The Bell Curve

The normal distribution — the bell curve — appears everywhere in statistics: test scores, measurement errors, biological traits. Its shape is defined by two parameters: the mean (center) and the standard deviation (spread).

The Formula

The probability density function for a normal distribution:

f(x) = (1 / (σ√2π)) · e^(-½((x-μ)/σ)²)

Where μ is the mean and σ is the standard deviation. As σ grows, the curve flattens. As μ shifts, the peak moves left or right without changing shape.

Interactive Explorer

Adjust the mean and standard deviation below to see how the curve responds. Notice that narrowing σ concentrates probability near the center — this is why small samples from a wide distribution can look surprisingly clustered.

mean: 0.0std dev: 1.0

Why It Matters

Many natural processes produce approximately normal distributions through the central limit theorem: the sum of many independent random variables tends toward normality. Understanding the bell curve helps you reason about outliers, confidence intervals, and the difference between typical and exceptional cases.

About

Dev is a minimal mono developer blog focused on readable essays and interactive demos. It uses MDX for content, Shiki for syntax highlighting, and a tight typographic system inspired by classic engineer personal sites.

Navigate the live demo above to read sample posts and try the demos. Scaffold your own copy with the create command below, then swap in your name, social links, and writing.

Template source

Browse every file in templates/dev.

templates/dev

README.md

# Dev Blog

A minimal mono developer blog template — MDX essays, projects, and interactive demos.

Design by [Hugo Lin](https://1chooo.com).

## Quick start

### Option A — create-next-app (recommended)

```bash
npx create-next-app@latest my-blog \
  --example "https://github.com/1chooo/tawny" \
  --example-path "templates/dev"
```

### Option B — create-tawny CLI (interactive prompts)

```bash
npx create-tawny@latest dev my-blog
```

Then:

```bash
cd my-blog
pnpm install   # or npm / yarn / bun
pnpm dev
```

Open [http://localhost:3000](http://localhost:3000).

## Customize these files

| File | What to change |
|------|----------------|
| `app/layout.tsx` | Site title and metadata |
| `app/page.tsx` | About / home copy |
| `components/site-header.tsx` | Brand name in the header |
| `components/site-footer.tsx` | Social links and location |
| `app/blog/_articles/` | Your essays (`.mdx` files) |
| `app/projects/page.mdx` | Projects page |

### Placeholders

Search for `{{AUTHOR_NAME}}`, `{{AUTHOR_EMAIL}}`, `{{GITHUB_USERNAME}}`, and `{{CITY_NAME}}` across the project and replace them.

## Stack

- Next.js 16 App Router & React Server Components
- MDX & Shiki for content
- Tailwind CSS v4
- Minimal mono typography

## License

MIT