.social · 24/01/2026

Dear @gluesenkampperez.house.gov @golden.house.gov et al Instead of standing for civil rights & human decency, you voted to increase funding for ICE’s domestic terrorism, currently in my city, coming soon to yours. You bent the knee. When we needed you, you refused the call. The North remembers.

The 7 House Democrats who voted with 213 Republicans to fully fund DHS and give ICE $10 billion dollars. The final vote was 220-207. Had these 7 voted against authoritarian overreach and stood with the US Constitution, the bill would have been defeated 214-213.

Tom Suozzi (NY), Henry Cuellar (TX), Don Davis (NC), Laura Gillen (NY), Jared Golden (ME), Vicente Gonzales (TX), and Marie Glusenkamp Perez (WA)

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Mark Trushkowsky @marktrushkowsky.bsky.social · 23/01/2026

7/7 This one looks at % of ICE arrests in NYC, Jan-Oct 2025, comparing targets who had criminal convictions versus those with pending criminal charges, and those with only civil immigration violations (no criminal charges). bit.ly/icearrestsin... #slowrevealgraph #ANNMath #ITeachMath #MTBoS

Numberless area graph. First image in a slow reveal graph sequence.

Area graph titled: Share of Arrests Each Week By Criminality
Final image from a slow reveal graph sequence

Numberless stacked bar graph. First image in a slow reveal graph sequence.

Stacked bar graph titled: Immigration Arrests in NYC Focus Far More on People Without Criminal Convictions or Charges Compared to U.S. Overall.

Final image from a slow reveal graph sequence

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Mark Trushkowsky @marktrushkowsky.bsky.social · 23/01/2026

6/7 This one compares the number of DHS officers in the state of Minnesota to the number of police officers in the largest Minneapolis/St. Paul metro area police forces. bit.ly/DHSinMNvsTCM... #slowrevealgraph #ANNMath #ITeachMath #MTBoS

Numberless circle graph/pictograph.
First image in a slow reveal graph sequence.

Circle Graph/Pictograph comparing Department of Homeland Security Forces in Minnesota to the Ten Largest Twin Cities Metro Police Forces.

Final image from a slow reveal graph sequence

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Mark Trushkowsky @marktrushkowsky.bsky.social · 23/01/2026

5/7 This one looks at the estimated population of undocumented immigrants by state. bit.ly/undocumented... #slowrevealgraph #ANNMath #ITeachMath #MTBoS

Numberless map graph. First image in a slow reveal graph sequence.

Graph titled: Estimated US undocumented population by state (2022)
Final image from a slow reveal graph sequence

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Mark Trushkowsky @marktrushkowsky.bsky.social · 23/01/2026

4/7 This one is a map graph that looks at what percentage of people arrested by ICE in each state had no criminal record. bit.ly/arrestedwith... #slowrevealgraph #ANNMath #ITeachMath #MTBoS

Map graph titled: Share of people arrested by ICE with no criminal record. Final image from a slow reveal graph sequence

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Mark Trushkowsky @marktrushkowsky.bsky.social · 23/01/2026

3/7 This one looks at the number of ICE arrests that have been people with violent convictions, people with other past convictions, people with pending criminal charges, and people with no criminal charges. bit.ly/ICEarrestsby... #slowrevealgraph #ANNMath #ITeachMath #MTBoS

Area Graph titled: Daily ICE arrests nationwide.
Final image from a slow reveal graph sequence

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Mark Trushkowsky @marktrushkowsky.bsky.social · 23/01/2026

2/7 This one looks at the the number of Immigration and Customs Enforcement (ICE) arrests that happened at prisons/jails and the number that have happened in communities, between 2024 and 2025. bit.ly/icearrestsby... #slowrevealgraph #ANNMath #ITeachMath #MTBoS

Numberless line graph. First image in a slow reveal graph sequence.

Graph titled: Daily ICE arrests nationwide.
Final image from a slow reveal graph sequence

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Mark Trushkowsky @marktrushkowsky.bsky.social · 23/01/2026

1/7 I've been making #slowrevealgraph sequences to help make sense of what is going on. Here's one that looks at the number of deportations each year within the past four presidential administrations. bit.ly/icedeportati... #ANNMath #ITeachMath #MTBoS

Numberless bar graph - first image from a slow reveal graph sequence

Graph titled: Deportations of People Arrested Within the United States. Final image from a slow reveal graph sequence

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Mark Trushkowsky @marktrushkowsky.bsky.social · 22/01/2026

All you have to do to see they are lying is pull up a map. The videos show ICE throwing gas canisters into the public park at W 25th and Bryant. The nearest gas stations are all blocks away. So “an agent moving to detain the person” means what… several cars of agents driving at least 4 blocks?

Quote from Tricia McLaughlin, DHS Assistant Secretary FM for Public Affairs:

“At one stop, individuals in the crowd thee food at the agents. At their final gas station stop, someone spit at an agent. When an agent moved to detain the person who spit on him, the crowd tackled and attacked the agents while surrounding them. To safely clear the area agents had to use crowd control measures to disperse the hostile crowd.”

A map of the Lowry Hills East neighborhood. The northeast corner of Mueller Park (W 25th and Bryant Ave) is circled in yellow. That is where ICE agents, including Greg Bovino, threw gas canisters into the crowd. The nearest gas stations are all at least four blocks away.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 22/01/2026

Hey Greg Bovino, what was in that green gas canister you threw into a the public park/play ground two blocks from my house? I walk my dog here every day and the snow is full of residue.

Dark green residue in the snow, partially covered by a cardboard sign.

A cardboard sign in the snow covering green residue. The sign, written by a concerned neighbor, reads: CAREFULLY. GREEN GAS Deployed. DO NOT TOUCH! HAZARD.

This is in a Minneapolis public park.

Dark green residue of a deployed gas canister in the snow after being thrown into a public park by Greg Bovino and other ICE Agents.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 13/11/2025

Like I said, I'm not quite there yet, but I wanted to share my work so far because I feel like there must be so many different ways to approach this, and I'm curious what others do. #ANNMath

A messy ZOOM whiteboard of thinking visualized, exploring the patterns in the table, making and testing conjectures and partially answering the question. The work generally moves from top to bottom. The culmination thus far is the 1000 does appear in the 8 row (not 8th row). The final sentence is "Upwards and onwards to a generalization to figure out the column!"

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Mark Trushkowsky @marktrushkowsky.bsky.social · 13/11/2025

Thank you, @triangleyou.bsky.social for sharing this task they got from @howiehua.bsky.social! What patterns do you notice in the table? Will 1000 appear? If so, where? I'm not quite there yet, but I'm having such fun, in the spirit in which I received it, I invite others to play! #ANNMath

A table of numbers.
Consecutive odd numbers across the top. Reading left to right: 1, 3, 5, 7...
The left column is made up of powers of 2 going down. Reading: 1, 2, 4, 8,...
The table can be completed by multiplying the odd numbers across the top by the powers of 2.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 12/11/2025

The Northern Lights (Minneapolis, MN)

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Mark Trushkowsky @marktrushkowsky.bsky.social · 28/10/2025

Minneapolis is doing me right on the jazz front these days.

Brandee Younger Trio at the Dakota with Rashaan Carter on bass

Makaya McCraven and Junius Paul at the Ice House

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Mark Trushkowsky @marktrushkowsky.bsky.social · 30/09/2025

Next I tried it with Fig. 13. I created a grid in the center of each square unit to see if it would that have the same area as the figure we can build with the corners from Figure 11, removing the center, and pushing the corners together.

A grid drawn over figure 13 resulting in an area of 60 sq units, which is the same area as the rearranged figure created with the corners of Figure 11.

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Mark Trushkowsky @marktrushkowsky.bsky.social · 30/09/2025

Another pattern emerged when I started playing around with creating a grid in the center of each sq unit The area of the blue figure is 61 sq units. I noticed the grid by itself had an area of 40 sq units. It also looked a lot like the figure we got we we added corners to our original figure

Figure 11 (area of 60 squares units). A grid made from connecting the center points of Figure 11.

The grid by itself, and area of 40 square units

The grid and the figure created from the corners of Figure 9, both with an area of 40 square units

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