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I'd like to talk to you a bit about my two favorite holidays that exist between Valentine's Day and my birthday (April 14th). The first is Pi Day (March 14th, 3/14), and the second is April Fool's Day (April 1st). Obviously, the former isn't recognized by unimportant non-nerds, and the second one can be abused (there is a fine line between subtle humor and blatant douchebaggery), but I do enjoy them both... and the past month has included my first ever Pi Day and April Fool's Day... as a college professor (of mathematics).
Pi Day
Every year, I celebrate Pi Day. I go out with my math friends, and occasionally we play beer pong with the cups line up in the shape of the pi symbol. I post a celebratory status at 1:59 AM or PM (to keep the digits going... and you should figure out why next year's Pi Day is going to be even more significant!). I eat pie and I wear my pi tie and pi shirts.
![[image loading]](http://i.imgur.com/czCAs4n.jpg)
Yes, plural.
But this year was special (although I did still wear my pi attire). I had classes of students to entertain! And as luck would have it, Pi Day fell on a Friday- the Friday right before our spring break.
I had given my precalculus and calculus classes exams on the Wednesday before break, and I wasn't about to start teaching them brand new material on the day before spring break. (Besides, I was already ahead of our syllabus.) So instead, I celebrated Pi Day with them.
Some students and I brought in pies, cookies, and anything else tasty and round (not that I had them compute circumference or area anyway). And so, for three hours (two 1.5-hour classes), I gave them math puzzles, paradoxes, interesting proofs, and other math-related entertainment that I had compiled into a powerpoint presentation. I gave the same presentation to both of my classes, as none of the problems required any math that the students couldn't handle.
1. The pictures and one-liners between math problems and activities, although corny, were much appreciated by my students. I also gave my calculus kids a pro-tip for dating- using the best pick up line ever: I wish I were your derivative so I could lie tangent to your curves  + Show Spoiler +The one I couldn't tell them was: I wish I were your second derivative so I could explore your concavities.
![[image loading]](http://i.imgur.com/XQBGqSA.jpg)
And one of my students thought Bill Cosby was Morgan Freeman.
2. I showed them two paradoxes in particular. I presented the students with the two questions, had them try their best to figure out the solutions, and then we all collaborated and talked about the problems, the math behind the procedures, and the surprising solutions.
I gave them the Birthday Problem and the Monty Hall Problem.
For those of you who are unfamiliar with either of them, here's a brief explanation for each:
+ Show Spoiler +Birthday Problem: This problem revolves around solving for the likelihood that a certain number of people in a room have at least two people that share a birthday. So basically, if there are five people in the room (or ten or fifty or a hundred people), what is the likelihood that at least two people share a birthday? How would you compute it? This framework sets the stage for the central question of the Birthday Problem: How many people must be in a room for there to be at least a 50% chance that you share a birthday with at least one other person? We make some general assumptions to make the problem manageable and minimize variables: -365 days in a year = 365 possible birthdays (ignore leap years/ February 29th) -The year doesn’t matter (October 6, 1989 = October 6, 1990; etc.) -All 365 days are equally likely to be a birthday (Sorry, “9 months after Valentine's Day”.) -There are no tricks or hidden variables (e.g., not considering P(twins) ). -Therefore, the probability of any two people sharing the same birthday is equal to 1/365, as the first person’s birthday is arbitrary but the second person has to match with the first’s, regardless of what day that ends up being. Most students (or people, really), tend to guess a number that's around half of 365 (so ~180). But the answer is, counterintuitively, + Show Spoiler +much smaller: 23. Only 23 people are needed in a room for there to be a 50% chance of at least one birthday match. I don't really feel like writing out the entire list of computations right now, but here's the Wiki on it, with different wordings for questions: http://en.wikipedia.org/wiki/Birthday_problem . Monty Hall Problem: Suppose you're on a game show, and you're given the choice of three closed doors, each of which is hiding a prize: Behind one door is a brand new car! Behind the other two are identical goats. (Let’s assume you want the car and don’t find goats particularly wonderful.) You pick one of the three doors (it stays shut for now), and then the host, who knows where each prize is, opens a different door (one of the two you haven’t chosen), purposely revealing a goat. He then offers you the choice to either keep the door you first selected, or switch your choice to the other unopened door. Which do you choose to do? Does switching help or hurt your chance of winning? Does it change anything? Interestingly enough, the answer is that + Show Spoiler +it's in your best interest, mathematically, to always switch to the other unopened door, as this increases the likelihood of selecting the car from 1/3 to 2/3. Can you figure out why? Here's the Wiki on it: http://en.wikipedia.org/wiki/Monty_Hall_problem
3. We discussed a series of false proofs. Here's the first slide with three very short false proofs. Surely you can figure out which step is "illegal" in each of these?
![[image loading]](http://i.imgur.com/vkyoJzV.jpg)
I also presented them a math "proof" for 1 = 2 that I had written out last semester... along with a poem to complement every step. I wrote another TL blog on this false proof and poem a few months ago, so I'll just link it here: http://www.teamliquid.net/blogs/436043-math-poetry I recited the poem to my students and scrolled through the slides (each slide showing the next step), and the students were quite impressed. I gave them time to figure out what was wrong with the proof, and then I finished the poem (it ends with the solution).
4. I ended with two of my favorite math problems. The first one, The Doubling Problem, was given to me in a problem solving class during college. The second one, The Perfect Square, was assigned to us on our first day of Introduction to Abstract Algebra. Here they are:
![[image loading]](http://i.imgur.com/TASIuEl.jpg)
I gave my students the remaining half hour or so in the period to pick one of these and focus their energy and attention and critical thinking skills (and ability to collaborate with others) to solve it. They were incredibly engaged in the problems, and slightly frustrated (which is good, as it showed they were emotionally invested in math!). At the end of the period, they insisted I tell them the solutions.
I told them: Maybe after break.
And remarkably, some of the students actually went back over the problems during their spring break and made more progress. I solved both for them the day we came back to class.
If you'd like the solutions to those two problems: + Show Spoiler +Nope. Not right now, anyway. Figure it out on your own!
April Fool's Day
April Fool's Day is the one day that my entire family understands the need to prank the hell out of each other. In good fun. I've flipped beds, switched out all the clothes in dressers for canned food in cabinets, rearranged pretty much everything in the house... and had similar things done back to me. Because my two younger brothers, my mom, and I have an agreement to enjoy our April Fool's Day together. It's consensual  And sometimes I'll recruit others to help (e.g., my girlfriend and I got "engaged" on Facebook last year and changed our pictures and everything). It's always in good fun.
Unfortunately, I had no time to prepare anything this year, except for the few Facebook statuses and one particular prank that I decided to play on my students.
One of the most annoying things that my students do is ask me questions that I've answered dozens of times already, and is explained in the syllabus, and can be solved via Google. I love them dearly, but sometimes they're just lazy.
And just as a frame of reference, all math midterm exams are always on Wednesdays (there are three midterm exams before the final exam).
And April Fool's Day was on a Tuesday this year.
And students kept asking me when the next exam was, despite that knowledge being available to them in about ten different ways other than "disrupt class and ask about the date of the exam which isn't for at least another month".
So... I sent out an e-mail on April 1st.
Heading: Review Sheet for Tomorrow's Exam
Body: The math coordinator has created a very thorough document containing review questions that will be related to tomorrow's exam, and he sent it out to the professors to then pass on to students. I strongly recommend completing the review for practice, along with our usual syllabus homework problems and our online assignments.
The document is attached to this e-mail. Please open it and quickly look through the problems to see if you have any questions about the topics presented. Do not hesitate to e-mail me if you have any concerns.
As you're all aware, tomorrow's exam is in the same place as the previous two exams, at the same time. Pretty easy to remember!
Attachment Title: Exam 3 Review
Attachment Body: April Fool’s!
No exam this week, but I’m looking forward to shocked responses from those who never look at the syllabus or online for answers to their basic questions about our class, and/ or are too lazy to actually save and open this seemingly vital document.
Within an hour, I had ten immediate responses, most of them flipping out. (Some of them recognized the joke and found it funny.) My top three favorite replies:
3. Dear Professor Mango,
I cried.
2. I literally started sweating and freaking out until I opened the attatchments. That was a good one professor but I really hate you now lol
1. AYO TEACH, NOT FUNNY. I ALMOST HAD A HEART ATTACK.
(She didn't really.)
I love being a math professor. Happy belated Pi Day and April Fool's Day to everyone ♥
~DPB
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your Country52678 Posts
Math blog, instant 5/5.
Reading now.
Perfect square:
+ Show Spoiler +Obviously, all even numbers have a square divisible by 4. Any odd number can be expressed as 2n+1 for some n. The square is 4n^2+4n+1, which is 4k+1 for some k.
Oh man, that exam story is evil.
As for the doubling problem, + Show Spoiler +There seem to be none with 2 or 3 digits, and I suspect it's impossible, for setting up an equation for digits a, b (and c) gives 200a+20b+2c = 100c+10a+b, which reduces to 190a+19b = 98c, meaning c would have to be divisible by 19. Similar thing for the tripling problem.
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On April 03 2014 00:52 The_Templar wrote:Math blog, instant 5/5. Reading now. Perfect square: + Show Spoiler +Obviously, all even numbers have a square divisible by 4. Any odd number can be expressed as 2n+1 for some n. The square is 4n^2+4n+1, which is 4k+1 for some k.
Oh man, that exam story is evil. As for the doubling problem, + Show Spoiler +There seem to be none with 2 or 3 digits, and I suspect it's impossible, for setting up an equation for digits a, b (and c) gives 200a+20b+2c = 100c+10a+b, which reduces to 190a+19b = 98c, meaning c would have to be divisible by 19. Similar thing for the tripling problem.
Glad you liked it
Perfect square response: + Show Spoiler +You've shown 4k+1 for odds, but you need to show 8k+1
Doubling problem response: + Show Spoiler +You're right that no 2-digit or 3-digit numbers work, but there do exist a few larger-digit numbers that work for doubling (and tripling, and quadrupling too!).
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You sound like a cool math teacher.
One solution to doubling problem:
+ Show Spoiler +105263157894736842
You can figure it out by going backwards.
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On April 03 2014 02:01 Laurens wrote:You sound like a cool math teacher. One solution to doubling problem: + Show Spoiler +105263157894736842
You can figure it out by going backwards.
Well done!
My students like me and they're doing well in the course, so I guess I'm doing something right lol.
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you sound like an awesome professor, I would've loved to have you.
maybe then I wouldn't have fallen asleep during all my college math classes and barely made it through with my GPA intact...
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your Country52678 Posts
On April 03 2014 01:54 DarkPlasmaBall wrote:Show nested quote +On April 03 2014 00:52 The_Templar wrote:Math blog, instant 5/5. Reading now. Perfect square: + Show Spoiler +Obviously, all even numbers have a square divisible by 4. Any odd number can be expressed as 2n+1 for some n. The square is 4n^2+4n+1, which is 4k+1 for some k.
Oh man, that exam story is evil. As for the doubling problem, + Show Spoiler +There seem to be none with 2 or 3 digits, and I suspect it's impossible, for setting up an equation for digits a, b (and c) gives 200a+20b+2c = 100c+10a+b, which reduces to 190a+19b = 98c, meaning c would have to be divisible by 19. Similar thing for the tripling problem. Glad you liked it Perfect square response: + Show Spoiler +You've shown 4k+1 for odds, but you need to show 8k+1 Doubling problem response: + Show Spoiler +You're right that no 2-digit or 3-digit numbers work, but there do exist a few larger-digit numbers that work for doubling (and tripling, and quadrupling too!).
Perfect square:
+ Show Spoiler +n^2 and n are both odd, so n^2+n is even, 4n^2+4n is divisible by 8, and 4n^2+4n+1 = 8k+1. Misread the problem 
Doubling problem: + Show Spoiler +Damn it I over-thought it. Smallest solution seems to be 105263157894736842 as already posted.
Tripling problem: + Show Spoiler +2068965517241379310344827586
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On April 03 2014 03:22 The_Templar wrote:Show nested quote +On April 03 2014 01:54 DarkPlasmaBall wrote:On April 03 2014 00:52 The_Templar wrote:Math blog, instant 5/5. Reading now. Perfect square: + Show Spoiler +Obviously, all even numbers have a square divisible by 4. Any odd number can be expressed as 2n+1 for some n. The square is 4n^2+4n+1, which is 4k+1 for some k.
Oh man, that exam story is evil. As for the doubling problem, + Show Spoiler +There seem to be none with 2 or 3 digits, and I suspect it's impossible, for setting up an equation for digits a, b (and c) gives 200a+20b+2c = 100c+10a+b, which reduces to 190a+19b = 98c, meaning c would have to be divisible by 19. Similar thing for the tripling problem. Glad you liked it Perfect square response: + Show Spoiler +You've shown 4k+1 for odds, but you need to show 8k+1 Doubling problem response: + Show Spoiler +You're right that no 2-digit or 3-digit numbers work, but there do exist a few larger-digit numbers that work for doubling (and tripling, and quadrupling too!). Perfect square: + Show Spoiler +n^2 and n are both odd, so n^2+n is even, 4n^2+4n is divisible by 8, and 4n^2+4n+1 = 8k+1. Misread the problem Doubling problem: + Show Spoiler +Damn it I over-thought it. Smallest solution seems to be 105263157894736842 as already posted.
Correct on both accounts You can create other doubling numbers using that solution too!
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your Country52678 Posts
On April 03 2014 03:26 DarkPlasmaBall wrote:Show nested quote +On April 03 2014 03:22 The_Templar wrote:On April 03 2014 01:54 DarkPlasmaBall wrote:On April 03 2014 00:52 The_Templar wrote:Math blog, instant 5/5. Reading now. Perfect square: + Show Spoiler +Obviously, all even numbers have a square divisible by 4. Any odd number can be expressed as 2n+1 for some n. The square is 4n^2+4n+1, which is 4k+1 for some k.
Oh man, that exam story is evil. As for the doubling problem, + Show Spoiler +There seem to be none with 2 or 3 digits, and I suspect it's impossible, for setting up an equation for digits a, b (and c) gives 200a+20b+2c = 100c+10a+b, which reduces to 190a+19b = 98c, meaning c would have to be divisible by 19. Similar thing for the tripling problem. Glad you liked it Perfect square response: + Show Spoiler +You've shown 4k+1 for odds, but you need to show 8k+1 Doubling problem response: + Show Spoiler +You're right that no 2-digit or 3-digit numbers work, but there do exist a few larger-digit numbers that work for doubling (and tripling, and quadrupling too!). Perfect square: + Show Spoiler +n^2 and n are both odd, so n^2+n is even, 4n^2+4n is divisible by 8, and 4n^2+4n+1 = 8k+1. Misread the problem Doubling problem: + Show Spoiler +Damn it I over-thought it. Smallest solution seems to be 105263157894736842 as already posted. Correct on both accounts You can create other doubling numbers using that solution too!
Yes. The tripling problem is slightly harder. -.-
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TLADT24596 Posts
Cool blog! Sounds like those were some fun classes. Also, you are an evil teacher for pulling that April fools joke. Sounds dark to me
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Canada7169 Posts
This blog gave me flashbacks to "explaining" the Monty Hall problem to people.
I swear it's the quickest way to lose patience.
Next year you should assign a proof of the Collatz Conjecture as homework.
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On April 03 2014 03:30 The_Templar wrote:Show nested quote +On April 03 2014 03:26 DarkPlasmaBall wrote:On April 03 2014 03:22 The_Templar wrote:On April 03 2014 01:54 DarkPlasmaBall wrote:On April 03 2014 00:52 The_Templar wrote:Math blog, instant 5/5. Reading now. Perfect square: + Show Spoiler +Obviously, all even numbers have a square divisible by 4. Any odd number can be expressed as 2n+1 for some n. The square is 4n^2+4n+1, which is 4k+1 for some k.
Oh man, that exam story is evil. As for the doubling problem, + Show Spoiler +There seem to be none with 2 or 3 digits, and I suspect it's impossible, for setting up an equation for digits a, b (and c) gives 200a+20b+2c = 100c+10a+b, which reduces to 190a+19b = 98c, meaning c would have to be divisible by 19. Similar thing for the tripling problem. Glad you liked it Perfect square response: + Show Spoiler +You've shown 4k+1 for odds, but you need to show 8k+1 Doubling problem response: + Show Spoiler +You're right that no 2-digit or 3-digit numbers work, but there do exist a few larger-digit numbers that work for doubling (and tripling, and quadrupling too!). Perfect square: + Show Spoiler +n^2 and n are both odd, so n^2+n is even, 4n^2+4n is divisible by 8, and 4n^2+4n+1 = 8k+1. Misread the problem Doubling problem: + Show Spoiler +Damn it I over-thought it. Smallest solution seems to be 105263157894736842 as already posted. Correct on both accounts You can create other doubling numbers using that solution too! Yes. The tripling problem is slightly harder. -.-
Yep, although I do recall one of the later ones (maybe it was quadrupling?) cycling quite quickly!
On April 03 2014 03:46 BigFan wrote:Cool blog! Sounds like those were some fun classes. Also, you are an evil teacher for pulling that April fools joke. Sounds dark to me
Haha touche ^^ Yeah the students had a good time
On April 03 2014 04:08 mikeymoo wrote:
This blog gave me flashbacks to "explaining" the Monty Hall problem to people.
I swear it's the quickest way to lose patience.
Next year you should assign a proof of the Collatz Conjecture as homework.
Haha or the Riemann hypothesis or the P vs. NP problem ^^;;
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Did you know pi day is also Steak and a Blow Job day?
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DarkPlasmaBall what classes do you teach? Let me get in on some of those :D
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On April 03 2014 04:46 neoghaleon55 wrote:
Did you know pi day is also Steak and a Blow Job day?
Yup I do You really can't get much better than the Unholy Trinity of Math, Meat, and Fellatio in a single day!
On April 03 2014 04:55 Yorkie wrote:
DarkPlasmaBall what classes do you teach? Let me get in on some of those :D
Haha last semester was just statistics and precalculus, while this semester is just precalculus and calculus 1 (right now I do a lot of other things besides teach college).
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your Country52678 Posts
On April 03 2014 04:24 DarkPlasmaBall wrote:Show nested quote +On April 03 2014 03:30 The_Templar wrote:On April 03 2014 03:26 DarkPlasmaBall wrote:On April 03 2014 03:22 The_Templar wrote:On April 03 2014 01:54 DarkPlasmaBall wrote:On April 03 2014 00:52 The_Templar wrote:Math blog, instant 5/5. Reading now. Perfect square: + Show Spoiler +Obviously, all even numbers have a square divisible by 4. Any odd number can be expressed as 2n+1 for some n. The square is 4n^2+4n+1, which is 4k+1 for some k.
Oh man, that exam story is evil. As for the doubling problem, + Show Spoiler +There seem to be none with 2 or 3 digits, and I suspect it's impossible, for setting up an equation for digits a, b (and c) gives 200a+20b+2c = 100c+10a+b, which reduces to 190a+19b = 98c, meaning c would have to be divisible by 19. Similar thing for the tripling problem. Glad you liked it Perfect square response: + Show Spoiler +You've shown 4k+1 for odds, but you need to show 8k+1 Doubling problem response: + Show Spoiler +You're right that no 2-digit or 3-digit numbers work, but there do exist a few larger-digit numbers that work for doubling (and tripling, and quadrupling too!). Perfect square: + Show Spoiler +n^2 and n are both odd, so n^2+n is even, 4n^2+4n is divisible by 8, and 4n^2+4n+1 = 8k+1. Misread the problem Doubling problem: + Show Spoiler +Damn it I over-thought it. Smallest solution seems to be 105263157894736842 as already posted. Correct on both accounts You can create other doubling numbers using that solution too! Yes. The tripling problem is slightly harder. -.- Yep, although I do recall one of the later ones (maybe it was quadrupling?) cycling quite quickly!
Quadrupling: 230769
Yeah, I think that's it.
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On April 03 2014 05:28 The_Templar wrote:Show nested quote +On April 03 2014 04:24 DarkPlasmaBall wrote:On April 03 2014 03:30 The_Templar wrote:On April 03 2014 03:26 DarkPlasmaBall wrote:On April 03 2014 03:22 The_Templar wrote:On April 03 2014 01:54 DarkPlasmaBall wrote:On April 03 2014 00:52 The_Templar wrote:Math blog, instant 5/5. Reading now. Perfect square: + Show Spoiler +Obviously, all even numbers have a square divisible by 4. Any odd number can be expressed as 2n+1 for some n. The square is 4n^2+4n+1, which is 4k+1 for some k.
Oh man, that exam story is evil. As for the doubling problem, + Show Spoiler +There seem to be none with 2 or 3 digits, and I suspect it's impossible, for setting up an equation for digits a, b (and c) gives 200a+20b+2c = 100c+10a+b, which reduces to 190a+19b = 98c, meaning c would have to be divisible by 19. Similar thing for the tripling problem. Glad you liked it Perfect square response: + Show Spoiler +You've shown 4k+1 for odds, but you need to show 8k+1 Doubling problem response: + Show Spoiler +You're right that no 2-digit or 3-digit numbers work, but there do exist a few larger-digit numbers that work for doubling (and tripling, and quadrupling too!). Perfect square: + Show Spoiler +n^2 and n are both odd, so n^2+n is even, 4n^2+4n is divisible by 8, and 4n^2+4n+1 = 8k+1. Misread the problem Doubling problem: + Show Spoiler +Damn it I over-thought it. Smallest solution seems to be 105263157894736842 as already posted. Correct on both accounts You can create other doubling numbers using that solution too! Yes. The tripling problem is slightly harder. -.- Yep, although I do recall one of the later ones (maybe it was quadrupling?) cycling quite quickly! Quadrupling: 230769 Yeah, I think that's it.
I prefer to start with 1 as my one's digit to generate a cycle... so I end up with 025641, 102564, etc.
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On April 03 2014 05:26 DarkPlasmaBall wrote:Show nested quote +On April 03 2014 04:46 neoghaleon55 wrote:
Did you know pi day is also Steak and a Blow Job day? Yup I do You really can't get much better than the Unholy Trinity of Math, Meat, and Fellatio in a single day! Show nested quote +On April 03 2014 04:55 Yorkie wrote:
DarkPlasmaBall what classes do you teach? Let me get in on some of those :D Haha last semester was just statistics and precalculus, while this semester is just precalculus and calculus 1 (right now I do a lot of other things besides teach college).
Damn I'm in Calc 2 now TT
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On April 03 2014 05:37 Yorkie wrote:Show nested quote +On April 03 2014 05:26 DarkPlasmaBall wrote:On April 03 2014 04:46 neoghaleon55 wrote:
Did you know pi day is also Steak and a Blow Job day? Yup I do You really can't get much better than the Unholy Trinity of Math, Meat, and Fellatio in a single day! On April 03 2014 04:55 Yorkie wrote:
DarkPlasmaBall what classes do you teach? Let me get in on some of those :D Haha last semester was just statistics and precalculus, while this semester is just precalculus and calculus 1 (right now I do a lot of other things besides teach college). Damn I'm in Calc 2 now TT
Best of luck!
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Damn I wish I had had you as my math teacher. In high school I had 3 math teachers. One of them reminds me a bit of you in the way you've described your class time and he was literally the most gifted teacher (or at least in the top 3) I'd had up until college (I'd still put him in the top 5 now). The other two were awful. Very cool blog DPB .
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EPT
