Annotations and Math

🎯 Matplotlib Annotations & Math: Adding Labels Like Sticky Notes!

The Big Picture: Your Plot’s Voice

Imagine you drew the most amazing picture ever. But wait! No one knows what they’re looking at. That’s where annotations come in – they’re like sticky notes you put on your drawing to say “Hey, look at THIS!”

And math expressions? They’re like writing fancy math homework directly on your picture – with symbols like π and √ that look super professional!

🏷️ Part 1: Annotations Basics

What is an Annotation?

Think of annotations like a tour guide pointing at something interesting. You’re walking through a museum, and the guide says: “Look here! This is important!”

In Matplotlib, we use annotate() to be that tour guide for our plots.

Your First Annotation

import matplotlib.pyplot as plt

x = [1, 2, 3, 4, 5]
y = [1, 4, 9, 16, 25]

plt.plot(x, y)

# Add a sticky note!
plt.annotate('Peak!',
             xy=(5, 25),      # Where to point
             xytext=(4, 20),  # Where the note sits
             arrowprops=dict(arrowstyle='->'))

plt.show()

Breaking It Down

Simple Flow of Annotation

graph TD
    A["📝 Write your text"] --> B["📍 Pick the point to highlight"]
    B --> C["📌 Choose where text goes"]
    C --> D["➡️ Add an arrow to connect"]
    D --> E["✨ Done! Your annotation appears"]

🎨 Part 2: Annotation Styling

Making Your Sticky Notes Pretty!

Plain notes are boring. Let’s make them POP! It’s like decorating your room – same room, but way cooler.

The Arrow Styles Menu

Think of arrow styles like choosing different kinds of pens:

# Simple arrow (like a pencil line)
arrowprops=dict(arrowstyle='->')

# Fancy arrow (like a marker)
arrowprops=dict(arrowstyle='-|>')

# Curvy arrow (like a brush stroke)
arrowprops=dict(arrowstyle='fancy',
                connectionstyle='arc3,rad=0.3')

Available Arrow Styles

Text Box Styling

Your sticky note can have a background color too!

plt.annotate('Important!',
    xy=(3, 9),
    xytext=(1, 15),
    arrowprops=dict(arrowstyle='->'),
    bbox=dict(
        boxstyle='round',
        facecolor='yellow',
        alpha=0.8
    )
)

Box Style Options

Full Styling Example

import matplotlib.pyplot as plt

fig, ax = plt.subplots()
ax.plot([1,2,3,4], [1,4,2,3])

ax.annotate('Look Here!',
    xy=(2, 4),
    xytext=(3, 3),
    fontsize=12,
    fontweight='bold',
    color='white',
    arrowprops=dict(
        arrowstyle='fancy',
        color='purple',
        connectionstyle='arc3,rad=0.2'
    ),
    bbox=dict(
        boxstyle='round,pad=0.3',
        facecolor='purple',
        edgecolor='gold',
        linewidth=2
    )
)
plt.show()

📐 Part 3: Mathematical Expressions

Writing Math That Looks Like a Textbook

Remember when your teacher wrote equations on the board? They used special symbols like:

• Fractions: ½
• Square roots: √
• Greek letters: α, β, π
• Powers: x²

Matplotlib can do ALL of that!

The Magic Dollar Signs

In Matplotlib, dollar signs are magic wrappers for math:

# Regular text
plt.title('Area = pi * r squared')

# Math text (pretty!)
plt.title(r'$Area = \pi \cdot r^2#x27;)

The r before the string means “raw” – it helps Python not get confused.

Common Math Symbols

Building Math Step by Step

Let’s write the famous formula: E = mc²

import matplotlib.pyplot as plt

plt.figure(figsize=(6, 3))
plt.text(0.5, 0.5,
         r'$E = mc^2#x27;,
         fontsize=40,
         ha='center')
plt.axis('off')
plt.show()

More Complex Example

The quadratic formula:

plt.text(0.5, 0.5,
    r'$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}#x27;,
    fontsize=24,
    ha='center')

Flow: How Math Gets Rendered

graph TD
    A["Write text with $ signs"] --> B["Matplotlib finds the $...quot;]
    B --> C["Sends to math engine"]
    C --> D["Converts to pretty symbols"]
    D --> E["Displays on your plot!"]

🎓 Part 4: LaTeX Rendering

The Ultimate Math Power Tool

LaTeX (pronounced “lay-tech” or “lah-tech”) is like the Rolls-Royce of math writing. Scientists and mathematicians use it to write beautiful documents.

Matplotlib can use the same LaTeX engine to make your math look publication-ready!

Enabling Full LaTeX

import matplotlib.pyplot as plt

# Turn on LaTeX power!
plt.rcParams['text.usetex'] = True
plt.rcParams['font.family'] = 'serif'

# Now ALL text uses LaTeX
plt.title(r'The Famous $\int_0^\infty e^{-x} dx#x27;)

⚠️ Note: Full LaTeX needs LaTeX installed on your computer. The basic math (without usetex=True) works everywhere!

Basic vs Full LaTeX

LaTeX Formatting Commands

# Bold math
r'$\mathbf{bold}#x27;

# Italic (default)
r'$italic#x27;

# Roman (upright)
r'$\mathrm{upright}#x27;

# Calligraphy
r'$\mathcal{FANCY}#x27;

Complex LaTeX Example

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 2*np.pi, 100)
y = np.sin(x)

plt.plot(x, y)
plt.title(r'$f(x) = \sin(x)#x27;, fontsize=16)
plt.xlabel(r'$x$ (radians)')
plt.ylabel(r'$\sin(x)#x27;)

# Add annotation with LaTeX
plt.annotate(
    r'$\frac{d}{dx}\sin(x) = \cos(x)#x27;,
    xy=(np.pi/2, 1),
    xytext=(2, 0.5),
    fontsize=12,
    arrowprops=dict(arrowstyle='->')
)
plt.show()

LaTeX Special Environments

For multi-line equations:

# Aligned equations
equation = r'''$\begin{aligned}
a &= b + c \\
d &= e + f
\end{aligned}#x27;''
plt.text(0.5, 0.5, equation, ha='center')

🌟 Putting It All Together

The Complete Annotation Toolkit

graph TD
    subgraph "Your Annotation Toolkit"
    A["📝 Annotations"] --> B["Basic: Point & Label"]
    A --> C["Styled: Pretty Arrows & Boxes"]
    D["📐 Math Text"] --> E["Basic: $...$ symbols"]
    D --> F["LaTeX: Full power"]
    end
    B --> G["✨ Professional Plots!"]
    C --> G
    E --> G
    F --> G

Real-World Example: Complete Plot

import matplotlib.pyplot as plt
import numpy as np

# Create data
x = np.linspace(0, 4, 100)
y = x**2

# Make the plot
fig, ax = plt.subplots(figsize=(8, 6))
ax.plot(x, y, 'b-', linewidth=2)

# Title with math
ax.set_title(r'$f(x) = x^2#x27;, fontsize=18)

# Styled annotation
ax.annotate(
    r'Minimum at $x=0#x27;,
    xy=(0, 0),
    xytext=(1, 5),
    fontsize=12,
    arrowprops=dict(
        arrowstyle='fancy',
        color='green',
        connectionstyle='arc3,rad=0.2'
    ),
    bbox=dict(
        boxstyle='round',
        facecolor='lightgreen',
        alpha=0.8
    )
)

# Another annotation
ax.annotate(
    r'$f(2) = 4#x27;,
    xy=(2, 4),
    xytext=(3, 8),
    fontsize=11,
    arrowprops=dict(arrowstyle='->')
)

ax.set_xlabel(r'$x#x27;)
ax.set_ylabel(r'$f(x)#x27;)
plt.grid(True, alpha=0.3)
plt.show()

🎁 Quick Reference

Annotation Cheat Code

plt.annotate(
    'text',           # Your message
    xy=(x, y),        # Arrow points here
    xytext=(x2, y2),  # Text sits here
    arrowprops={},    # Arrow style
    bbox={}           # Text box style
)

Math Symbol Cheat Code

🎉 You Did It!

You now know how to:

1. ✅ Add annotations to point out important stuff
2. ✅ Style your annotations with arrows and boxes
3. ✅ Write math expressions that look professional
4. ✅ Use LaTeX for publication-quality math

Your plots are no longer silent pictures – they can speak to your audience!

Go ahead and annotate your next masterpiece! 🚀