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Solving Problems Submitted to MAA Journals (Part 2a) – Mean Green Math
The following problem appeared in Volume 53, Issue 4 (2022) of The College Mathematics Journal. This was the first problem that was I able to solve in over 30 years of subscribing to MAA journals. Suppose that $latex X$ and $latex Y$ are independent, uniform random variables over $latex [0,1]$. Now define the random variable…
Solving Problems Submitted to MAA Journals (Part 1) – Mean Green Math
I first became a member of the Mathematical Association of America in 1988. My mentor in high school gave me a one-year membership as a high school graduation present, and I've maintained my membership ever since. Most years, I've been a subscriber to three journals: The American Mathematical Monthly, Mathematics Magazine, and College Mathematics Journal.…
500,000 page views – Mean Green Math
I'm taking a break from my usual posts on mathematics and mathematics education to note a symbolic milestone: meangreenmath.com has had more than 500,000 total page views since its inception in June 2013. Many thanks to the followers of this blog, and I hope that you'll continue to find this blog to be a useful…
My Favorite One-Liners: Index – Mean Green Math
I'm doing something that I should have done a long time ago: collecting a series of posts into one single post. The links below show my series on my favorite one-liners. Mathematical Wisecracks for Almost Any Occasion: Part 2, Part 7, Part 8, Part 12, Part 21, Part 28, Part 29, Part 41, Part 46,…
Confirming Einstein’s General Theory of Relativity with Calculus: Index – Mean Green Math
I'm doing something that I should have done a long time ago: collecting a series of posts into one single post. The links below show my series on general relativity and the precession of Mercury's orbit. Part 1: Introduction Part 1a: Introduction Part 1b: Observed precession of Mercury Part 1c: Outline of argument Part 2:…
My Mathematical Magic Show: Index – Mean Green Math
I'm doing something that I should have done a long time ago: collecting a series of posts into one single post. The links below show the mathematical magic show that I'll perform from time to time. Part 1: Introduction. Part 2a, Part 2b, and Part 2c: The 1089 trick. Part 3a, Part 3b, and Part…
Lagrange Points and Polynomial Equations: Part 5 – Mean Green Math
This series was motivated by a terrific article that I read in the American Mathematical Monthly about Lagrange points, which are (from Wikipedia) "points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies." There are five such points in the Sun-Earth system, called $latex L_1$, $latex L_2$, $latex L_3$, $latex L_4$, and…
Lagrange Points and Polynomial Equations: Part 4 – Mean Green Math
From Wikipedia, Lagrange points are points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies. There are five such points in the Sun-Earth system, called $latex L_1$, $latex L_2$, $latex L_3$, $latex L_4$, and $latex L_5$. The stable equilibrium points $latex L_4$ and $latex L_5$ are easiest to explain: they are the…
Happy Pythagoras Day! – Mean Green Math
Let me take a break from my current series of posts to wish everyone an early Happy Pythagoras Day! Tomorrow will be 10/26/24 (or 26/10/24 in other parts of the world), and $latex 26^2 = 10^2 + 24^2$. Bonus points if you can figure out (without Googling) when the next Pythagoras Day will be.
Lagrange Points and Polynomial Equations: Part 3 – Mean Green Math
From Wikipedia, Lagrange points are points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies. There are five such points in the Sun-Earth system, called $latex L_1$, $latex L_2$, $latex L_3$, $latex L_4$, and $latex L_5$. The stable equilibrium points $latex L_4$ and $latex L_5$ are easiest to explain: they are the…
Lagrange Points and Polynomial Equations: Part 2 – Mean Green Math
From Wikipedia, Lagrange points are points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies. There are five such points in the Sun-Earth system, called $latex L_1$, $latex L_2$, $latex L_3$, $latex L_4$, and $latex L_5$. The stable equilibrium points $latex L_4$ and $latex L_5$ are easiest to explain: they are the…
Lagrange Points and Polynomial Equations: Part 1 – Mean Green Math
I recently read a terrific article in the American Mathematical Monthly about Lagrange points, which are (from Wikipedia) "points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies." There are five such points in the Sun-Earth system, called $latex L_1$, $latex L_2$, $latex L_3$, $latex L_4$, and $latex L_5$. To describe these…
Predicate Logic and Popular Culture: Index – Mean Green Math
I'm doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on using examples from popular culture to illustrate principles of predicate logic. My experiences teaching these ideas to my discrete mathematics students led to my recent publication (John…
Mathematical Allusions in Shantaram (Part 4) – Mean Green Math
I recently finished the novel Shantaram, by Gregory David Roberts. As I'm not a professional book reviewer, let me instead quote from the Amazon review: Crime and punishment, passion and loyalty, betrayal and redemption are only a few of the ingredients in Shantaram, a massive, over-the-top, mostly autobiographical novel. Shantaram is the name given Mr. Lindsay,…
Mathematical Allusions in Shantaram (Part 3) – Mean Green Math
I recently finished the novel Shantaram, by Gregory David Roberts. As I'm not a professional book reviewer, let me instead quote from the Amazon review: Crime and punishment, passion and loyalty, betrayal and redemption are only a few of the ingredients in Shantaram, a massive, over-the-top, mostly autobiographical novel. Shantaram is the name given Mr. Lindsay,…
Mathematical Allusions in Shantaram (Part 2) – Mean Green Math
I recently finished the novel Shantaram, by Gregory David Roberts. As I'm not a professional book reviewer, let me instead quote from the Amazon review: Crime and punishment, passion and loyalty, betrayal and redemption are only a few of the ingredients in Shantaram, a massive, over-the-top, mostly autobiographical novel. Shantaram is the name given Mr. Lindsay,…
Mathematical Allusions in Shantaram (Part 1) – Mean Green Math
I recently finished the novel Shantaram, by Gregory David Roberts. As I'm not a professional book reviewer, let me instead quote from the Amazon review: Crime and punishment, passion and loyalty, betrayal and redemption are only a few of the ingredients in Shantaram, a massive, over-the-top, mostly autobiographical novel. Shantaram is the name given Mr. Lindsay,…
My Mathematical Magic Show: Part 11 – Mean Green Math
A couple years ago, I learned the 27-card trick, which is probably the most popular trick in my current repertoire. In this first video, Matt Parker performs this trick as well as the 49-card trick. https://www.youtube.com/watch?v=G_OuIVOGDr8 Here's a quick explanation from the American Mathematical Society for how the magician performs this trick. In short, the…
My Mathematical Magic Show: Part 10 – Mean Green Math
This magic trick is an optical illusion instead of a pure magic trick, but it definitely is a crowd-pleaser. This illusion is called Sugihara's Impossible Cylinder: https://www.youtube.com/watch?v=oWfFco7K9v8 https://www.youtube.com/watch?v=QTNg0ofgB78 This is actually a mathematical magic trick. As detailed by David Richeson in Math Horizons, there is a fair amount of math that goes into creating this…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 9: Pedagogical Thoughts – Mean Green Math
At long last, we have reached the end of this series of posts. The derivation is elementary; I'm confident that I could have understood this derivation had I seen it when I was in high school. That said, the word "elementary" in mathematics can be a bit loaded --- this means that it is based…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 8: Second- and Third-Order Approximations – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. In…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 7e: Computing Precession – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 7d: Predicting Precession IV – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 7c: Predicting Precession III – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 7b: Predicting Precession II – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 7a: Predicting Precession I – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 6k: Solving New Differential Equation with Method of Undetermined Coefficients – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 6j: Rationale for Method of Undetermined Coefficients VII – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 6i: Rationale for Method of Undetermined Coefficients VI – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. In…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 6h: Rationale for Method of Undetermined Coefficients V – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 6g: Rationale for Method of Undetermined Coefficients IV – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 6f: Rationale for Method of Undetermined Coefficients III – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 6e: Rationale for Method of Undetermined Coefficients II – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 6d: Rationale for Method of Undetermined Coefficeints I – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 6c: Solving New Differential Equation with Variation of Parameters – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. Under…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 6b: Checking Solution of New Differential Equation with Calculus – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. In…
Confirming Einstein’s Theory of General Relativity With Calculus, Part 6a: New Differential Equation – Mean Green Math
In this series, I'm discussing how ideas from calculus and precalculus (with a touch of differential equations) can predict the precession in Mercury's orbit and thus confirm Einstein's theory of general relativity. The origins of this series came from a class project that I assigned to my Differential Equations students maybe 20 years ago. We…