ruby-on-rails-3 - [POST] "/contacts/1" に一致するルートはありません

Question

アプリ/ビュー/連絡先/show.html/erb

<%= form_for(@contact) do |f| %>
<p id="notice"><%= notice %></p>

<p>
  <b>Firstname:</b>
  <%= @contact.firstname %>
</p>

<p>
  <b>Lastname:</b>
  <%= @contact.lastname %>
</p>

<p>
  <b>Email:</b>
  <%= @contact.email %>
</p>

<p>
  <b>Mobilephone:</b>
  <%= @contact.mobilephone %>
</p>
<% end %>

<%= link_to 'Edit', edit_contact_path(@contact) %> |
<%= link_to 'List', contacts_path %>

私のview/contact/index.html.erbにはボタンがあります

<%= button_to 'show', contact %>

私のcontacts_controller.rbでは、次のような自動設定を使用しています：

def show
    @contact = Contact.find(params[:id])

    respond_to do |format|
      format.html # show.html.erb
      format.json { render json: @contact }
    end
  end

私のルートファイルで

match '/contacts/:id/edit', :controller => 'contacts', :action => 'edit'
  match '/contacts/contact_:id/show', :controller => 'contacts', :action => 'show'
  resources :contacts
  resources :connections
  resources :addresses
  root :to => 'contacts#index'

そしてレーキルートを実行した後、私は得ました

/contacts/:id/edit(.:format)    contacts#edit
                       /contacts/:id/show(.:format)    contacts#show
       contacts GET    /contacts(.:format)             contacts#index
                POST   /contacts(.:format)             contacts#create
    new_contact GET    /contacts/new(.:format)         contacts#new
   edit_contact GET    /contacts/:id/edit(.:format)    contacts#edit
        contact GET    /contacts/:id(.:format)         contacts#show
                PUT    /contacts/:id(.:format)         contacts#update
                DELETE /contacts/:id(.:format)         contacts#destroy
    connections GET    /connections(.:format)          connections#index
                POST   /connections(.:format)          connections#create
 new_connection GET    /connections/new(.:format)      connections#new
edit_connection GET    /connections/:id/edit(.:format) connections#edit
     connection GET    /connections/:id(.:format)      connections#show
                PUT    /connections/:id(.:format)      connections#update
                DELETE /connections/:id(.:format)      connections#destroy
      addresses GET    /addresses(.:format)            addresses#index
                POST   /addresses(.:format)            addresses#create
    new_address GET    /addresses/new(.:format)        addresses#new
   edit_address GET    /addresses/:id/edit(.:format)   addresses#edit
        address GET    /addresses/:id(.:format)        addresses#show
                PUT    /addresses/:id(.:format)        addresses#update
                DELETE /addresses/:id(.:format)        addresses#destroy
           root        /                               contacts#index

そして、「表示」ボタンをクリックすると、Routes Error No route matches [POST] "/contacts/1" が表示されました。助けてくれてありがとう。