Another Pi Day is upon us. This is the sixth ceremonial anniversary of the blog, and so I make every effort to post every year on Pi Day, even if it's on the weekend.
Today on her Daily Epsilon on Math 2021, Rebecca Rapoport writes:
How many integer values of x are there such that there is a triangle with side lengths x, 15, 17 and all angles acute?
Recall that last year, Pi Day was one of three special days when Rapoport wrote a joke (in this case it was "I 8 sum pi") instead of a problems whose answer was the date. This year she again will have three exceptional days, but Pi Day isn't one of them. Instead we have a regular problem that has nothing to do with pi or Pi Day -- but at least it's a Geometry song.
Without the last four words, this would be a Triangle Inequality problem. This tells us that the sum of the lengths of two sides of a triangle is greater than the length of the third side. Applying this to our triangle, we have both x + 15 > 17 and 15 + 17 > x. Combining gives:
17 - 15 < x < 17 + 15
But now we need to worry about those last four words "and all angles acute." While Triangle Inequality appears in Lesson 1-9 of the U of Chicago text, the Pythagorean Inequalities don't appear in at all. In other Geometry texts, we learn that:
a^2 + b^2 > c^2 iff the triangle is acute
Applying this to our triangle, we have both x^2 + 15^2 = 17^2 and 15^2 + 17^2 > x^2. Combining gives:
17^2 - 15^2 < x^2 < 17^2 + 15^2
Notice that x can't be 8 (this would produce a right triangle), but it can equal any integer from 9 up to 22, since 22^2 = 484 and 23^2 = 529. The set {9, 10, 11, .., 20, 21, 22} has fourteen elements. Thus there are 14 possible side lengths -- and of course, today's date is the fourteenth of March, Pi Day.
Last year, I subbed in a special ed English classroom on the last three days before Pi Day. This year, I subbed in another special ed class, this time a self-contained one, on Pi Day Adam. In fact, I do more math in the class this year than last year, since the students have several math worksheets -- including the simple circumference/diameter worksheets that I give them.
Let's get to my favorite part of my annual Pi Day post -- the videos:
1. "Pi Day Music Video" by musicnotes online
This video is a few years old, but I include it often in my Pi Day post. It's the only song I know that actually mentions the exact time 3/14 at 1:59, and so I like to play it at exactly 1:59.
2. Parody of "Dynamite" by Taio Cruz
I've watched this video several times before. The students who create this video are 5th graders.
3. "Song from Pi" by Song Scout
I post this one almost every year. Song Scout writes a song where each pitch corresponds to one of the digits of pi.
By the way, I enjoy some of Song Scout's other music videos, even the ones that aren't directly related to the number pi. Here's one of them, about a piano with "two middle Cs::
4. "This Piano's Defect Makes It Impossible to Play":
5. Christopher Bill turns pi into music
This is one was first posted last year. Chris Bill uses the digits of pi as Song Scout and so many others have done, except the digits of pi correspond to the lengths, rather than pitches, of the notes.
6. Parody of "Thrift Shop" by Macklemore
This is another one that I post almost every year.
7. "Using Rubik's Cubes to Calculate Pi" by Z3Cubing:
This is a new video for this year. The length of the video is 3:14.
8. "Calculating Pi with Avogadro's Number" by Stand-Up Maths (Matt Parker):
This is also a new video for this year. It's also a great video for Mole Day on October 23rd. I also watched a video about the possibility that pi^pi^pi^pi (that is, pi^^4 or pi tetrated to the fourth) might even be an integer (or at least rational).
9. "Legendary Test Question -- pi is less than 22/7" by MindYourDecisions (Presh Talwalker):
This is also a new video for this year. It's also a great video for Pi Approximation Day on July 22nd (and Talwalker even mentions the PUTNAM exam that college students took last month).
10. Pi Song from Wonder Park:
I've never watched the film Wonder Park, so I didn't know that there even is a Pi Day scene in this movie until it popped up in a Google search. The movie was first released two years ago on the day after Pi Day (the math holiday was on a Thursday that year, and most films come out on Friday). Who knows -- perhaps if I'd known that there was a Pi Day song in this movie, I would have watched it.
11. "How Pi Sounds as Music:
This is yet another one of those songs based on the digits of pi, first posted on Pi Day of the Century.
12. "Pi Day Anthem" by John Sims and Vi Hart
This duet is mostly just reciting digits. The length of the song is also 3:14, although there are a few extra seconds at the end of the video.
13. Vi Hart's Pi Day video 2021
Vi begins with 3.1415 (E-C-F-C-G) and its Mobius inversion (A-C-G-G-F -- recall that my old first day of school song at my old charter school was also based on inversion). Then Vi repeats sets of digits that go together, such as ..926.. (D-A-D, a D power chord) and 5-3-5-8 (G-E-G-C, which is C major chord).
By the way, I usually post my annual first day of DST post on the first post after the time change -- which is this post. Since today is Pi Day, I'll save it for tomorrow's post instead.
Oh, and I decided to complete my regained hour of Vi Hart videos by adding this other half-hour video to make a full hour:
14. Twelve Tones by Vi Hart:
Oh, and let's not leave Mocha out of the fun:
http://www.haplessgenius.com/mocha/
70 N=1
80 FOR X=1 TO 32
90 READ A
100 SOUND 261-N*(18-A),4
110 NEXT X
120 DATA 3,1,4,1,5,9,2,6,5,3
130 DATA 5,8,9,7,9,3,2,3,8,4
140 DATA 6,2,6,4,3,3,8,3,2,7
150 DATA 9,5
As usual, click on the Sound button before you RUN the program.
This song is based on 18EDL. As I've said before with pi, 0 doesn't first appear until relatively late, which is way some musicians cut off the song just before the first 0.
For 18EDL, we use 0 and 9 as the tonic -- the beginning and ending of the scale. This might sound strange when there's no 0 to represent the root note.
This year, we can change our program so that 1 and 10 are the tonic. This follows the video that Vi Hart posted this year -- Vi tends to treat the digit 0 as 10 (as you can see in that video, where the 0 note is to the right of the 9 note). We'll also fix it so that all 70 digits that appear in the video are in this song:
80 FOR X=1 TO 70
90 READ A
100 SOUND 261-N*(19-A),4
110 NEXT X
120 DATA 3,1,4,1,5,9,2,6,5,3
130 DATA 5,8,9,7,9,3,2,3,8,4
140 DATA 6,2,6,4,3,3,8,3,2,7
160 DATA 1,6,9,3,9,9,3,7,5,1
170 DATA 10,5,8,2,10,9,7,4,9,4
180 DATA 4,5,9,2,3,0,7,8,1,1
I don't want this to turn into a music post, but the Vi Hart and Song Scout videos are also giving me ideas for finishing some of my other songs that are waiting for tunes. For example, Vi's Twelve Tones strategy can be changed to with the nine tones of 18EDL (counting the two tonics as one).
Song Scout's "Piano Piece with Perfect Harmony" gives hints as to how to give perfect harmony to my songs in 18EDL. Meanwhile, his broken piano with "two middle Cs" doesn't play our standard 12EDO scale well, but it could play other possible EDO scales such as 17EDO (with the black keys divided into sets of 2, 2, 3 just like the piano in the video, leading to a scale of 17 notes). This is an EDO scale that's not compatible with the EDL scales of Mocha.
Meanwhile, another video kept popping up on my YouTube feed while searching for Pi Day songs, even though it has nothing to do with the number pi. It's a new video by Sevish -- the only known musician who has posted an EDL video (he used 10EDL). He uses nonstandard scales often. But unfortunately, this Centaur scale isn't fully playable in Mocha. Still, any Sevish song provides hints for me to finish my songs.
This isn't a music post, so I'm done with scales for now. I'll let you know when I complete these tunes.
Last year, Pi Day marked the start of the coronavirus shutdowns -- Pi Day Eve was the last day for standard instruction, and as we saw, I didn't have in-person students again until October 6th.
Well, this Pi Day represents some positive developments. Today, Orange County officially returns to the red tier which allows schools and some businesses to reopen. And it appears that LA County will reach the red tier tomorrow.
I wrote that nothing less than a coronavirus vaccine will allow crowded LA County to reach the red -- and that's exactly what happened. Governor Newsom announced that the levels for reaching the red tier would become less stringent if a certain vaccination rate was reached -- and it was. Then the virus rates in each county has to stay below a certain level for two weeks -- it's been 14 days in Orange County but only 13 days in LA County, which is why LA has to wait until tomorrow.
And so while last Pi Day marked the beginning of the pandemic, this Pi Day appears to mark the beginning of the end of the pandemic. I hope that by next Pi Day -- which will fall on a Monday -- virus levels will be low enough to allow students to be on campus on Mondays, so that we can have a real Pi Day party once again.
If I timed this post properly, this should be posted on 3/14 at 1:59 PM Pacific Daylight Time. I will be eating my slice of cherry pie within the next hour.
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