Happy pi day
I just learned that today is pi day.
No, not that kind of pie. National Pie Day comes on January 23rd – and now that I’ve learned that, I plan to celebrate next year. Pie is one of my very favorite desserts.
Today is Pi Day – this kind of pi:
Pi Day is supposed to be a celebration of math. Good luck with that – it’s been my experience that people either like math or they don’t. My mother hated it, my father liked it, and I liked it to right up to some point in college where it suddenly became opaque to me. Perhaps that was because my professor at the time couldn’t speak English and therefore could explain nothing to us. Or perhaps I had simply reached my math ceiling, like the guy in the photo.
So, let’s celebrate!
After all these years, and with no reason to use the knowledge, I can still recite 3.14159.
In the spirit of a celebration of math, here’s maybe the nerdiest question in the history of this blog – which is saying something. Anyone have a favorite formula? Because I do. It’s the formula for adding velocities accounting for special relativity (no object’s speed can exceed the speed of light). I can’t write a good formula in here, so here’s a picture of it:
https://jabberwocking.com/wp-content/uploads/2021/07/blog_velocity_addition.jpg
C = the speed of light.
I love how a mind-boggling complex idea like relativity can be expressed in such an approachable formula.
How about the next 3 digits Kate? Really useless knowledge.
I loved science and I was very good at math. But I didn’t have any particular affection for math. I guess I liked it a little, but no passion for it. And I studied a ton of it, because I thought it would be useful and unlike some of the tough physics courses, the math classes seemed to be a sure A for me.
I do recall a course in abstract algebra. I did fine on all of it until the take-home mid-term exam. Ouch. I got something like a C+ of B- on it. The prof. had extended the difficulty moderately beyond the homeworks & I was stumped on a few problems. I suppose that I had been mastering the mechanics of it, without fully grasping the concepts. My other work pulled the overall grade up enough.
Youtube channel “Stand-up Maths” always does something special for Pi day. This year they calculated pi with colliding blocks.
Unless you had SMSG “new math” forced on you by teaches who couldn’t explain it to a 14 year old high school student back in the 60’s, you don’t fully know how to hate math. What does even an above average kid at that age understand about set theory or statistical probability when he just needs to learn plain old geometry? Memorize the damn theorems and postulates and be done with it already. Fortunately I caught up in summer school after the exposure to willful uncertainty when certainty is exactly what an adolescent needs in his life.
TommyJay, I could do math well in school, but I didn’t love it.
The Other Chuck
I took Illinois Math (UICSM), another variant of New Math, in high school. Through 8th grade I did well in math, but found it boring. I can’t speak for SMSG, but Illinois Math had us do proofs from day one–which I found fun and easy. My 9th grade math teacher, a family friend who attended my mother’s memorial service, was a Phi Beta Kappa Math graduate of U Michigan. She knew math, but had no grasp of classroom management. The UICSM textbook was good enough that I could ignore the classroom chaos and teach myself from the textbook. For my 10th and 12th grade math courses, I had an exceptionally good teacher, perhaps the best teacher I ever had.
I had two teachers for 11th grade. For the first half of the year, my teacher was very good, but she left to give birth. Her replacement wasn’t as comfortable teaching all those inductive proofs, but I had enough experience to finesse that. Our class President, a good but not brilliant student, was in my math class. In my yearbook, she wrote, “No more math misery.” What prompted the misery–the material or the less than outstanding teacher or both–I don’t know.
Max Beberman developed Illinois Math while teaching at the University of Illinois lab school. Illinois Math was good for teaching faculty brats, but not so good for lower ability students.
Years later I had a Geometry class in college from a professor who had met Max Beberman. He told me that Max made the point that it wasn’t his intention to throw out competence in basic multiplication or division in favor of set theory or the like. However, lower level teachers who had a poor grasp of math did just that.
Re: School Mathematics Study Group (SMSG)
My Catholic high school was trying hard to keep up with the latest, greatest so it jumped right on board with the SMSG New Math. Several years ago I was curious to revisit my first algebra text. It was worse than I recalled.
There is the smell of Ivy League arrogance to the whole project and its inability to relate to anyone with an IQ below 130. I read the text today and I am flabbergasted that they imagine that they are talking to ninth graders.
Here are the second and third problems on the very first problem set:
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3. Find U, the set of all whole numbers from 1 to 4, inclusive. Then find T, the set of squares of all members of U. Now find V, the set of all numbers belonging to both U and T. (Did you include 2 in V? But 2 is not a member of T, so that it cannot belong to both U and. T.) Does every member of V belong to U? Is V a subset of U? Is V a subset of T? Is U a subset of T?
4. Returning to problem 3, let K be the set of all numbers each of which belongs either to U or to T or to both. (Did you include 2 in K? You are right, because 2 belongs to U and hence belongs to either U or to T. The numbers 1 and h belong to both U and T but we include them only once in K.) Is K a subset of U? Is U a subset of K? Is T a subset of K? Is U a subset of U?
http://static.cemseprojects.org/smsg/Algebra_Geometry_ST/First_Course_In_Algebra_Part_1_Student.pdf
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Can you imagine?
@Mike Plaiss: Anyone have a favorite formula?
I have:
e^(pi i) – 1 = 0
The relationship between the five most important numbers.
Next favorite would the Poisson distribution, after that the harmonic oscillator. The Poisson distribution describes rare events and the harmonic oscillator physical systems near equilibrium.
Huxley,
I find your problems pretty easy and probably could have solved them by the sixth grade, depending on when we learned what a square is in this context (I don’t remember when that was). But I was always pretty good at math up to differential equations.
I came well after the “new math” fad, but my 10th/11th-grade math teacher used to talk about it. He didn’t much like it for general instruction. We still did set theory at some point, but it was just a chapter in a curriculum. No courses were designed around it. I can only imagine doing that for months on end. What a way to destroy students’ fondness for math.
Our 9th-grade geometry class was almost all proofs. It was an easy A, but I didn’t really care for it. Algebra and calculus were much more fun.
huxley
The latest, greatest gets Math turned into Mashed Potatoes.
@Huxley: “Can you imagine?”
Definitely yes. Maybe as Gringo said, it was the teacher, but the samples you put up are pretty much what I remember. Having completed 9th grade Algebra at Catholic School I was forced into public school because we didn’t have a Catholic High School in town. My mother saw to it that I was removed from the “gifted” group of new math students and put back into the regular Geometry (summer school catch up plus tutoring), Algebra, Trig program.
I liked math, for the most part. My one real regret with it was that I never got to take Diff. Eq. – couldn’t fit it into my schedule at college.
huxley, those set problems seem kind of dull. Doable, sure, but why would anybody care about the answers?
Mike Plaiss, I like that choice of formula – elegant. I suppose if I were to pick one, and if I could remember them in any detail, perhaps one of the Maxwell equations.
At work today, someone brought in doughnuts for pi day and got razzed for it a little bit.