Welcome to Leaf's Library

Leaf's Library is our first picture book. I hope the kids in your life will love and learn from it!

Brown Fairies and Binary Search in a STEM Picture Book

Leaf loves her library, but it has become too large for her to look through! Luckily the new arrivals section is short, so she can handle those fine. But when she needs to get something from the back, it could take a whole day to find it!

Come along with Leaf as she learns how to quickly find books in the back! Luckily she keeps all her books sorted, but how will that help her? Without binary search, it could take days. But maybe she'll figure it out before the day is over!

Babies First Binary Search

For those who don't know, binary search is a very important algorithm in computer science and mathematics. It helps us search through large databases quickly, but is also useful in many algorithms. For instance, a common proof of the intermediate value theorem in calculus uses a variation of binary search. It can be used to calculate square roots, logarithms, exponentials, and many other functions. It is an extremely generic and useful tool.

Let's take square root for instance. The fastest methods for calculating square roots usually involve calculus and Newton's method, but those are complicated. We just want something that works. Binary search gives us a fast algorithm that is much simpler. For any positive number a, we can easily tell if b is greater than or less than the square root of a. How? By squaring b and comparing it to a. So we start by noting the square root of a is some number between zero and a + 1. Then we use binary search to find a b that is very close to the square root of a. Often b is irrational, so we may not find it exactly, but neither would a calculator.