How do you organize screen sharing?

Question

Work organization

Given:

• cozy office
  
• TV set
  
• 3 people using 3 different operating systems (OS X, Windows 8.1, Ubuntu 12.04)
  
• all 3 computers are connected by one WiFi network
  

Task:

• give each person the opportunity to show something on the TV (desktop, picture, video, etc.)
  
• if possible, do without wires between computers and TV
  
• if possible, organize the whole thing "locally", without the need for Internet access
  

We thought about taking a netbook / Android whistle, plugging in a TV set and launching TeamViewer. The idea seemed deviant and "clumsy".
How did you solve such a problem?