**The Asymptote. **This representation of one of the coolest behaviors a function can have is also good for germaphobes afraid of physical contact.

**The High 5, Mod 5**. Ever wondered, “What exactly *is* the difference between a fist bump and a high-five?” The pedestrian mind might say, “One uses closed fists, and one uses open palms.” But I reply that in modular arithmetic, there is no difference at all.

**The Point-Slope**. It’s not just the best form for a linear equation. Now, it’s also the best form for a spontaneous expression of enthusiasm and/or friendship.

**The Tangency**. “Let’s high-five!” “No, let’s fist-bump!” This argument has unfolded thousands of times, at least in my mind. The solution: a high-five lying tangent to a fist. The geometric best of both worlds!

**Completing the Square**. This indispensable algebraic technique is now *also* a technique for securing the the wide-eyed respect and burning envy of bystanders. As they say: “Every good high-five is a visual metaphor for friendship.”

**The Distributive Fist Bump**. If fists were numbers, and bumping were multiplication, then oh what a world that would be.

**The High Five with No Real Solutions**. This is a high-five so complex, so cool, so imaginary, that the collision between the hands is invisible to the naked eye, taking place in a higher-dimensional space than our meager “real” world. (Also useful as a post-hoc excuse when you accidentally whiff on a regular high-five.)

**The High Roman Five**. How did they celebrate in Rome, you ask? Probably like this. (But don’t ask historians. They’re conspiring to conceal this cool high-five for themselves.)

**The Exponential**. For situations when your enthusiasm is growing so rapidly that a polynomial high-five just won’t suffice.

**The High 10, Base Five**. What is math for, if not giving a fancy technical name to a totally intuitive object that has been around for ages?

**The Sine**. Seeking a little extra credit in the timeless gradebook of awesomeness? Look no further, trigonometry students.

**The Inverse Five**. Every operation needs its inverse: addition has subtraction, exponentials have logarithms, differentiation has integration. Now, if you need to undo a regrettable high-five, the power is in your hands. Literally.

**The Conjugation Five** **(fgf ^{-1})**. An expert-level high-five. Don’t try this at home until you have spoken seriously with your family about the fact that, even though you are growing more amazing than they can ever truly fathom, you still love them just as much.

**The Transitive Five**. That’s right. High fives are transitive. Which means that you now get credit for high-fiving everyone who’s ever high-fived anyone that *you* high-fived. What I’m saying is that I’m pretty sure you and I just high-fived, and it was the best.

*Filmed in 2014 in the lobby of my high school; this is pretty much what a regular day is like there. **Thanks to my gorgeous hand models: Alex George, Ben Miller, Becca Thal, Miriam Newman, Jon Kominsky, and Mr. Rob Sherry. For a little more detail on the math, hold your mouse over each gif.*

I’ve never wanted to high five someone more than right now.

The negated Roman/Fascist salute is being used now as a covert sign of Antisemitism.

Wait, really? The Spock hand gesture?

No, it’s a stiff arm, but angled down to the ground instead of up in the air. The finger-spreading Vulcan salute is strictly Orthodox Jewish.

I can’t believe I recognized the Commonwealth lobby from that one piece of molding…

So did I! And then, scrolling down, I saw Mr. Sherry, and felt very vindicated.

Great, you have written another one of those posts that I love and must now share with all my friends… who will have to learn some new ways to high five…

Well, this is the best damned thing I’ve seen in days!

Priceless!

Reblogged this on `The Penguin' says… and commented:

When I first loaded the article, the first thing I saw was the first image (a good blogging tip to keep in mind, by the way) and instantly I knew this was going to be good.

Transitive High Fives… How many degrees of separation do you think there are on average between any two given people via the high five? In other words, have I high fived Kevin Bacon?

Also, along the lines of “High 10 Base 5”, I sometimes High-31 if I feel like counting in binary.

Reblogged this on thom dunn and commented:

The trick to connecting is to always look at the elbow.

This made me so happy. Thank you!

themathmaster, Cindy, Justin, Mark, tPenguinLTG, and stupidbadmemes: Thanks for reading, guys. I owe you all a high-five of your choice if I ever run into you.

Rob and Asa: Yeah, Mallory Rome sent me a message saying she’d recognized it, too. Does this mean that the Commonwealth Lobby is just super-iconic molding? Or does this mean that we’d recognize any square foot of the school?

ths17: It’s a great question. I saw the argument once that for handshakes, six degrees of separation suffices to connect the world. I imagine an extra degree or two would do it for high-fives. It depends on the cultural specificity of high-fives (we’ll never be connected to someone who has never high-fived), but I suspect 6 degrees should get us to Kevin Bacon, at least.

I now want all my best friends to love this as much as me so we can do this (sadly they wont)

I tried completing the square high five on myself, and sprained my wrist!