Beautiful Mathematics/Beautiful Mathematicians
In this week's topic, the source is you! The answers this week are entirely subjective: but your job is to "justify" your responses.
These may serve as part of the core of your final presentation, our "virtual poster".
I think that it will be interesting to see what you find beautiful, and how personal experiences have led you here (with people living or perhaps even long dead, like my favorite mathematicians!).
- What is the most amazingly beautiful mathematical object you know of? I am going to feature mine, because I'm pretty sure that no one would ever take it. So it's not like I'm stealing. Here it is: It's an icosahedron, with three golden rectangles interlocking into the Borromean rings in its heart. (I could swoon a little more, but I'm going to leave that to you!)
- What is the singularly most beautiful equation/theorem/result/application you've ever encountered? I'm going to steal one obvious candidate, and ask you to find others:
This equation, known as Euler's equation, ties together five of the most important constants in mathematics, into one neat and tidy package. So slim, so elegant! I could go on and on. But I won't!:) (You should go on and on a little more....)
- Describe an encounter with another person that has personally impacted you mathematically in a direct and positive way.
- Who is your favorite mathematician, and why? (Mine is Archimedes -- if you don't have one already, look him up!)
Question 1 Response
What is the most amazingly beautiful mathematical object you know of?
A few students chose architecture, namely bridges, as the most beautiful mathematical objects that they know of. Chelsea Debord featured the Roebling Bridge right down the road in Covington, Ky, and Shawn Huesman featured the Chinese Lucky Knot Bridge.
Madison Goodwin chose the ancient Arabic numerals.
Each number is represented by the equivalent angles for that number. Counting systems in many cultures are base 10 or 20 due to the number of fingers and toes a human has. These numbers take it a step further by representing geometrical equivalences.
Amber Manning chose the Eiffel Tower as the most beautiful mathematical object she could think of. In her response, she mentioned that she found the Eiffel Tower to be exceptionally beautiful and that she hopes to visit it in person one day.
Question 2 Response
What is the singularly most beautiful equation/theorem/result/application you've ever encountered?
There are certainly a lot of equations, theorems, results, and applications of mathematics. John Nuestro pointed out how he enjoyed parametric equations and graphs. He says that they give "a different way of looking at graphs." An underlying part to parametric functions is that both the x-variable and the y-variable are functions of another variable (perhaps t), and are able to create amazing graphics. John's example:
Amber Manning Chose ((x^2+y^2-1)^3)-(x^2)(y^3)=0 because if you graph this equation you will find that it makes a heart shape and that is her favorite shape.
It's fascinating what numbers on a page can turn into when you look at the big picture. That seems to be a theme in this course. Students are being challenged to see the beauty and the big picture of math; not just performing by memorization to get an answer.
Chelsea Debord stated that she has always been fascinated by the Pythagorean theorem, a²+b²=c². She mentioned that she was fascinated by the fact that you could find a, b, or c with all or no variables. The fact that you can use this formula with angles or sides is very interesting. She also stated that she loves this and the fact that math as a whole is pretty interchangeable.
Question 3 Response
Describe an encounter with another person that has personally impacted you mathematically in a direct and positive way.
Since most students in MAT 194 are mathematics majors, it's only fitting that someone such as a teacher or another person have positively impacted their perception of mathematics. Ganga Adhikari says that the reason he came to NKU in the first place was to pursue a degree in Data Science. This wouldn't have been his reason if it weren't for his statistics professor in high school.
Zhen Bao reflected on somewhat "mixed-emotions" with his experience in math. Zhen had a unique upbringing, where he lived in China and it was very insistent on children to achieve mathematically. Zhen remembers hating math and having to work with a private tutor hired by his mother on weekends and holidays. However, somewhere along the lines, Zhen found peace with math. Even though it can be annoying to him, it's famliar and comfortable and he admits he loves it deeply.
Amber Manning stated that she has always been fascinated by math but her best, most influential experience happened to her when she was in sixth-grade. She stated that her sixth-grade math teacher was likely one of the best teachers she had ever had. She would eat lunch with her and help her run errands such as grading papers in her spare time. This teacher helped her fall in love with math and ultimately had a huge impact on her now choosing to major in statistics.
Madison Goodwin had many people impact her mathematically. She lists Ms. Smith, Mr. Manker, Dr. Waters, and Dr. Herman all as people who have had a positive impact on her math journey.
Question 4 Response
Who is your favorite mathematician, and why? (Mine is Archimedes -- if you don't have one already, look him up!)
We've all had someone inspire us. Since we're "junior" mathematicians, we have (or should have!) a list of mathematicians who we think are awesome! The famous mathematician Alan Turing (well known for the Turing Test in the previous discussion) was mentioned by John Nuestro and Craig McGhee. John says Turing is interesting because of the Turing Test and describes it as a test to "determine whether a computer can think". Craig goes on to mention how Turing is "the father of modern computing" and basically has done what "Newton did for physics." He also goes to mention that the world would be a different world if we didn't have Alan Turing. It's no wonder that Turing is a favorite.
Jenna Henderson has a two-fold appreciation for one mathematician, Hypatia of Alexandria (360-415AD). She is the first known female mathematician. Not only did she contribute to "algebraic equations and conic sections and inventing the astrolabe for ship navigation and devices for measuring the density of fluids," but she also conquered despite discrimination due to sexism and her pagan beliefs in a Christian society. She was a pioneer for women in the field. She went against the grain in many ways, she entered a "man's world career" and made new discoveries all while being discriminated. She made academic and social history!
Nevaeh Moore states that her favorite mathematician is Sophie Germain. Germain lived in an era in which it was frowned upon for women to learn and be interested in math. Despite this, she pursued her love of math. She even used a fake name to help her follow her passion. She was the first woman to win a prize from the French Academy of Sciences. Her work and dedication are what inspire Moore most. Germain's persistence and experiences make Moore grateful to be able to study math freely.