The Toast Derivation

The Toast Derivation is the seventeenth episode of the fourth season of the CBS sitcom, The Big Bang Theory. This episode first aired on February 24, 2011.

Summary
Sheldon realizes he is not the center of his group, thus he attempts to form a different social group where he can be the center. Meanwhile, Penny tries to get over Leonard who just got into a new relationship with Priya.

Extended Plot
Leonard is going over to Raj's for dinner with the gang, Sheldon insists he stays because of their Thursday tradition of eating pizza at their apartment. Leonard is still going so Sheldon tags along. After a brief unsatisfactory experience at Raj's, Sheldon heads to the Cheesecake Factory's Bar alone and tries to get Penny to empathize with him. Amy video calls him and points out that Leonard is the "nucleus" of their social group.

Later, Sheldon prepares some snack for his forthcoming guests Stuart, Kripke, Zack and LeVar Burton whom he invited via Twitter; he does this to form a new social group where he is the "nucleus". At Sheldon's event, he announces that it seems LeVar Burton will not be attending, and kicks off the gathering with some introductory activities, in which all of the guests receive a goody bag containing a free copy of The New England Journal of High Energy Physics.

Amy and Bernadette come over to Penny's to invite her out for dancing to get over Leonard; she agrees if the two agree not to pester her about Leonard any further. They try to get Penny to go to a place where she can get a young guy to have sex with. She refuses, but then Amy and Bernadette point out the preserved snow flake from the North Pole which Leonard gave her. She then changes her mind.

Back at Sheldon's event, Zack impresses the gang (exception from Sheldon) with his racy story, next Sheldon asks the gang to choose between an array of boring old games. Because of that, Kripke decides to bring up his Karaoke Machine.

Back at Raj's, the gang is reminiscing about their experiences with Sheldon. Sheldon is suddenly at the door; he is greeted with a warm welcome. At the final scene, LeVar Burton makes an appearance to join them, but swiftly changes his mind after seeing Stuart, Kripke and Zack singing Walking On Sunshine, with Stuart in a towel.

Trivia

 * Raj's flat screen HD television has 2% dead pixels on the upper left corner.
 * Kripke is fond of gambling (e.g., "waffles"/raffles).
 * Priya ponders Sheldon buying a loom and weaving, while Leonard and Raj mention their serapes that Sheldon made; this is a reference to The Luminous Fish Effect. Also, Priya talks about Sheldon adopting 25 cats, which occurred in The Zazzy Substitution.
 * Sheldon once got punched by Bill Gates after telling him that maybe if he weren't so distracted by sick children in Africa, he could have put a little more thought into Windows Vista.
 * Sheldon hates haggis and blood pudding.
 * Amy Farrah Fowler has an electric tooth brush which she calls "Gerard" used for personal pleasuring.
 * When Sheldon goes to Raj's apartment and knocks, he says, "All my friends" 3 times between knocks.