What are the last two digits of 20192019? These types of questions are popular in tests like the AMC or MMPC, and often seem daunting, but modular arithmetic simplifies the problem down easily. Modular arithmetic can be described as using the remainder of a number when it's divided by another number. Before we solve the…

Cat's Out of Box

30.11.2022

LR 1: Mean Value Theorem – Cat's Out of Box

As you're driving through a highway with a speed limit of 75 mph, you notice that cops are logging cars' speeds (because they have nothing better to do, I guess). Let's call this checkpoint A. 20 miles and 15 minutes later, you notice another cop car, but this time, the cops are pulling you over…

Cat's Out of Box

30.11.2022

Gabriel’s Horn – Cat's Out of Box

How can something have a finite volume and infinite surface area? In the physical world, it can’t. Simply because infinite anything isn’t possible as far as we know. But logically, it’s completely possible. In fact, that’s what Gabriel’s Horn is.

Cat's Out of Box

30.11.2022

Explaining Derivatives – Cat's Out of Box

Purpose Some people told me that I should explain derivatives in my Mean Value Theorem post if I wanted it to be accessible to younger readers. Because that post was already long, I decided to make a separate post for it. This took a while because I wanted to find an intuitive explanation for derivatives,…

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Cat's Out of Box

Science

Modular Arithmetic and Large Exponents – Cat's Out of Box

LR 1: Mean Value Theorem – Cat's Out of Box

Gabriel’s Horn – Cat's Out of Box

Explaining Derivatives – Cat's Out of Box

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