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A deerstalker is a type of hat that is typically worn in rural areas, often for hunting, especially deer stalking. Because of the hat's popular association with Sherlock Holmes,  it is also a stereotypical hat of a detective.
The deerstalker's main feature is a pair of fore and aft brims and two flexible side flaps. The dual brims provide sun protection for the face and neck of the wearer. The side flaps can be worn down or tied under the chin to protect the ears in cold weather and high winds, or tied up above the crown to keep them out of the way when not in use. The checkered pattern in the twill fabric also serves as camouflage, and modern hunting clothes, including deerstalkers, are often made with either a red-and-black or an orange-and-black check pattern or tweed for both this purpose and hunter safety.
Sherlock Holmes 
The most famous wearer of this kind of hat is the fictional character Sherlock Holmes, who is popularly depicted favouring this style of hat. Holmes is never actually described as wearing a deerstalker by name in Arthur Conan Doyle's stories, but in The Adventure Of Silver Blaze, the narrator, Doctor Watson, describes him as wearing "his ear-flapped travelling cap", and in The Boscombe Valley Mystery, as wearing a "close-fitting cloth cap". As the deerstalker is the only hat of the period matching both descriptions, it is not surprising that the original illustrations for the stories by Sidney Paget, Frederic Dorr Steele, and others depicted Holmes as a "deerstalker man", which then became the popular perception of him.
Later uninformed depictions of Holmes that depict him wearing this hat in the city fail to take into account that the fashion-conscious Holmes would never commit such a sartorial faux pas; the deerstalker is traditionally a rural outdoorsman's cap, not the appropriate headgear for the properly dressed urban gentleman. Indeed, Paget and the other contemporaneous illustrators who portrayed Holmes as wearing a deerstalker always placed him in the proper setting for such attire, travelling cross-country or operating in a rural outdoor setting. The character is nevertheless frequently depicted wearing the hat regardless of the setting, popularized on screen by the commonplace depictions of the hat in the 1939 films The Hound of the Baskervilles and The Adventures of Sherlock Holmes starring Basil Rathbone.
In the second season of the BBC television series Sherlock which places Holmes and Watson (portrayed by Benedict Cumberbatch and Martin Freeman, respectively) in contemporary London, the deerstalker cap is a recurring gag; here Sherlock Holmes gained the iconic look by trying to hide his face from paparazzi in the deerstalker, which he personally despises. John Watson tells him "It's not a deerstalker anymore, it's a Sherlock Holmes hat... you're this far from famous" as Sherlock tries to understand why it's called a deerstalker, even asking whether it's used as a "death frisbee."
See also 
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|Look up deerstalker hat in Wiktionary, the free dictionary.|