The notebooks we commonly use have lines drawn on them.
Usually we don't think about the lines, we think about what to write between the lines.
Let's focus on the lines drawn on the note.
Those lines are a constant function (y=c) and a group of parallel lines! The two eccentric mathematicians try something new in their notebooks.
What happens when you change the pattern of parallel lines? "Non-Standard Notes" contains artistic drawings depicting various formulas, including straight lines with different directions, parabolas and waves, and the overlapping and division of circles.
It visually demonstrates the beauty of mathematics, which is often referred to, while also helping anyone approach mathematics in a comfortable way through the form of notes.
How will the new rules of note-taking change your flow of thought? Let's enjoy math with a lighter heart by experiencing a different way of writing and drawing.

Our civilization has a curious habit of printing reams of paper full of lines.

--- From "First Sentence"

How would changing the lines affect the flow of thought? What if straight, parallel lines were replaced with curves, clusters of lines, or crosshairs? What if each plane, once uniformly identical, was given its own unique character?
--- p.10

A stone thrown into the air flies along a parabolic trajectory.
Comets wandering through space also trace parabolic trajectories.
Isaac Newton considered this fact about the orbit of a comet to be very important, and he wrote the proof of the parabolic orbit of a comet as the finale of his masterpiece of modern physics, Principia.
--- p.39

Triangles and squares form the basic shapes of great bridges, ornate opera houses, and many other monumental structures.
Another example is computer animation.
To simulate the fluidity of water or the curvature of a face, 3D animators work by layering polygons on top of each other until the desired effect is achieved.

--- p.57

Japanese Zen Buddhist Zen master Shunryu Suzuki said, “Waves are the movement of water.
“It is a mistake to talk about waves as separate from water or water as separate from waves,” he wrote.
Maybe so.
But for mathematicians, the practice of waves doesn't stop at water.
Waves are the primal form of repetition.
It is the embodiment of periodicity.

--- p.89

The concept of infinite access, which no matter how hard you try, try, and try, you can never reach, is the engine that drives modern mathematics.
In the pages that follow, you will encounter lines that get closer and closer together, vortices that grow larger and closer together, and waves that get faster and faster.
The key concept here is the limit, a destination that we are forever approaching but never reaching.

--- p.103

We are drawn to the beauty of the five-armed starfish, the six-branched snowflake, and the seven-petaled flower.
In such a form, rotation is symmetrical, an action that preserves the structure without changing it.
An object with rotational symmetry appears to rotate while at rest, and also appears to remain at rest while rotating.

--- p.119

This chapter unfolds by utilizing both concepts of size.
A passage from Neil Gaiman's book American Gods comes to mind.
There, a character looks at the night sky and says this.
“Shadow couldn’t tell if he was looking at a moon the size of a dollar a foot above his head, [or] a moon the size of the Pacific Ocean thousands of miles away.”
--- p.133

Apophenia refers to the human tendency to see patterns in everything, even when there are none in reality.
We connect the scattered stars to see constellations, and hear names and whispers amidst the noisy noise.
Sometimes, they connect unrelated events to create a huge conspiracy.
Our minds, always searching for patterns, seem never to be able to accept true randomness.
This is our blind spot.

Fortunately, that is also our extraordinary ability.

--- p.179