How does Rails handle routing and request handling? Provide an example of defining routes in Rails.

In Ruby on Rails, routing and request handling are core components responsible for mapping incoming requests to the appropriate controller actions. Rails provides a robust and flexible routing system that simplifies the process of defining routes and handling HTTP requests.

The routing system in Rails follows the principle of RESTful routing, which aligns with the standard CRUD operations (Create, Read, Update, Delete) used in web applications. This approach allows developers to define routes that correspond to specific controller actions, providing a clear and consistent structure for handling requests.

Rails routes are defined in the `config/routes.rb` file within the application. This file serves as the central location for configuring the routing behavior of the application. Let's consider an example to understand how routes are defined in Rails:

```
ruby`Rails.application.routes.draw do
root 'welcome#index'

get 'articles', to: 'articles#index'
post 'articles', to: 'articles#create'
get 'articles/new', to: 'articles#new', as: 'new\_article'
get 'articles/:id', to: 'articles#show', as: 'article'
get 'articles/:id/edit', to: 'articles#edit', as: 'edit\_article'
patch 'articles/:id', to: 'articles#update'
delete 'articles/:id', to: 'articles#destroy'
end`
```
In this example, we can see various types of routes defined:

1. Root route: The `root` method sets the default landing page for the application. In this case, it maps the root URL ('/') to the `index` action of the `WelcomeController`.
2. Basic routes: The `get` and `post` methods are used to define routes for handling HTTP GET and POST requests, respectively. In the example, we have routes for listing articles (`/articles`), creating new articles (`/articles/new`), and showing a specific article (`/articles/:id`).
3. Custom route names: The `as` option is used to provide custom names for routes. These names can be used to generate URL helpers, making it easier to reference routes in the application. For example, the `new_article` route is assigned the name `new_article_path`, which can be used to generate the URL for creating a new article.
4. Dynamic segments: Routes can include dynamic segments denoted by the `:id` placeholder. These segments allow for handling requests with variable values. In the example, the `show` and `edit` routes for articles include a dynamic segment `:id` to identify the specific article.
5. Additional HTTP methods: Besides `get` and `post`, Rails supports other HTTP methods like `patch` and `delete`. These methods are used to handle update and delete operations, respectively.

Once the routes are defined, Rails uses the routing system to map incoming requests to the corresponding controller actions based on the requested URL and HTTP method. When a request matches a defined route, Rails invokes the specified controller action, passing any necessary parameters extracted from the URL.

For example, when a user visits `/articles/1` with a GET request, Rails maps it to the `show` action of the `ArticlesController` and passes the value `1` as the `id` parameter. Similarly, a POST request to `/articles` would map to the `create` action of the `ArticlesController`.

Rails' routing system provides a convenient way to define and manage routes in an application. It follows RESTful conventions and allows for customization and flexibility when handling incoming requests. By mapping URLs to specific controller actions, Rails simplifies the process of request handling and helps developers build well-structured and organized web applications.