Abstract GAMES and PUZZLES ORIGAMI In Science ...
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Abstract GAMES and PUZZLES ORIGAMI In Science & Engineering Fractal Analysis of Gerrymandering Acknowledgements 1. Strips/Friezes: Rotations, Glides; Reflections 2. Weaves: Cellular Automata 3. Tiles: Tessellations 4. Quilts:17 Wallpaper Patterns 5. Tangrams: Combinatorics 6. Games: Game Theory 7. Puzzles: Graph Theory 1: Paths, Cycles 8. Origami: Graph Theory 2: Trees 9. Maps 1: Voronoi tessellations & Segregation 10. Maps 2: Perspective & Projections 11. Maps 3: Fractals Geometry: Gerrymandering 12. Matching: Graph Theory 3: Bipartite Graphs 13. Fair Voting Methods 14. Time: Clocks &Calendars 15. Fair Counting => Census 16. Equity vs Equality: Admissions Jungck, John R. (2012). "Incorporating Quantitative Reasoning in Common Core Courses: Mathematics for The Ghost Map.” Numeracy: Advancing Education in Quantitative Literacy 5 (1): Article 7. REFERENCES Jungck, John R. and Jon Manon. (2019). Brave Spaces: Augmenting Interdisciplinary STEM Education by Using Quantitative Data Explorations to Engage Conversations on Equity." Numeracy 12 (1): Article 4. (36 pages) To address the continuing need to engage students with how mathematics can contribute to issues of equity versus equality, civil rights, social justice, and the historical contributions to mathematics from cultures around the world, ethnomathematics educators have developed numerous educational materials. Activities from a recent first year, general education course which applied mathematics such as fractals, tessellations, cellular automata, groups, symmetries, graph theory, and game theory are illustrated with various student projects. I argue that by engaging students in “Brave Spaces” (Jungck & Manon, 2019) with mathematical tools and data, students will tackle difficult complex issues with minimal professorial facilitation. SYLLABUS Weekly Topics & Mathematics Mastermind and Protein Sequencing Build an origami model of a scientific or engineering application, demonstrate your folding approach, and present a pdf poster on your work. SOCIAL JUSTICE Voronoi Tessellations & Segregation Prepare a poster where you apply Voronoi tessellations to analyze the lasting impact of segregation My sincere thanks to the 22 students in Ethnomathematics who continued to produce wonderful work even after we moved to synchronous online classes. Box Optimization Origami History and Culture ● Erdo Period ○ 1603-1868 ○ Paper became affordable ● New art form of folding paper ○ Orikata -> Origami ● Pioneers in Origami ○ Akisato Rito’s ○ Adachi Kazuyuki ● By the 20th century Origami was widespread especially among children and older people ● Moors also developed paper folding ● Modern Origami ○ Akira Yoshizawa ■ Pioneer ■ Manuels ○ Mathematical Interest ■ Euclidean ideas Mathematics ● Euclidean Geometry ● Function Optimization ○ Sol 1. ■ Similar triangles ○ Sol 2. ■ Dimension Scaling ○ Sol 3. ■ Geometric Scaling ● Values have high rate of error ● Folding Methods: ○ Sol 1. ■ Square ○ Sol 2 & 3 ■ Rectangular ● 8.5cm by 11cm paper for all Sol. Figures Solution # V e (cm) V (cm) 1 5.6 9.5 2 49 39.3 3 45.7 78.9 David Bichara Bio-Inspired Spring Origami Katya Raskin The bio inspiration I looked into were earwig wings. Earwig wings are a special case because they unfold on their own to be 10x larger than the closed position, and no muscle power is needed to keep them open. The self-folding and locking capabilities of the wings is dependent on resilin-based joints. Resilin is an elastic biopolymer that is associated with symmetrical arrangements in wings, and symmetrical arrangements cause extensional springs. The wings have been studied and a program has been created that can 3D print a self-folding structure that mimics the mechanisms of the earwig wings. During folding, it is a classic Miura-Ori pattern with three convex and one concave fold. After fully opening and passing through an unstable flat state, it becomes a concave pyramid. In different positions, there is an energy barrier that must be overcome in order to switch to a different position, and since no muscle movement is used, those barriers are overcome by the angles in which the joint is in. 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Harris: Supreme court trial in which Cooper argued that the redistricting in North Carolina was biased against African Americans. ◂ Argued that more black voters were placed in districts 1 in order to lower the black voting influence in other districts in North Carolina. Discussion As shown by the fractal dimension of the border of North Carolina District 1, much planning went into the shape of the district. This may influence legal decisions, such as the outcome of Cooper v. Harris, as it shows that the higher number of black voters placed in District 1 was not a coincidence, rather it was strategically planned by those who determined this intricately shaped border. By Alison Cunney and Hannah Schell References “Cooper v. Harris.” Oyez. Accessed April 3, 2020. https://www.oyez.org/cases/2016/15-1262 “Minkowski–Bouligand Dimension.” Wikipedia. Wikimedia Foundation, November 20, 2019. https://en.wikipedia.org/wiki/Minkowski–B ouligand_dimension. The Fractal Dimension value of North Carolina District 1 is 1.4219. Having a high fractal dimension indicates that the border of District 1 is highly irregular. In turn, one can infer that those who determined the border did in a specific way to include and exclude certain populations. By: Adam Dickert, Sylvie Hautbois Fractal Analysis of the Former Florida 14th Congressional District Controversy The Florida 14 District was heavily gerrymandered by the republican Florida congress. It added a portion of land across Tampa Bay from Tampa, FL in St. Petersburg, FL. This areas was more heavily populated, and had a higher black population than the surrounding areas. The district was redistricted in 2017. References Bump, Philip. “How the Florida GOP's Gerrymander Went Too Far, in 4 Cool Visuals.” The Washington Post. WP Company, July 10, 2015. https://www.washingtonpost.com/news/the-fix/ wp/2015/07/10/how-the-florida-gops-gerryma nder-went-too-far-in-4-cool-visuals/. “Redistricting in Florida.” Ballotpedia. https://ballotpedia.org/Redistricting_in_Florida #State_legislation_and_ballot_measures. Fractal Images Data Table Richardson Plot Statistical Analysis: r^2: 0.994 Equation: -1.31x+3.26 # Points: 6 Our Fractal Dimension: 1.41863 What does it mean? The more bends in the boundary of the district, the higher the fractal dimension. Since our fractal dimension is around 1.42, this shows that our district was not as irregular as others and the fractal number is comparatively lower. Discussion There is a lot of talk about how the loop for the 14th District was created to contain those who would vote democratic, allowing other districts to remain Republican. Some of Florida’s other districts were obviously gerrymandered around cities and other locations that vote blue to keep the majority of Florida red. District 5 on this map would have a higher fractal dimension and be more problematic than some other districts like District 14. Discussion cont. A lot of these issues have already been presented to the Florida Supreme Court due to unconstitutional intent in gerrymandering, which forced the 14th District to be redistricted. I think that because so many heads were already turned, they will have to be cautious during future redistricting to avoid more backlash. Redrawn 14th district, as of 2017 Desegregation in Virginia - Ishika and Sylvie Public: Analysis: Most of the schools in this region have similar demographics. The only exceptions are Annandale and Falls Church High Schools, who have a majority Hispanic makeup. These are also the two schools that have over 50% of their students getting free or reduced fee lunches. In Fairfax County Public Schools, if you have a household of four people, the maximum household income to receive free meals is $33,475. The household income to receive reduced price meals is $33,475.01-47,638. This means that the majority of households with students at those two schools are earning less than $47,638. The Voronoi cell for Annandale is located at the bottom right, and the Voronoi cell for Falls Church is located right above it. It appears that this area on the map has a higher percentage of minorities living there and also a lower income. Oakton 47.07% White, 31.41% Asian, 10.98% Hispanic or Latino, 4.65% Black, and 5.89% other. 13.40% free/reduced fees lunches. Madison 64.55% White, 14.30% Asian, 11.83% Hispanic or Latino, 1.87% Black, 7.45% Other. 10.32% free/reduced fee lunches. Marshall 48.36% White, 20.35% Asian, 18.73% Hispanic or Latino, 5.45& Black, 7.11% Other. 17.60% free/reduced fee lunches. Fairfax 38.53% White, 23.73% Hispanic or Latino, 23.33% Asian, 8.93% Black, 5.48% Other. 23.46% free/reduces fee lunches. Woodson 51.84% White, 25.03% Asian, 12.62% Hispanic, 4.60% Black, 5.91% Other. 12.83% free/reduced fee lunches Lake Braddock 46.79% White, 21.36% Asian, 18.08% Hispanic, 7.67% Black, 6.09% Other. 16.17% free/reduced fee lunches. Robinson 59.05% White, 14.66% Hispanic or Latino, 13.69% Asian, 5.89% Black, 6.71% Other. 11.52% free/reduced fees lunches Annandale 45.48% Hispanic or Latino, 21.24% Asian, 16.27% Black, 15.21% White, 1.80% other. 63.09% free/reduced fees lunches. Falls Church 51.16% Hispanic or Latino, 20.21% Asian, 18.19% White, 6.31% black, 4.14% other. 54.21% free/reduced fee lunches Desegregation in Virginia - Ishika and Sylvie Charter: Idea PCS 96.6% Black, 2.8% Hispanic, 0.3% Native $20,249/pupil (second in DC) Haynes 46.2% Black, 48.7% Hispanic, 1.6% Asian $16,651/pupil spending (in top 10 DC) Thurgood Marshall PCS 98% African American, 1.8% Hispanic, 0.2% other. 5,840/pupil spending. 71.8% require discounted lunches Kingsman 98.2% Black, 1.4% Hispanic, 0.4 Asian $6692/pupil Friendship 94.5% Black, 3.2% Hispanic, 0.7% Native. $13,691/pupil spent Two Rivers 92.6% White, 3.18% Hispanic. $14,537/pupil spent Basis 9% Asian, 8% Hispanic, 37% Black, 39% White. (top 5 in diversity in DC) $7771/pupil spending VA Virtual 66% White, 17% Black, 10% Hispanic $3700/pupil spending Circles: public schools, Stars: charter schools Analysis: The schools circled in red are Haynes and Idea charter school. Their Voronoi cells are the largest compared to the other charter schools, and both these schools also spend the most per pupil that the other charter schools. Idea has a majority black population, while Haynes as a majority Hispanic. However, most of these charter schools have similar race distributions, meaning that race likely isn’t a factor in the high spending per pupil. Note: Virginia did not have Charter schools until 1998, and to date there are only 9 charter schools in VA, only one near Oakton HS. Therefore, we chose to work with schools from DC. Desegregation in Virginia - Ishika and Sylvie Private: Circles: Public Squares: Private Stars: Charter Flint Hill 62.4% White, 8.7% Asian, 5.7% Black, 3.6% Hispanic, 19.1% Other. Tuition: $44,475 per year, including MacBook Air and lunch. Oak Hill Christian 48% White, 62% Otther. Tuition available upon request - need based grants given Trinity Christian 76% White, 11% Asian, 5% Hispanic, 3% Black, 6% Other. Tuition: $18,450 per year. Pinnacle Academy 90% White, 3% Asian, 2% Black, 4% Other. Tuition: $14,500. Basis Independent McLean Ethnicity of students is unknown. Tuition: $30,000 and $50 application fee. Oakcrest School 66.9% White, 5.4% Hispanic, 4.2% Asian, 1.2% African American, 22.3% Other. All Girls School. Tuition: $29,125. Paul VI 78.9% White, 8.9% Asian, 4.6% African American, 7.6% Other. Tuition: $18,615 Madeira 52.8% White, 12% African American, 8% Asian, 3.4% Hispanic, 23.7% Other. All girls private school with boarding: $62,000. Analysis: The Voronoi cell for Madeira is the middle cell at the very top of the graph, and the Voronoi cell for Flint Hill is the highlighted yellow cell to the very left. The cell for Madeira is a lot larger than the cell for Flint Hill; however, their tuition and demographics are similar. Madeira and Flint Hill have the most expensive tuition, and they are also two of the most diverse private schools listed. Pinnacle Academy has the lowest tuition and has the highest percentage of white students. Among private schools, I do not think race specifically plays a role in the cost of tuition. Most of these schools have a set tuition but also offer need-based grants and scholarships to help students of any ethnicity who need financial help. Works cited: https://www.dcfpi.org/wp-content/uploads/2015/08/8.5.15-Revenue-and-Spending-Per-Student-TP-Final.pdf http://schoolprofiles.fcps.edu/schlprfl/f?p=108:13:3504987145922807::::P0_CURRENT_SCHOOL_ID:050 https://www.fcps.edu/sites/default/files/media/pdf/4%20HSBoundariesSY2019-20%20County%20Outline.pdf https://www.niche.com/ MASTERMIND Emma Cohen Chinese Rings and Genetic Codes Rubrik’s Snake and Protein Folding Rubik’s Snake (Rubik’s Twist) Also called Smiggle Snake, Serpent Snake, and Fidget Snake, among other things on the toy market Images: https://www.wondergears.com/products/snake-puzzle?varia nt=15818798137418 (not this, this is the Snake Cube, which is something totally different) Hajae Ko Gray Code ● ● ○ ● ● ● Chinese Rings
Transcript of Abstract GAMES and PUZZLES ORIGAMI In Science ...
Abstract GAMES and PUZZLES ORIGAMI In Science & Engineering
Fractal Analysis of Gerrymandering
Acknowledgements
1. Strips/Friezes: Rotations, Glides; Reflections2. Weaves: Cellular Automata3. Tiles: Tessellations4. Quilts:17 Wallpaper Patterns5. Tangrams: Combinatorics6. Games: Game Theory7. Puzzles: Graph Theory 1: Paths, Cycles8. Origami: Graph Theory 2: Trees9. Maps 1: Voronoi tessellations & Segregation10. Maps 2: Perspective & Projections11. Maps 3: Fractals Geometry: Gerrymandering12. Matching: Graph Theory 3: Bipartite Graphs13. Fair Voting Methods14. Time: Clocks &Calendars15. Fair Counting => Census16. Equity vs Equality: Admissions
Jungck, John R. (2012). "Incorporating Quantitative Reasoning in Common Core Courses: Mathematics for The Ghost Map.” Numeracy: Advancing Education in Quantitative Literacy 5 (1): Article 7.
REFERENCES
Jungck, John R. and Jon Manon. (2019). Brave Spaces: Augmenting Interdisciplinary STEM Education by Using Quantitative Data Explorations to Engage Conversations on Equity." Numeracy 12 (1): Article 4. (36 pages)
To address the continuing need to engage students with how mathematics can contribute to issues of equity versus equality, civil rights, social justice, and the historical contributions to mathematics from cultures around the world, ethnomathematics educators have developed numerous educational materials.
Activities from a recent first year, general education course which applied mathematics such as fractals, tessellations, cellular automata, groups, symmetries, graph theory, and game theory are illustrated with various student projects.
I argue that by engaging students in “Brave Spaces” (Jungck & Manon, 2019) with mathematical tools and data, students will tackle difficult complex issues with minimal professorial facilitation.
SYLLABUSWeekly Topics & Mathematics
Mastermind and Protein Sequencing
Build an origami model of a scientific or engineering application, demonstrate your folding approach, and present a pdf poster on your work.
SOCIAL JUSTICE
Voronoi Tessellations & SegregationPrepare a poster where you apply Voronoi tessellations to analyze the lasting impact of segregation
My sincere thanks to the 22 students in Ethnomathematics who continued to produce wonderful work even after we moved to synchronous online classes.
Box Optimization Origami
History and Culture
● Erdo Period○ 1603-1868○ Paper became affordable
● New art form of folding paper○ Orikata -> Origami
● Pioneers in Origami○ Akisato Rito’s○ Adachi Kazuyuki
● By the 20th century Origami was widespread especially among children and older people
● Moors also developed paper folding● Modern Origami
○ Akira Yoshizawa■ Pioneer■ Manuels
○ Mathematical Interest■ Euclidean ideas
Mathematics
● Euclidean Geometry● Function Optimization
○ Sol 1. ■ Similar triangles
○ Sol 2.■ Dimension Scaling
○ Sol 3. ■ Geometric Scaling
● Values have high rate of error● Folding Methods:
○ Sol 1.■ Square
○ Sol 2 & 3■ Rectangular
● 8.5cm by 11cm paper for all Sol.
Figures
Solution # Ve (cm) V (cm)
1 5.6 9.5
2 49 39.3
3 45.7 78.9
David Bichara
Bio-Inspired Spring OrigamiKatya Raskin
The bio inspiration I looked into were earwig wings. Earwig wings are a special case because they unfold on their own to be 10x larger than the closed position, and no muscle power is needed to keep them open. The self-folding and locking capabilities of the wings is dependent on resilin-based joints. Resilin is an elastic biopolymer that is associated with symmetrical arrangements in wings, and symmetrical arrangements cause extensional springs. The wings have been studied and a program has been created that can 3D print a self-folding structure that mimics the mechanisms of the earwig wings. During folding, it is a classic Miura-Ori pattern with three convex and one concave fold. After fully opening and passing through an unstable flat state, it becomes a concave pyramid. In different positions, there is an energy barrier that must be overcome in order to switch to a different position, and since no muscle movement is used, those barriers are overcome by the angles in which the joint is in.
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North Carolina District #1Background
◂ Gerrymandering is when a political map is manipulated in order to favor a certain political party.
◂ One example of gerrymandering is the redistricting of North Carolina which took place after the 2010 census
◂ Cooper v. Harris: Supreme court trial in which Cooper argued that the redistricting in North Carolina was biased against African Americans.
◂ Argued that more black voters were placed in districts 1 in order to lower the black voting influence in other districts in North Carolina. Discussion
As shown by the fractal dimension of the border of North Carolina District 1, much planning went into the shape of the district. This may influence legal decisions, such as the outcome of Cooper v. Harris, as it shows that the higher number of black voters placed in District 1 was not a coincidence, rather it was strategically planned by those who determined this intricately shaped border.
By Alison Cunney and Hannah Schell
References“Cooper v. Harris.” Oyez. Accessed April 3, 2020.
https://www.oyez.org/cases/2016/15-1262.“Minkowski–Bouligand Dimension.” Wikipedia.
Wikimedia Foundation, November 20, 2019. https://en.wikipedia.org/wiki/Minkowski–Bouligand_dimension.
The Fractal Dimension value of North Carolina District 1 is 1.4219. Having a high fractal dimension indicates that the border of District 1 is highly irregular. In turn, one can infer that those who determined the border did in a specific way to include and exclude certain populations.
By: Adam Dickert, Sylvie HautboisFractal Analysis of the Former Florida 14th Congressional District
Controversy
The Florida 14 District was heavily gerrymandered by the republican Florida congress. It added a portion of land across Tampa Bay from Tampa, FL in St. Petersburg, FL. This areas was more heavily populated, and had a higher black population than the surrounding areas. The district was redistricted in 2017.
ReferencesBump, Philip. “How the Florida GOP's
Gerrymander Went Too Far, in 4 Cool Visuals.” The Washington Post. WP Company, July 10, 2015. https://www.washingtonpost.com/news/the-fix/wp/2015/07/10/how-the-florida-gops-gerrymander-went-too-far-in-4-cool-visuals/.
“Redistricting in Florida.” Ballotpedia. https://ballotpedia.org/Redistricting_in_Florida#State_legislation_and_ballot_measures.
Fractal Images
Data Table
Richardson Plot
Statistical Analysis:r^2: 0.994Equation: -1.31x+3.26# Points: 6
Our Fractal Dimension: 1.41863
What does it mean?The more bends in the boundary of the district, the higher the fractal dimension. Since our fractal dimension is around 1.42, this shows that our district was not as irregular as others and the fractal number is comparatively lower.
DiscussionThere is a lot of talk about how the loop for the 14th District was created to contain those who would vote democratic, allowing other districts to remain Republican. Some of Florida’s other districts were obviously gerrymandered around cities and other locations that vote blue to keep the majority of Florida red. District 5 on this map wouldhave a higher fractaldimension and be more problematic than some other districts like District 14.
Discussion cont.A lot of these issues have already been presented to the Florida Supreme Court due to unconstitutional intent in gerrymandering, which forced the 14th District to be redistricted. I think that because so many heads were already turned, they will have to be cautious during future redistricting to avoid more backlash.
Redrawn 14th district, as of 2017
Desegregation in Virginia - Ishika and SylviePublic:
Analysis: Most of the schools in this region have similar demographics. The only exceptions are Annandale and Falls Church High Schools, who have a majority Hispanic makeup. These are also the two schools that have over 50% of their students getting free or reduced fee lunches. In Fairfax County Public Schools, if you have a household of four people, the maximum household income to receive free meals is $33,475. The household income to receive reduced price meals is $33,475.01-47,638. This means that the majority of households with students at those two schools are earning less than $47,638. The Voronoi cell for Annandale is located at the bottom right, and the Voronoi cell for Falls Church is located right above it. It appears that this area on the map has a higher percentage of minorities living there and also a lower income.
Oakton 47.07% White, 31.41% Asian, 10.98% Hispanic or Latino, 4.65% Black, and 5.89% other.
13.40% free/reduced fees lunches.
Madison 64.55% White, 14.30% Asian, 11.83% Hispanic or Latino, 1.87% Black, 7.45% Other.
10.32% free/reduced fee lunches.
Marshall 48.36% White, 20.35% Asian, 18.73% Hispanic or Latino, 5.45& Black, 7.11% Other.
17.60% free/reduced fee lunches.
Fairfax 38.53% White, 23.73% Hispanic or Latino, 23.33% Asian, 8.93% Black, 5.48% Other.
23.46% free/reduces fee lunches.
Woodson 51.84% White, 25.03% Asian, 12.62% Hispanic, 4.60% Black, 5.91% Other.
12.83% free/reduced fee lunches
Lake Braddock
46.79% White, 21.36% Asian, 18.08% Hispanic, 7.67% Black, 6.09% Other.
16.17% free/reduced fee lunches.
Robinson 59.05% White, 14.66% Hispanic or Latino, 13.69% Asian, 5.89% Black, 6.71% Other.
11.52% free/reduced fees lunches
Annandale 45.48% Hispanic or Latino, 21.24% Asian, 16.27% Black, 15.21% White, 1.80% other.
63.09% free/reduced fees lunches.
Falls Church
51.16% Hispanic or Latino, 20.21% Asian, 18.19% White, 6.31% black, 4.14% other.
54.21% free/reduced fee lunches
Desegregation in Virginia - Ishika and SylvieCharter: Idea PCS 96.6% Black, 2.8% Hispanic, 0.3%
Native$20,249/pupil (second in DC)
Haynes 46.2% Black, 48.7% Hispanic, 1.6% Asian
$16,651/pupil spending (in top 10 DC)
Thurgood Marshall PCS
98% African American, 1.8% Hispanic, 0.2% other.
5,840/pupil spending. 71.8% require discounted lunches
Kingsman 98.2% Black, 1.4% Hispanic, 0.4 Asian
$6692/pupil
Friendship 94.5% Black, 3.2% Hispanic, 0.7% Native.
$13,691/pupil spent
Two Rivers 92.6% White, 3.18% Hispanic. $14,537/pupil spent
Basis 9% Asian, 8% Hispanic, 37% Black, 39% White. (top 5 in diversity in DC)
$7771/pupil spending
VA Virtual 66% White, 17% Black, 10% Hispanic
$3700/pupil spending
Circles: public schools, Stars: charter schoolsAnalysis: The schools circled in red are Haynes and Idea charter school. Their Voronoi cells are the largest compared to the other charter schools, and both these schools also spend the most per pupil that the other charter schools. Idea has a majority black population, while Haynes as a majority Hispanic. However, most of these charter schools have similar race distributions, meaning that race likely isn’t a factor in the high spending per pupil.
Note: Virginia did not have Charter schools until 1998, and to date there are only 9 charter schools in VA, only one near Oakton HS. Therefore, we chose to work with schools from DC.
Desegregation in Virginia - Ishika and SylviePrivate:
Circles: PublicSquares: Private
Stars: Charter
Flint Hill 62.4% White, 8.7% Asian, 5.7% Black, 3.6% Hispanic, 19.1% Other.
Tuition: $44,475 per year, including MacBook Air and lunch.
Oak Hill Christian 48% White, 62% Otther. Tuition available upon request - need based grants given
Trinity Christian 76% White, 11% Asian, 5% Hispanic, 3% Black, 6% Other.
Tuition: $18,450 per year.
Pinnacle Academy 90% White, 3% Asian, 2% Black, 4% Other. Tuition: $14,500.
Basis Independent McLean
Ethnicity of students is unknown. Tuition: $30,000 and $50 application fee.
Oakcrest School 66.9% White, 5.4% Hispanic, 4.2% Asian, 1.2% African American, 22.3% Other. All Girls School.
Tuition: $29,125.
Paul VI 78.9% White, 8.9% Asian, 4.6% African American, 7.6% Other.
Tuition: $18,615
Madeira 52.8% White, 12% African American, 8% Asian, 3.4% Hispanic, 23.7% Other.
All girls private school with boarding: $62,000.
Analysis: The Voronoi cell for Madeira is the middle cell at the very top of the graph, and the Voronoi cell for Flint Hill is the highlighted yellow cell to the very left. The cell for Madeira is a lot larger than the cell for Flint Hill; however, their tuition and demographics are similar. Madeira and Flint Hill have the most expensive tuition, and they are also two of the most diverse private schools listed. Pinnacle Academy has the lowest tuition and has the highest percentage of white students. Among private schools, I do not think race specifically plays a role in the cost of tuition. Most of these schools have a set tuition but also offer need-based grants and scholarships to help students of any ethnicity who need financial help. Works cited: https://www.dcfpi.org/wp-content/uploads/2015/08/8.5.15-Revenue-and-Spending-Per-Student-TP-Final.pdf
http://schoolprofiles.fcps.edu/schlprfl/f?p=108:13:3504987145922807::::P0_CURRENT_SCHOOL_ID:050https://www.fcps.edu/sites/default/files/media/pdf/4%20HSBoundariesSY2019-20%20County%20Outline.pdfhttps://www.niche.com/
MASTERMINDEmma Cohen
Chinese Rings and Genetic Codes
Rubrik’s Snake and Protein FoldingRubik’s Snake (Rubik’s Twist)
Also called Smiggle Snake, Serpent Snake, and Fidget Snake, among other things on the toy market
Images: https://www.wondergears.com/products/snake-puzzle?variant=15818798137418
(not this, this is the Snake Cube, which is something totally different)
Hajae Ko
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Chinese Rings
