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In mathematics, Shephard's problem, is the following geometrical question asked by Geoffrey Colin Shephard in 1964: if K and L are centrally symmetric
Shephard's_problem
tied into it? Does every convex polyhedron have Rupert's property? Shephard's problem (a.k.a. Dürer's conjecture) – does every convex polyhedron have a
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
British mathematician (1927–2016)
He asked Shephard's problem on the volumes of projected convex bodies, posed another problem on polyhedral nets, proved the Shephard–Todd theorem in invariant
Geoffrey_Colin_Shephard
Family name
artist Sidney Shephard (1894–1953), British politician Shephard Mayer (1923–2005), Canadian ice hockey player Shephard's lemma Shephard's problem Chevalley–Shephard–Todd
Shepherd_(name)
and Schneider (1967) used projection bodies in their solution to Shephard's problem. For K {\displaystyle K} a convex body, let Π ∘ K {\displaystyle \Pi
Projection_body
Problem in convex geometry
Schlumprecht (1999) gave a uniform solution for all dimensions. Shephard's problem Ball, Keith (1988), "Some remarks on the geometry of convex sets"
Busemann–Petty_problem
On surrounding polygons by layers of copies
corresponding problem in the hyperbolic plane, the Heesch number may be arbitrarily large. Heesch (1968), as cited by Grünbaum & Shephard (1987) and Fontaine
Heesch's_problem
Association football club in London, England
their relegation from the top-flight in 1998. This was due to financial problems which saw Palace go into administration twice, in 1999 and 2010. They steadily
Crystal_Palace_F.C.
American breed of dog
noted by owners were eye problems (red eye, epiphora, conjunctivitis, and cataracts). Dermatological and respiratory problems also ranked high. The Australian
Australian_Shepherd
German breed of dog
also recommends testing for haemophilia and hip dysplasia, other common problems with the breed. German Shepherds have been featured in a wide range of
German_Shepherd
Edge-joined polygons which fold into a polyhedron
Unsolved problem in mathematics Does every convex polyhedron have a simple edge unfolding? More unsolved problems in mathematics In 1975, G. C. Shephard asked
Net_(polyhedron)
Square tiles with a color on each edge
halting problem (the problem of testing whether a Turing machine eventually halts) then implies the undecidability of Wang's tiling problem. Combining
Wang_tile
Lemma
Shephard's lemma is a result in microeconomics having applications in the theory of the firm and in consumer choice. The lemma states that if indifference
Shephard's_lemma
German mathematician
of Salzburg in 2004. Rolf Schneider is known for his solution of Shephard's problem, his books on stochastic and integral geometry in long-standing collaboration
Rolf_Schneider
economics that describes the Minkowski addition of sets in a vector space Shephard's problem - a geometrical question Simplex - a generalization of the notion
List_of_convexity_topics
Covering by shapes without overlaps or gaps
if, the Turing machine does not halt. Since the halting problem is undecidable, the problem of deciding whether a Wang domino set can tile the plane
Tessellation
Existence of a line through two points
all of them. It is named after James Joseph Sylvester, who posed it as a problem in 1893, and Tibor Gallai, who published one of the first proofs of this
Sylvester–Gallai_theorem
American reality television series
season 3, Sardinia (Italy) in season 4 and Ibiza (Spain) in season 5. Glenn Shephard — Captain Byron Hissey — Chief Engineer Paget Berry — First Officer Adam
Below_Deck_Sailing_Yacht
Mathematical problem
Squaring the square is the problem of tiling an integral square using only other integral squares. (An integral square is a square whose sides have integer
Squaring_the_square
Tool for managing livestock
route. This variant, which has a prevalence of about 5%, imposes technical problems in angioplasty procedures. The letter lamed originated as a representation
Shepherd's_crook
Mathematical spiral tiling
with Form eines Neunecks eine Lösung zu einem Problem von Reinhardt ["On a nonagon as a solution to a problem of Reinhardt"]. Voderberg tiling is monohedral
Voderberg_tiling
which causes viewership to decrease, though clarified that he has "no problem with a comic book movie". As a solution to the lack of "investment in the
Cinema_of_the_United_States
1999 video game
Hazardous Environment Combat Unit (HECU). The player character, Adrian Shephard, is sent in to neutralize the Black Mesa Research Facility when a scientific
Half-Life:_Opposing_Force
Variety. Retrieved May 13, 2026. Bitran, Tara (May 31, 2024). "3 Body Problem Will Return For Seasons 2 and 3". Tudum. Archived from the original on
List of Netflix original programming
List_of_Netflix_original_programming
American street artist and activist (born 1970)
artists. O'Donoghue later posted an article, titled "Shepard Fairey’s Image Problem", on several independent media sites. O' Donoghue explored Fairey's use
Shepard_Fairey
Series of SUV models
Designer, Dies at 85". The New York Times. Retrieved 23 February 2016. Shephard, Dave. "The History of the Range Rover Marque". Archived from the original
Range_Rover
Mathematics book
patterns is a book by mathematicians Branko Grünbaum and Geoffrey Colin Shephard published in 1987 by W.H. Freeman. The book was 10 years in development
Tilings_and_patterns
Family of multi-role combat aircraft
Fish, Tim (16 July 2014). "Farnborough: Tornado will go out in style". Shephard Media. "Libya: UK planes to be deployed." BBC News, 18 April 2011. "Libya:
Panavia_Tornado
English singer and dancer (born 1978)
that Dixon's vocal strengths lie with more up-tempo songs, saying "the problem is that her bubbly personality (and voice) is simply not as well suited
Alesha_Dixon
"DSA 2022: Malaysian UNIFIL contingent to receive Ejder Yalçin 4x4s | Shephard". "Malaysian Defence - The More The Merrier". "Appreciation Parade for
List of equipment of the Malaysian Army
List_of_equipment_of_the_Malaysian_Army
American television series (2004–2010)
on what seems to be an uninhabited tropical island. Spinal surgeon Jack Shephard becomes their leader. Their survival is threatened by a number of mysterious
Lost_(TV_series)
System that relates geologic strata to time
Dalrymple, G. Brent (2001). "The age of the Earth in the twentieth century: a problem (mostly) solved". Special Publications, Geological Society of London. 190
Geologic_time_scale
Natural number
Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved
7
Political party in the United States
ISBN 978-0190086350. Smith, Jordan Michael; Logis, Rich; Logis, Rich; Shephard, Alex; Shephard, Alex; Kipnis, Laura; Kipnis, Laura; Haas, Lidija; Haas, Lidija
Republican Party (United States)
Republican_Party_(United_States)
Non-periodic tiling of the plane
colored edges, now known as Wang dominoes or tiles, and posed the "Domino Problem": to determine whether a given set of Wang dominoes could tile the plane
Penrose_tiling
Generalization of a polytope in real space
polytope the symmetry group (here a complex reflection group, called a Shephard group) acts transitively on the flags, that is, on the nested sequences
Complex_polytope
Canadian woman convicted of manslaughter and ex-wife of Paul Bernardo (born 1970)
80 km northeast of Montreal. In 1999, Toronto Star reporter Michelle Shephard came into possession of copies of her application to transfer to the Maison
Karla_Homolka
American political commentator (born 1961)
and reflects the irresistible temptation to attribute African American problems to a history of white racist oppression." A reviewer for The Journal of
Dinesh_D'Souza
American cable television news channel
original on November 15, 2019. Retrieved January 18, 2021. Shephard, Alex (August 6, 2020). "The Problem With MSNBC Isn't That It's Too Liberal". The New Republic
MS_NOW
American businessman and philanthropist (born 1955)
existential threat to civilization, stating that while it remains a serious problem, it was more important to give money to other causes such as solving poverty
Bill_Gates
American actor (born 1962)
manosphere. In 2004, McCarthy announced that he once had a serious alcohol problem, which began at age 12. He entered a detoxification program in 1992, and
Andrew_McCarthy
Geometry problem on tiling by hypercubes
higher dimensions. The proofs of these results use a reformulation of the problem in terms of the clique number of certain graphs now known as Keller graphs
Keller's_conjecture
Fictional character of the TV series Lost
past as a research specialist recruited to solve the Island's fertility problem where pregnant women die after conception. Prevented from leaving the Island
Juliet_Burke
American college football season
Retrieved December 3, 2025. Antonik, John (November 1, 2025). "Houston Had a Problem". wvusports.com. West Virginia University. Retrieved December 3, 2025.
2025 NCAA Division I FBS football season
2025_NCAA_Division_I_FBS_football_season
2023 maritime disaster
Adrienne Mahsa; Aronoff, Kate; Otten, Tori; Shephard, Alex; Otten, Tori; Otten, Tori; Otten, Tori; Shephard, Alex (1 November 2022). "Missing Titanic Sub
Titan_submersible_implosion
2011 American science fiction crime drama television series
privacy and "the greater good", the concept of justifiable homicide, and problems caused by working with limited information programs. Person of Interest
Person of Interest (TV series)
Person_of_Interest_(TV_series)
American politician (born 1972)
O'Rourke called the 2021 Texas power crisis a "symptom of a much larger problem". With no serious primary challenge, O'Rourke won the Democratic nomination
Beto_O'Rourke
Family of interceptor and reconnaissance aircraft
wartime and was studied on both sides of the Iron Curtain. The perennial problem with engines dedicated to vertical lift is they become mere dead weight
Mikoyan-Gurevich_MiG-25
Huey family of American military utility helicopters
control system. The four-member flight crew attempted to deal with the problem, but due to the very low altitude, the incident resulted in a crash.
Bell_UH-1_Iroquois
former Cabinet ministers Estelle Morris, Paul Boateng, Chris Smith, Gillian Shephard, Virginia Bottomley and Michael Portillo; the Father of the House of Commons
2005 United Kingdom general election
2005_United_Kingdom_general_election
British television series
May 2020. Retrieved 13 April 2020. Busby, Mattha (18 July 2018). "The problem with Love Island – by the people who turned it down". The Guardian. Archived
Love_Island_(2015_TV_series)
American actor and director (b.1943)
Year Title Role Notes 1967 Dragnet 1967 Billy Jones Episode: "The Big Problem" 1968 Judd, for the Defense Harry Crews Episode: "The Ends of Justice" 1968
Georg_Stanford_Brown
American journalist and political commentator (born 1984)
substantial criticism from left-leaning outlets. In The New Republic, Alex Shephard called the resignation a form of "self-cancellation" part of a pattern
Bari_Weiss
Israeli military technology company
DA-Group to offer GNSS immune technology – DB – Digital Battlespace – Shephard Media". www.shephardmedia.com. Retrieved November 19, 2019. Fortin, Matt
Elbit_Systems
Economics theorem
v(p_{1},p_{2},w)} is the value function of the constrained optimization problem characterized by the following Lagrangian: L = u ( x 1 , x 2 ) + λ ( w
Roy's_identity
Ian; Nanji, Noor (16 February 2024). "This Morning: Cat Deeley and Ben Shephard replace Holly Willoughby and Phillip Schofield". BBC News. BBC. Retrieved
2024_in_British_television
Chinese stealth fighter aircraft
original on 9 July 2021. Retrieved 8 July 2021. Axe, David (3 January 2019). "Problem: China's J-20 Stealth Fighter Doesn't Have a Gun". The National Interest
Chengdu_J-20
English media personality, actress and singer (born 1971)
series Hearts and Bones with Damian Lewis, the Jonathan Creek episode "The Problem at Gallowes Gate", and a Boxing Day special Agatha Christie's Marple episode
Amanda_Holden
2007 video game
Portal "makes physics, math, logic, spatial reasoning, probability, and problem-solving interesting, cool, and fun", a necessary feature to draw children
Portal_(video_game)
Expand description
assault and pay a small fine so he can avoid jail time. This becomes a problem when the shoving victim later goes into a coma and dies. Benny asks Bull
List of Bull (2016 TV series) episodes
List_of_Bull_(2016_TV_series)_episodes
Largest Civilian Rotorcraft Manufactured by Airbus Helicopters
H225 Super Puma helicopters. On 25 October 2012 it was announced that the problem was suspected to relate to the main gearbox vertical shaft; the AS 332
Eurocopter_EC225_Super_Puma
Possible degenerative disease
Brunswick Public Health (NBPH) website include memory problems, muscle spasms, balance problems, difficulty walking or falls, blurred vision or visual
New Brunswick neurological syndrome of unknown cause
New_Brunswick_neurological_syndrome_of_unknown_cause
British crime drama television series (2014–2023)
what local police in the Calder Valley call the area because of its drug problem. In the first episode of series one, Ryan points out to Catherine, visiting
Happy_Valley_(TV_series)
Earth Band 48 February 6, 2000 Stroud, Gloucestershire, England Liver problems Dave Peverett Foghat 56 February 7, 2000 Orlando, Florida, U.S. Renal cancer
List of 2000s deaths in popular music
List_of_2000s_deaths_in_popular_music
Difesa. Retrieved 19 August 2025. "The Italian Army's ambitious IFV plan | Shephard". www.shephardmedia.com. Retrieved 2024-06-14. Technologies, Italian Defence
List of equipment of the Italian Army
List_of_equipment_of_the_Italian_Army
American politician (born 1969)
2022. Shephard, Alex; Bacharach, Jacob; Bacharach, Jacob; Shiner, Meredith; Shiner, Meredith; Linkins, Jason; Linkins, Jason; Shephard, Alex; Shephard, Alex
John_Fetterman
Subdivision of the plane into polygons that are all regular
triangles and a single regular hexagon. However, this notation has two main problems related to ambiguous conformation and uniqueness. First, when it comes
Euclidean tilings by convex regular polygons
Euclidean_tilings_by_convex_regular_polygons
Shape bounded by non-intersecting line segments
Simple polygons are commonly seen as the input to computational geometry problems, including point in polygon testing, area computation, the convex hull
Simple_polygon
American actress (born 1980)
February 18, 2026. Waxman, Olivia B. (June 28, 2013). "Kristen Bell and Dax Shephard are PETA's Sexiest Celebrity Vegetarians". Time. Archived from the original
Kristen_Bell
becoming more political and less outrageous." Also, due to serious health problems, Michael Dunn appeared as Dr. Loveless in only one episode during this
List of The Wild Wild West episodes
List_of_The_Wild_Wild_West_episodes
American lawyer and politician (born 1957)
by moderate Republicans who run the Senate! Their problem is not me and the Democrats; their problem is themselves. Who are they? Are they these extreme
Andrew_Cuomo
Natural number
Sloane, N. J. A. (ed.). "Sequence A003432 (Hadamard maximal determinant problem: largest determinant of a (real) {0,1}-matrix of order n.)". The On-Line
32_(number)
Type of rotorcraft
maintaining steady flight with a crosswind presents an additional flight control problem, where strong crosswinds from certain angles will increase or decrease
Helicopter
American online newsletter platform
publication of extremist views because attempting to censor them would make the problem worse. Creators like Casey Newton, Molly White, and Ryan Broderick left
Substack
2014 book by Yuval Harari
review: 'urgent questions'". The Telegraph. Retrieved 29 October 2014. Ben Shephard. Sapiens: A Brief History of Humankind review – thrilling story, dark message
Sapiens: A Brief History of Humankind
Sapiens:_A_Brief_History_of_Humankind
Private liberal arts university in Austin, Texas
announced in October of 2021, billed as a new institution that could address problems in higher education. The announcement was met with significant media attention
University_of_Austin
Electric guitar shape
has been converted to hard-tail ("blocked"), which has solved the tuning problem and also improved tuning stability and provided even more sustain. Rosa
Star_(guitar)
from the original on 31 July 2023. Retrieved 31 July 2023. "No Army, No Problem: Iceland's Aid To Ukraine". Oryx. 20 July 2023. Archived from the original
List of military aid to Ukraine during the Russo-Ukrainian war
List_of_military_aid_to_Ukraine_during_the_Russo-Ukrainian_war
Japanese wheeled armoured fighting vehicle
(PDF). January 2025. "Japan selects Patria's AMV XP for WAPC replacement | Shephard". www.shephardmedia.com. Retrieved 10 November 2024. "Page 16 - Defence
Common tactical wheeled vehicle
Common_tactical_wheeled_vehicle
Major event in the run-up to the 2024 United states presidential election
18, 2024. Retrieved July 16, 2024. Bidgood, Jess (July 1, 2024). "The Problem in Plain Sight". The New York Times. Retrieved March 22, 2025. Garrison
Withdrawal of Joe Biden from the 2024 United States presidential election
Withdrawal_of_Joe_Biden_from_the_2024_United_States_presidential_election
Flat-sided three-dimensional shape
characteristics and the solution for the Seven Bridges of Königsberg's problem, underlying the field of topology. Johannes Kepler discovered two non-convex
Polyhedron
American defense technology company
products are used for reconnaissance in close-quarters combat and solving problems like room-clearing and fatal funnel. Nova is an autonomous quadcopter drone
Shield_AI
Transport aircraft family by Dornier
February 2016). "Singapore Airshow: Dornier 228 production ramps uu". Shephard Media. Retrieved 1 June 2017. Batey, Angus (15 June 2015). "RUAG, Dornier
Dornier_228
Convex polyhedron property
determine whether a given polyhedron is equiprojective. Shephard, G. C. (1968). "Twenty Problems on Convex Polyhedra: Part I". The Mathematical Gazette
Equiprojective_polyhedra
"Supporting roles – why forward repair systems are an in-demand capability | Shephard". plus.shephardmedia.com. Retrieved 31 January 2025. "FRSN – FORWARD REPAIR
List of equipment of the Royal Danish Army
List_of_equipment_of_the_Royal_Danish_Army
Islands (Disputed between Vanuatu and France so it could be in here or not) Shephard Islands Torres Islands Caroline Islands Faichuk Islands Nomiwisofo Group
List_of_archipelagos
American actress (1946–2025)
2025. James, Caryn (September 1, 1990). "Review/Film; Cat Lover With a Problem: Asthma". The New York Times. Archived from the original on December 11
Diane_Keaton
Finnish rifle cartridge
pressure limit before undergoing plastic deformation. Lapua tackled this problem by creating a hardness distribution ranging from the head and web (hard)
.338_Lapua_Magnum
American maritime patrol aircraft
February 2021. "Canada orders 14 Poseidon P-8A maritime patrol aircraft | Shephard". www.shephardmedia.com. Retrieved 16 June 2024. "Boeing: Orders and Deliveries
Boeing_P-8_Poseidon
at the Wayback Machine, Jian Junbo, Asia Times, 9 October 2009. Jessica Shephard (2007), 'Not a propaganda tool': China's Confucius Institutes are proliferating
Criticism of Confucius Institutes
Criticism_of_Confucius_Institutes
British and American comedian and television personality (born 1977)
2018 to 2019, Oliver worked as an executive producer for Wyatt Cenac's Problem Areas. On 30 August 2023, Oliver began hosting the comedy podcast Strike
John_Oliver
Bohdana Howitzer: 30 Units in Service, None Destroyed, and the "Positive Problem" With the Chassis | Defense Express". en.defence-ua.com. Retrieved 2024-02-20
List of wheeled self-propelled howitzers
List_of_wheeled_self-propelled_howitzers
Educational curriculum used in England since 1988
as an opportunity to promote cultural and moral values. Under Gillian Shephard's tenure as Education Secretary, a review of the National Curriculum was
National Curriculum for England
National_Curriculum_for_England
Skynyrd fan who first appeared in Mike Judge's animated short "The Honky Problem." He has a major role in "Way Down Mexico Way" as a drug mule and has cameos
List of Beavis and Butt-Head characters
List_of_Beavis_and_Butt-Head_characters
Polyhedron which tiles 3D space
tile space (such as various polycubes). Hilbert's eighteenth problem, one of Hilbert's problems, consisting of three subproblems, one of which is a three-dimensional
Space-filling_polyhedron
German-American political scientist and journalist (born 1982)
2024. The Purpose of Persuasion, persuasion.community. Shephard, Alex (8 July 2020). "The Problem With Yascha Mounk's Persuasion". The New Republic. ISSN 0028-6583
Yascha_Mounk
Concept in microeconomics
from the Utility Maximization Problem, Hicksian Demand comes from the Expenditure Minimization Problem. The two problems are mathematical duals, and hence
Hicksian_demand_function
Transport helicopter family by Sikorsky
deprecated archival service (link) "SAR-H bidders announce helicopter types". Shephard Group. March 11, 2009. Archived from the original on July 25, 2009. Retrieved
Sikorsky_S-92
UK school that specialises in certain subject areas
pioneer Cyril Taylor dies aged 82". Schools Week. Retrieved 28 October 2022. Shephard, Gillian (7 July 1995). Design & Technology: the future (Speech). DATA
Specialist schools in the United Kingdom
Specialist_schools_in_the_United_Kingdom
Pictures with The Learning Channel (TLC) 22 December Moscow, We Have a Problem, about the Mir EO-23 collision in 1997; Mir had a fire on 24 February 1997;
List_of_Equinox_episodes
SHEPHARDS PROBLEM
SHEPHARDS PROBLEM
Boy/Male
Hindu
Delightful
Surname or Lastname
English
English : variant spelling of Shepherd.Americanized form of some Jewish surname sounding like or meaning ‘shepherd’.
Boy/Male
British, English
Shepherd
Boy/Male
Irish
Shepherd.
Boy/Male
English
Shepherd.
Surname or Lastname
English
English : variant spelling of Shepherd.
Boy/Male
American, British, English
Shepherd
Boy/Male
English
Shepherd
Boy/Male
Latin
Shepherd.
Boy/Male
American, Anglo, British, English
Shepherd
Surname or Lastname
English
English : variant spelling of Shepherd.
Surname or Lastname
English
English : variant spelling of Shepherd.
Boy/Male
Muslim
Shepherd
Boy/Male
British, English, Jamaican
Shepherd
Boy/Male
Australian, British, English
Shepherd
Boy/Male
Anglo, British, English
Shepherd
Boy/Male
Hindu, Indian
Charming; Delightful
Boy/Male
Basque
Shepherd.
Boy/Male
British, English
Shepherd
Surname or Lastname
English
English : from Middle English schepherde ‘shepherd’ (composed of words meaning ‘sheep’ + ‘herdsman’ or ‘guardian’), hence an occupational name for a shepherd. This English form of the name has absorbed cognates and equivalents from several other languages (for forms, see Hanks and Hodges 1988).
SHEPHARDS PROBLEM
SHEPHARDS PROBLEM
Boy/Male
Tamil
Good qualities
Male
Greek
(Πελάγιος) Greek name derived from the word pelagos ("the sea"), PELAGIOS means "of the sea."
Girl/Female
Tamil
Talented, Performer
Boy/Male
Hindu, Indian
Replicate; Format
Girl/Female
Tamil
Tasteful
Boy/Male
Tamil
Lord Murugan
Boy/Male
Indian, Punjabi, Sikh
Radiating the Light of Holy Word
Girl/Female
Tamil
Prasuti | பà¯à®°à®¸à¯à®¤à®¿
Daughter of Manu and wife of Daksha Prajapathi
Boy/Male
Muslim
Heart of Love in the sea
Girl/Female
Muslim
Princess
SHEPHARDS PROBLEM
SHEPHARDS PROBLEM
SHEPHARDS PROBLEM
SHEPHARDS PROBLEM
SHEPHARDS PROBLEM
n.
A hut or shelter for shepherds of fishers. See Sheeling.
n.
A gray plaid; -- used by shepherds in Scotland.
v. i.
To act as a herdsman or a shepherd.
n.
A hook fastened to pole, by which shepherds lay hold on the legs or necks of their sheep; a shepherd's crook.
a.
Of or pertaining to shepherds; hence, relating to rural life and scenes; as, a pastoral life.
n.
The conductir of a mule team; also, a head shepherd.
p. p. & a.
Clothed; arrayed; dressed; as, he was habited like a shepherd.
a.
Of or pertaining to the life and occupation of a shepherd; pastoral; rustic.
n.
A little shepherd.
n.
A silicle, or short pod, as of the shepherd's purse.
n.
A poem describing the life and manners of shepherds; a poem in which the speakers assume the character of shepherds; an idyl; a bucolic.
n.
The pastor of a church; one with the religious guidance of others.
a.
Resembling, or becoming to, a shepherd; pastoral; rustic.
n.
A shepherd; one who has the care of flocks and herds.
imp. & p. p.
of Shepherd
n.
Resembling a shepherd; suiting a shepherd; pastoral.
p. pr. & vb. n.
of Shepherd
v. t.
To tend as a shepherd; to guard, herd, lead, or drive, as a shepherd.
n.
The god of shepherds, guardian of bees, and patron of fishing and hunting. He is usually represented as having the head and trunk of a man, with the legs, horns, and tail of a goat, and as playing on the shepherd's pipe, which he is said to have invented.
n.
A man employed in tending, feeding, and guarding sheep, esp. a flock grazing at large.