Quaternions in Everyday Life

Topograph

Joe Rabino↵

Duke University

4 February 2021

I’ll introduce Hamilton’s quaternions, a kind of 4-dimensional non-commutative relative of the complex numbers. We’ll talk about severalareas where they appear: number theory (the four square theorem),physics (if you turn around 360 degrees, you don’t actually get backto where you started), and computer graphics (representing orthogonaltransformations).

Abstract for 08 March 2018

Phil Tosteson

Normally, we think of [0, 1) and [0, 1] as having the same size, eventhough [0, 1] has one more point. If we keep track of this extra pointwhen we measure shapes, it leads to surprising math involving geome-try, topology, and their interaction.

Let RS (resp., RA) denote the average number of runs scored (resp.,allowed) in a baseball game by a team. It was numerically observedyears ago that a good predictor of a team’s win-loss percentage isRS2/(RS2 +RA2), though no one knew WHY the formula worked. Wereview elementary concepts of probability and statistics and discusshow one can build and solve a model for this problem. In the course ofinvestigating this problem we discuss how one attacks problems like thisin general (what are the features of a good model, how to solve it, andso on). The only prerequisite is simple calculus (no baseball knowledgeis required, though Red Sox knowledge is always a plus).

Steven Miller earned his BS in mathematics and physics from Yale andhis PhD in mathematics from Princeton. He has taught at numerouscolleges and universities, including Brown, Mount Holyoke, NYU, TheOhio State University, Princeton, Smith and Williams. He is the authorof over 100 papers in accounting, computer science, economics, geology,marketing, mathematics, physics, sabermetrics, and statistics, as wellas five books. He has taught continuing education classes at the Teach-ers As Scholars program for years, and been supported by multiple NSFgrants for both research and expository writing. He has also workedwith numerous Michigan students (undergraduate and graduate) overthe years, and hopes to work with more this summer at the WilliamsCollege SMALL REU.

Cookie Monster meets1

Quaternions in Everyday Life

Topograph

Joe Rabino↵

Duke University

4 February 2021

I’ll introduce Hamilton’s quaternions, a kind of 4-dimensional non-commutative relative of the complex numbers. We’ll talk about severalareas where they appear: number theory (the four square theorem),physics (if you turn around 360 degrees, you don’t actually get backto where you started), and computer graphics (representing orthogonaltransformations).

Abstract for 08 March 2018

Phil Tosteson

Normally, we think of [0, 1) and [0, 1] as having the same size, eventhough [0, 1] has one more point. If we keep track of this extra pointwhen we measure shapes, it leads to surprising math involving geome-try, topology, and their interaction.

Let RS (resp., RA) denote the average number of runs scored (resp.,allowed) in a baseball game by a team. It was numerically observedyears ago that a good predictor of a team’s win-loss percentage isRS2/(RS2 +RA2), though no one knew WHY the formula worked. Wereview elementary concepts of probability and statistics and discusshow one can build and solve a model for this problem. In the course ofinvestigating this problem we discuss how one attacks problems like thisin general (what are the features of a good model, how to solve it, andso on). The only prerequisite is simple calculus (no baseball knowledgeis required, though Red Sox knowledge is always a plus).

Steven Miller earned his BS in mathematics and physics from Yale andhis PhD in mathematics from Princeton. He has taught at numerouscolleges and universities, including Brown, Mount Holyoke, NYU, TheOhio State University, Princeton, Smith and Williams. He is the authorof over 100 papers in accounting, computer science, economics, geology,marketing, mathematics, physics, sabermetrics, and statistics, as wellas five books. He has taught continuing education classes at the Teach-ers As Scholars program for years, and been supported by multiple NSFgrants for both research and expository writing. He has also workedwith numerous Michigan students (undergraduate and graduate) overthe years, and hopes to work with more this summer at the WilliamsCollege SMALL REU.

Cookie Monster meets1

Quaternions in Everyday Life

Topograph

Joe Rabino↵

Duke University

4 February 2021

I’ll introduce Hamilton’s quaternions, a kind of 4-dimensional non-commutative relative of the complex numbers. We’ll talk about severalareas where they appear: number theory (the four square theorem),physics (if you turn around 360 degrees, you don’t actually get backto where you started), and computer graphics (representing orthogonaltransformations).

Abstract for 08 March 2018

Phil Tosteson

Normally, we think of [0, 1) and [0, 1] as having the same size, eventhough [0, 1] has one more point. If we keep track of this extra pointwhen we measure shapes, it leads to surprising math involving geome-try, topology, and their interaction.

Let RS (resp., RA) denote the average number of runs scored (resp.,allowed) in a baseball game by a team. It was numerically observedyears ago that a good predictor of a team’s win-loss percentage isRS2/(RS2 +RA2), though no one knew WHY the formula worked. Wereview elementary concepts of probability and statistics and discusshow one can build and solve a model for this problem. In the course ofinvestigating this problem we discuss how one attacks problems like thisin general (what are the features of a good model, how to solve it, andso on). The only prerequisite is simple calculus (no baseball knowledgeis required, though Red Sox knowledge is always a plus).

Steven Miller earned his BS in mathematics and physics from Yale andhis PhD in mathematics from Princeton. He has taught at numerouscolleges and universities, including Brown, Mount Holyoke, NYU, TheOhio State University, Princeton, Smith and Williams. He is the authorof over 100 papers in accounting, computer science, economics, geology,marketing, mathematics, physics, sabermetrics, and statistics, as wellas five books. He has taught continuing education classes at the Teach-ers As Scholars program for years, and been supported by multiple NSFgrants for both research and expository writing. He has also workedwith numerous Michigan students (undergraduate and graduate) overthe years, and hopes to work with more this summer at the WilliamsCollege SMALL REU.

Cookie Monster meets1

Meeting virtually for Winter 2021 Thursdays at 4pm EST

Quaternions ineveryday life

Joe Rabino↵

Duke University

4 February 2021

I’ll introduce Hamilton’s quaternions, a kind of 4-dimensional non-commutative relative of the complex numbers. We’ll talk about severalareas where they appear: number theory (the four square theorem),physics (if you turn around 360 degrees, you don’t actually get backto where you started), and computer graphics (representing orthogonaltransformations).

Abstract for 08 March 2018

Phil Tosteson

Normally, we think of [0, 1) and [0, 1] as having the same size, eventhough [0, 1] has one more point. If we keep track of this extra pointwhen we measure shapes, it leads to surprising math involving geome-try, topology, and their interaction.

Let RS (resp., RA) denote the average number of runs scored (resp.,allowed) in a baseball game by a team. It was numerically observedyears ago that a good predictor of a team’s win-loss percentage isRS2/(RS2 +RA2), though no one knew WHY the formula worked. Wereview elementary concepts of probability and statistics and discusshow one can build and solve a model for this problem. In the course ofinvestigating this problem we discuss how one attacks problems like thisin general (what are the features of a good model, how to solve it, andso on). The only prerequisite is simple calculus (no baseball knowledgeis required, though Red Sox knowledge is always a plus).

Steven Miller earned his BS in mathematics and physics from Yale andhis PhD in mathematics from Princeton. He has taught at numerouscolleges and universities, including Brown, Mount Holyoke, NYU, TheOhio State University, Princeton, Smith and Williams. He is the authorof over 100 papers in accounting, computer science, economics, geology,marketing, mathematics, physics, sabermetrics, and statistics, as wellas five books. He has taught continuing education classes at the Teach-ers As Scholars program for years, and been supported by multiple NSFgrants for both research and expository writing. He has also workedwith numerous Michigan students (undergraduate and graduate) overthe years, and hopes to work with more this summer at the WilliamsCollege SMALL REU.

Cookie Monster meets1

Quaternions in Everyday Life

Topograph

Joe Rabino↵

Duke University

4 February 2021

I’ll introduce Hamilton’s quaternions, a kind of 4-dimensional non-commutative relative of the complex numbers. We’ll talk about severalareas where they appear: number theory (the four square theorem),physics (if you turn around 360 degrees, you don’t actually get backto where you started), and computer graphics (representing orthogonaltransformations).

Abstract for 08 March 2018

Phil Tosteson

Normally, we think of [0, 1) and [0, 1] as having the same size, eventhough [0, 1] has one more point. If we keep track of this extra pointwhen we measure shapes, it leads to surprising math involving geome-try, topology, and their interaction.

Let RS (resp., RA) denote the average number of runs scored (resp.,allowed) in a baseball game by a team. It was numerically observedyears ago that a good predictor of a team’s win-loss percentage isRS2/(RS2 +RA2), though no one knew WHY the formula worked. Wereview elementary concepts of probability and statistics and discusshow one can build and solve a model for this problem. In the course ofinvestigating this problem we discuss how one attacks problems like thisin general (what are the features of a good model, how to solve it, andso on). The only prerequisite is simple calculus (no baseball knowledgeis required, though Red Sox knowledge is always a plus).

Steven Miller earned his BS in mathematics and physics from Yale andhis PhD in mathematics from Princeton. He has taught at numerouscolleges and universities, including Brown, Mount Holyoke, NYU, TheOhio State University, Princeton, Smith and Williams. He is the authorof over 100 papers in accounting, computer science, economics, geology,marketing, mathematics, physics, sabermetrics, and statistics, as wellas five books. He has taught continuing education classes at the Teach-ers As Scholars program for years, and been supported by multiple NSFgrants for both research and expository writing. He has also workedwith numerous Michigan students (undergraduate and graduate) overthe years, and hopes to work with more this summer at the WilliamsCollege SMALL REU.

Cookie Monster meets1