Septimus Hodge and Thomasina Coverly sit in the front room of an old estate in Derbyshire, England. The house is surrounded by beautiful, traditional park-like landscape, which is lush and green. Thomasina, a curious and rather impetuous girl of thirteen, is the student of Septimus, who is twenty-two. Each is working on separate problems when Thomasina asks Septimus what "carnal embrace" might be. Thomasina overheard Jellaby, a servant at the estate, telling the cook that Mrs. Chater, wife of the poet Ezra Chater, had been found in carnal embrace in the gazebo. Jellaby had heard the story from Mr. Noakes, gardener of the estate, who had actually witnessed the event. Septimus tells Thomasina that the act of "carnal embrace" is throwing ones arms around a side of beef.
Thomasina, quite perceptive, tells Septimus that a gazebo is not a "meat larder" and asks if carnal embrace is kissing. Thomasina demands that Septimus tells her the truth, and so Septimus gives her the true scientific meaning: the insertion of the male genital into the female. Uncomfortable with this disclosure, Septimus quickly returns to work. Thomasina pesters Septimus to tell her more about sexual intercourse. Jellaby, the butler, interrupts the conversation. Jellaby brings a letter to Septimus from Mr. Chater. Septimus reads the letter and tells Jellaby to tell Mr. Chater that he will have to wait until the lesson is finished.
After Jellaby leaves, Thomasina asks Septimus if he thinks it is odd that when one stirs jam in his or her rice pudding into swirls in one direction, the jam will not come together again if they swirl the pudding in the opposite direction. In other words, she asks why one cannot stir things apart. Thomasina's question leads to a discussion about Newton's Law of Motion. Thomasina believes that if one could stop every atom in motion, a person could write a formula for the future.
Mr. Chater suddenly swings the door to the room open. Septimus bids Thomasina to leave the room. Chater accuses Septimus of "insulting" his wife in the gazebo. Septimus tells Chater that he is wrong and that he made love to Mrs. Chater in the gazebo the day before at Mrs. Chater's request. Chater challenges Septimus to a duel, but Septimus declines. Septimus tells Chater that he cannot shoot him because there are only two or three first rank poets living, Chater apparently one of them. Septimus distracts Mr. Chater by complementing him on his new poem, "The Couch of Eros," and tells Chater he will write a good review of the work. Chater, flattered, forgives Septimus for his indiscretion and even offers to sign Septimus's copy of "The Couch of Eros." Septimus only means to distract Chater.
Noakes enters the room, soon followed by Lady Croom, mistress of the estate, and Captain Edward Brice. Lady Croom is very upset by Noakes's plans for the landscaping of Sidley Park. Lady Croom thinks that Noakes's plans are too modern, Sidley park is beautiful and an "Arcadia" as it is. The sound of hunting fire outside the window precedes Lady Croom's exit. Lady Croom, in the style of a grand general, orders Noakes, Brice, and Chater to follow her. As Mr. Chater leaves, he shakes Septimus's hand in friendship. Thomasina and Septimus are again alone. Thomasina remarks that she has grown up with the sound of hunting guns and that her father's life is recorded in the game book by the game he has shot. Thomasina delivers a secret note to Septimus from Mrs. Chater.
It has been suggested that one of Tom Stoppard's favorite ideas is "all men desire to know." This seems particularly evident in Arcadia, a play obsessed with knowledge of many kinds. The characters in Arcadia seek three different sorts of knowledge: mathematical knowledge, historical knowledge and sexual knowledge.