The Square-Sum Problem

Pick some integer N. Given all of the integers from 1 to N, can you arrange all elements such that each adjacent pair sums to a square number? This is a fun problem to think about. Let’s begin with an easier subset than \(\{1, ..., N \}\). Say we want...

Pick some integer N. Given all of the integers from 1 to N, can you arrange all elements such that each adjacent pair sums to a square number? This is a fun problem to think about. Let’s begin with an easier subset than \(\{1, ..., N \}\). Say we want...

The Paradox of Set Notation

(written at some point in 2015) When I took my first upper level math class, I learned about Sets. In principle, sets are simple. Sets are collections of things. Sets can be big or sets can be small. Sets can contain people. Sets can contain musicians, molecules, and animals. However,...

(written at some point in 2015) When I took my first upper level math class, I learned about Sets. In principle, sets are simple. Sets are collections of things. Sets can be big or sets can be small. Sets can contain people. Sets can contain musicians, molecules, and animals. However,...

Sorting with Color

Different Color Spaces There is no correct way to sort a list of colors. Every color can be mapped to a vector in a three-dimensional space. In other words, each color is defined by three unique numbers. There are competing models for representing this space in Computer Science. Probably the...

Different Color Spaces There is no correct way to sort a list of colors. Every color can be mapped to a vector in a three-dimensional space. In other words, each color is defined by three unique numbers. There are competing models for representing this space in Computer Science. Probably the...

Mapping the D.C. Metro

Labels Pause How I Made This Map I was inspired by this map online to create a similar map of the Washington, D.C. metro system. The map of the subway system plots stations with uniform spacing, often placing them in a straight line, improving map readability but distorting the size...

Labels Pause How I Made This Map I was inspired by this map online to create a similar map of the Washington, D.C. metro system. The map of the subway system plots stations with uniform spacing, often placing them in a straight line, improving map readability but distorting the size...

The Best Time to Post on Instagram

I recently argued with a friend about the best time of day to post on Instagram to maximize the number of likes on a given picture. We agreed that people view Instagram most frequently in nighttime hours, from around 8 to 11 PM. I posited that the best strategy was...

I recently argued with a friend about the best time of day to post on Instagram to maximize the number of likes on a given picture. We agreed that people view Instagram most frequently in nighttime hours, from around 8 to 11 PM. I posited that the best strategy was...

Recreating the Star Wars Opening Crawl

With all the recent news about Rogue One, I wanted to pay a tribute to the Star Wars franchise. One interesting change I noticed in the new movie was a lack of scrolling introductory text before the beginning of the film. This sparked me to do research on the signature...

With all the recent news about Rogue One, I wanted to pay a tribute to the Star Wars franchise. One interesting change I noticed in the new movie was a lack of scrolling introductory text before the beginning of the film. This sparked me to do research on the signature...

Traveling Salesman Art

Imagine you’re planning a road trip across the United States. You pick thirty different cities to visit during the trip and have no preference on order. A question arises: what is the shortest possible trip that visits each city once and finishes home? And the problem is more complicated than...

Imagine you’re planning a road trip across the United States. You pick thirty different cities to visit during the trip and have no preference on order. A question arises: what is the shortest possible trip that visits each city once and finishes home? And the problem is more complicated than...

Largest World Cities Over Time

I recently created this interactive map of the largest city at any point in time in world history. I used DataMaps to make the plotting easy and obtained the data from Professor Ian Morris via this Wikipedia article. Some cities' historic names were changed to current ones so as to...

I recently created this interactive map of the largest city at any point in time in world history. I used DataMaps to make the plotting easy and obtained the data from Professor Ian Morris via this Wikipedia article. Some cities' historic names were changed to current ones so as to...

Animation with K-D Trees

Many animations appear simple but actually require complex calculation on each frame. This week, I worked to simplify an animation algorithm using a data structure called the k-dimensional tree. To demonstrate k-d trees, I created an HTML canvas visualization of a nearest-neighbor search. The animation involves a group of nodes...

Many animations appear simple but actually require complex calculation on each frame. This week, I worked to simplify an animation algorithm using a data structure called the k-dimensional tree. To demonstrate k-d trees, I created an HTML canvas visualization of a nearest-neighbor search. The animation involves a group of nodes...

Expected Salaries of NBA Players

I’ve always wondered what it would look like if one were to calculate the money a professional athlete deserves based on their production. The other day, Reddit user /u/aeisenst posted a rant that mentioned how a player’s productivity can be viewed as the number of wins they generate for their...

I’ve always wondered what it would look like if one were to calculate the money a professional athlete deserves based on their production. The other day, Reddit user /u/aeisenst posted a rant that mentioned how a player’s productivity can be viewed as the number of wins they generate for their...