Examples Library

Ready-to-use code examples for LaTeX formulas and Mermaid diagrams. Copy any example into the macro editor and customize it for your use case.

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LaTeX Formula Examples

1. Quadratic Formula

The solution to ax^2 + bx + c = 0:

LaTeX source (paste into LaTeX Block macro):

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Result: renders the quadratic formula centered on the page.

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2. Definite Integral

A common calculus example - the integral of x from 0 to 1:

LaTeX source:

\int_0^1 x^2 \, dx = \left[ \frac{x^3}{3} \right]_0^1 = \frac{1}{3}

Tips:

• Use \, for thin space before dx
• Use \left[ and \right] for auto-sized brackets

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3. Matrix

A 3×3 identity matrix:

LaTeX source:

\begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{pmatrix}

Variants:

• \begin{pmatrix} - parentheses
• \begin{bmatrix} - square brackets
• \begin{vmatrix} - vertical bars (determinant)

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4. Multi-line Aligned Derivation

Show step-by-step algebra with aligned equals signs:

LaTeX source:

\begin{aligned}
(a + b)^2 &= (a + b)(a + b) \\
          &= a^2 + ab + ba + b^2 \\
          &= a^2 + 2ab + b^2
\end{aligned}

Tips:

• Use &= to align at the equals sign
• Use \\\\ for line breaks inside aligned

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5. Machine Learning - Precision & Recall

Document ML metrics with labeled equations:

LaTeX source:

\begin{aligned}
\text{Precision} &= \frac{TP}{TP + FP} \\[6pt]
\text{Recall}    &= \frac{TP}{TP + FN} \\[6pt]
F_1               &= 2 \cdot \frac{\text{Precision} \cdot \text{Recall}}{\text{Precision} + \text{Recall}}
\end{aligned}

Tip: \\[6pt] adds extra vertical space between lines.

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Mermaid Diagram Examples

6. Flowchart - Decision Process

A simple decision flowchart with styled nodes:

Mermaid source (paste into Diagrams macro):

flowchart TD
    Start([Start]) --> Input[/Receive Request/]
    Input --> Valid{Valid Input?}
    Valid -->|Yes| Process[Process Request]
    Valid -->|No| Reject[Return Error]
    Process --> DB[(Save to DB)]
    DB --> Respond[/Send Response/]
    Reject --> Respond
    Respond --> End([End])

    style Start fill:#E3FCEF,stroke:#00875A
    style End fill:#E3FCEF,stroke:#00875A
    style Reject fill:#FFEBE6,stroke:#DE350B

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7. Sequence Diagram - API Authentication

Show a login flow across frontend, API, and database:

Mermaid source:

sequenceDiagram
    participant U as User
    participant F as Frontend
    participant A as API
    participant D as Database

    U->>F: Submit credentials
    F->>A: POST /auth/login
    activate A
    A->>D: SELECT user WHERE email=?
    activate D
    D-->>A: User record
    deactivate D
    A->>A: Verify password hash
    A-->>F: JWT token
    deactivate A
    F->>U: Redirect to dashboard

    Note over U,D: Full authentication flow

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8. Entity Relationship Diagram

Model a simple order management schema:

Mermaid source:

erDiagram
    CUSTOMER ||--o{ ORDER : places
    ORDER ||--|{ ORDER_ITEM : contains
    PRODUCT ||--o{ ORDER_ITEM : "included in"

    CUSTOMER {
        int id PK
        string name
        string email
    }
    ORDER {
        int id PK
        int customer_id FK
        date order_date
        string status
    }
    ORDER_ITEM {
        int id PK
        int order_id FK
        int product_id FK
        int quantity
        float unit_price
    }
    PRODUCT {
        int id PK
        string name
        float price
        int stock
    }

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9. Gantt Chart - Project Timeline

Track phases and milestones across a project:

Mermaid source:

gantt
    title Q1 Product Launch Timeline
    dateFormat YYYY-MM-DD
    section Discovery
    Requirements       :done, req, 2024-01-01, 2024-01-10
    Design Review      :done, design, 2024-01-10, 2024-01-20
    section Development
    Backend API        :active, api, 2024-01-20, 2024-02-15
    Frontend UI        :ui, 2024-01-28, 2024-02-20
    section QA
    Testing            :test, 2024-02-15, 2024-03-01
    Bug Fixes          :fix, 2024-03-01, 2024-03-10
    section Launch
    Staging Deploy     :staging, 2024-03-10, 2024-03-15
    Production Release :milestone, prod, 2024-03-15, 1d

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