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Structured problem improvement approach
A3 problem solving is a structured problem-solving and continuous-improvement approach, first employed at Toyota and typically used by lean manufacturing
A3_problem_solving
Process of achieving a goal by overcoming obstacles
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from
Problem_solving
Topics referred to by the same term
Konkin III A3 problem solving, a structured problem solving and continuous improvement approach, first employed at Toyota Samsung Galaxy A3, a smartphone
A3
Problem-solving tools
lit. 'theory of inventive problem solving') is a methodology which combines an organized, systematic method of problem-solving with analysis and forecasting
TRIZ
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Method of identifying the fundamental causes of faults or problems
A3 problem solving – Structured problem improvement approach Eight disciplines problem solving – Eight disciplines of team-oriented problem solving method
Root-cause_analysis
Measures of product quality
constant level Eight disciplines problem solving – Eight disciplines of team-oriented problem solving method A3 problem solving Garvin, David A. (1987). "Competing
Eight_dimensions_of_quality
Iterative interrogative technique
Fantin, Ivan (2014). Applied Problem Solving. Method, Applications, Root Causes, Countermeasures, Poka-Yoke and A3. Ivan Fantin. ISBN 978-1499122282
Five_whys
Decision problem in computer science
ISBN 0-7167-1045-5. A3.2: SP13, pg.223. Lagarias, J. C.; Odlyzko, A. M. (1985-01-01). "Solving low-density subset sum problems". Journal of the ACM.
Subset_sum_problem
Problem optimization method
sub-problems means that the space of sub-problems must be small, that is, any recursive algorithm solving the problem should solve the same sub-problems over
Dynamic_programming
Problems which attempt to find the most efficient way to pack objects into containers
asymptotically O(a3/5). Packing squares in a circle: Good solutions are known for n ≤ 35. Packing identical rectangles in a rectangle: The problem of packing
Packing_problems
Recreational mathematics planar boundary and area problem
problem is either of two related problems in recreational mathematics involving a tethered goat grazing a circular area: the interior grazing problem
Goat_grazing_problem
Polynomial-time algorithm for the assignment problem
Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods
Hungarian_algorithm
Geometry problem about finding touching circles
circles be denoted as C1, C2 and C3. Van Roomen solved the general problem by solving a simpler problem, that of finding the circles that are tangent to
Problem_of_Apollonius
a_{1}a_{2}a_{3}\ldots \ } where a0 is an integer, the integer part of x, and a1, a2, a3, ... are integers between 0 and 9. Given this representation the number x
Hermite's_problem
Controlled-access highway in Italy
The Autostrada A3 is an autostrada (Italian for "motorway") 53.6 kilometres (33.3 mi) long in Italy located in the region of Campania, which runs from
Autostrada_A3_(Italy)
Polynomial equation of degree 3
Hippocrates, Menaechmus and Archimedes are believed to have come close to solving the problem of doubling the cube using intersecting conic sections, though historians
Cubic_equation
Problem in computer science
A3.1: SP3, pg.221. Vazirani, Vijay V. (2001). Approximation Algorithms. Springer-Verlag. ISBN 978-3-540-65367-7. [1]: A Pascal program for solving the
Set_packing
Type of mathematical expression
equation. Solving Diophantine equations is generally a very hard task. It has been proved that there cannot be any general algorithm for solving them, or
Polynomial
Form of reasoning
rhetoric Case-based reasoning – Process of solving new problems based on the solutions of similar past problems Correlation does not imply causation – Refutation
Deductive_reasoning
Decision problem pertaining to equivalence of expressions
problems are undecidable, i.e. there is no general algorithm for solving this problem. This even holds if we limit the systems to have finite presentations
Word_problem_(mathematics)
Humorous chess puzzle
only legal moves lead directly to the "solution": 1. d4 b5 2. d5 b4 3. axb4 a3 4. b5 a2 5. b6 a1=any 6. b7# Tim Krabbé provides other examples on his chess
Joke_chess_problem
Nazi ballistic missile series
area. As part of Operation Lighthouse the first A3 was launched on 4 December 1937, but suffered problems with premature parachute deployment and engine
Aggregat
Polynomial function of degree 4
F_{1}(x)\times F_{2}(x)=x^{4}+cx^{2}+dx+e.} We therefore can solve the quartic by solving for s and then solving for the roots of the two factors using the quadratic
Quartic_function
Chess opening
E24 – 4.a3 (E24–E29 cover the Sämisch Variation) E25 – 4.a3 Bxc3+ 5.bxc3 c5 E26 – 4.a3 Bxc3+ 5.bxc3 c5 6.e3 E27 – 4.a3 Bxc3+ 5.bxc3 0-0 E28 – 4.a3 Bxc3+
Nimzo-Indian_Defence
Computer that uses photons or light waves
Hamiltonian path problem. The simplest problem is the subset sum problem. An optical device solving an instance with four numbers {a1, a2, a3, a4} is depicted
Optical_computing
Strongly NP-complete problem in computer science
The 3-partition problem is a strongly NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned
3-partition_problem
Appendix on analytic geometry by Descartes
the distances to the other two lines (in the four line case). In solving these problems and their generalizations, Descartes takes two line segments as
La_Géométrie
Abstract strategy board game
8×8 board with a computer search, solving all the possible openings. In 2013, Jakub Pawlewicz and Ryan B. Hayward solved all openings for 9×9 boards, and
Hex_(board_game)
Chess opening
Nc6 6.Ngf3 Be7 7.0-0 0-0 8.e5 Nd7 9.Re1 b5 10.Nf1 b4 11.h4 a5 12.Bf4 a4 13.a3 bxa3 14.bxa3 Na5 15.Ne3 Ba6 16.Bh3 d4 17.Nf1 Nb6 18.Ng5 Nd5 19.Bd2 Bxg5 20
King's_Indian_Attack
Australian and American mathematician (born 1975)
medal 2026 – Companion of the Order of Australia — (2006). Solving mathematical problems. A personal perspective (Second edition of 1992 original ed
Terence_Tao
Method of exponentiation using a minimal number of multiplications
addition chain for a15 above, the subproblem for a6 must be computed as (a3)2, since a3 is re-used (as opposed to, say, a6 = a2(a2)2, which also requires three
Addition-chain_exponentiation
Expression of symbolic information
to model the movement of the tides in a bay, may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations
Formula
Chess variant played on a 6×6 board without bishops
ISBN 0-9524142-0-1. Newell, Allen; Simon, Herbert Alexander (2019). Human problem solving. Brattleboro, Vermont: Echo Point Books & Media. ISBN 978-1-63561-792-4
Los_Alamos_chess
Thought experiment on artificial intelligence
981. Searle 2009, p. 1. Simon, H., & Newell, A. (1958). Heuristic Problem Solving: The Next Advance Operations Research, 6(1), 1-10 Quoted in Crevier
Chinese_room
Chess opening
Black to trade the b4-bishop with 11.Nb3 followed by 12.a3, Black has the reply 11...a4 12.a3 Bc3! keeping the balance. The move ...Bb4+ can also be effective
Budapest_Gambit
years. Attempts have been made to solve the problem pointed out by Pryce, known as Pryce's theorem, and other problems with the composite photon theory
Neutrino_theory_of_light
3rd-century Greek mathematician
Diophantine equations. The methods for solving such equations is called Diophantine analysis. Most of the Arithmetica problems lead to quadratic equations. Diophantus
Diophantus
American children's television show
for the problem-solving portions of an episode, as did their comprehension and problem solving. Anderson stated, "As children learned how to solve the problems
Blue's_Clues
Chess opening
abandon protection of the d5-knight with 9.a3, a move Yakov Estrin recommended, but Black is quite strong after 9.a3 Nxc2+ 10.Kd1 Nd4!? or 10...Nxa1! 11.Nxd5
Fried_Liver_Attack
Networking protocol for clock synchronization
packet, t 3 + θ − δ / 2 = t 2 {\displaystyle t_{3}+\theta -\delta /2=t_{2}} Solving for θ yields the definition of the time offset. The values for θ and δ
Network_Time_Protocol
Alternate storytelling in media
lessons of ARGs to similarly take advantage of new media and collective problem–solving". As such, implementation of ARGs in these different settings involves
Alternate_reality_game
17th-century conjecture proved by Andrew Wiles in 1994
centuries and was solved with mathematics Fermat would not have known. The claim eventually became one of the most notable unsolved problems of mathematics
Fermat's_Last_Theorem
Geometric technique for designing mechanical linkages
center point for A is the center of the circle that passes through A1, A2 and A3 in the three positions. Similarly, the center point for B is the center of
Burmester's_theory
Artificial helium-like atom with a harmonic instead of Coulomb potential
force a2 = 0 and a3 = 0 respectively, and as a consequence of the three term recession, all higher coefficients also vanish. Solving for k {\displaystyle
Hooke's_atom
Properties underlying modern physics
powerful methods for solving problems and predicting what can happen. While conservation laws do not always give the answer to the problem directly, they form
Symmetry_in_quantum_mechanics
educational measurement refers to a "simplified description of human problem solving on standardized educational tasks, which helps to characterize the
Attribute_hierarchy_method
Chess opening
dxe4 5.a3, followed by either 5...Be7 6.Nxe4, returning the pawn, or 5...Bxc3+ 6.Nxc3 Nc6, holding on to the pawn. 4.Bd3, defending e4. 4.a3 Bxc3+ 5
French_Defence
Unproved conjecture in mathematics
curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after
Birch and Swinnerton-Dyer conjecture
Birch_and_Swinnerton-Dyer_conjecture
Graph structure studied in group theory
a, a2, a3} in the multiplication table, with a4 = e. The inverse a−1 = a3 is also a generator of this cycle: (a3)2 = a2, (a3)3 = a, and (a3)4 = e. Similarly
Cycle_graph_(algebra)
Compact astronomical body
for the existence of black holes". Classical and Quantum Gravity. 16 (12A): A3–A21. arXiv:astro-ph/9912186. Bibcode:1999CQGra..16A...3C. doi:10.1088/0264-9381/16/12A/301
Black_hole
1974 book by Robert M. Pirsig
usually able to diagnose and repair himself through the use of rational problem-solving skills. For example, when the narrator and his friends come into Miles
Zen and the Art of Motorcycle Maintenance
Zen_and_the_Art_of_Motorcycle_Maintenance
Mathematical relation making a non-equal comparison
Inequalities (Lecture notes). Shapiro, Harold (2005). "Mathematical Problem Solving". The Old Problem Seminar. Kungliga Tekniska högskolan. "3rd USAMO". Archived
Inequality_(mathematics)
Polynomial equation of degree 4
F_{1}F_{2}=x^{4}+cx^{2}+dx+e\qquad \qquad (4)} We therefore can solve the quartic by solving for w and then solving for the roots of the two factors using the quadratic
Quartic_equation
Problem-solving technique in applied mathematics using order-of-magnitude approximations
equilibrium equation: Scale analysis is very useful and widely used tool for solving problems in the area of heat transfer and fluid mechanics, pressure-driven wall
Scale_analysis_(mathematics)
Root-finding algorithm
= 9.26891, so we set a3 = a2 and b3 = −1.42897. In the fourth iteration, we use inverse quadratic interpolation between (a3, f(a3)) = (−4, −25) and (b2
Brent's_method
Arithmetic operation
in essence modern notation, when in L'algèbre de Viète he wrote Aiii for A3. Early in the 17th century, the first form of our modern exponential notation
Exponentiation
Chess opening
.Bb7 5.a3 became the more common move order to reach the Petrosian system by the mid-1980s, where White has avoided 4.a3 c5 5.d5 Ba6 and 4.a3 Ba6. 5.Bg5
Queen's_Indian_Defense
German battle rifle
mount. The Ak 4D will be used by the Swedish Army as a stop-gap DMR. DIO G3-A3 Bullpup: Iranian bullpup variant of the G3. The Pakistani models are manufactured
Heckler_&_Koch_G3
Graph without triples of adjacent vertices
triangle detection can be solved in time O ( m 1.407 ) {\displaystyle O(m^{1.407})} . Another approach is to find the trace of A3, where A is the adjacency
Triangle-free_graph
Irish scriptwriter and actor
completely. Emily Porter's Diary: Down Above Above Above won first prize in the A3: Fiction for Young People (13–15) Competition in the Oireachtas Literary Competitions
Richie_Conroy
in fact 3 values: Low, High, Unknown. A Positive Logical Algebra solves this problem via virtualization, by creating a Virtual Environment which allows
Virtual_finite-state_machine
In business operations, controlling the process of production of goods
operations research and management science (as multi-disciplinary fields of problem solving). While systems engineering concentrated on the broad characteristics
Operations_management
Submarine-launched ballistic missile
achieve their goals. To obtain the major gains in performance of the Polaris A3 in comparison to early models, there were many improvements, including propellants
UGM-27_Polaris
Type of prime number
1978 that if all the factors of p − 1 are less than logc p, then the problem of solving discrete logarithm modulo p is in P. Therefore, for cryptosystems
Strong_prime
Soviet super heavy-lift launch vehicle (1965–1972)
still experiencing combustion stability problems. Rocketdyne eventually solved the F-1 instability problems by adding copper dividers as baffles, but
N1_(rocket)
Small family car range produced by Cupra and SEAT
fourth generation use the Volkswagen Group MQB platform, also used by the Audi A3 Mk3 and Mk4, Volkswagen Golf Mk7 and Mk8 and Škoda Octavia Mk3 and Mk4. The
SEAT_León
Hungarian mathematician
open problems. In 2016, Pyber and Endre Szabó proved that in a finite simple group L of Lie type, a generating set A of L either grows, i.e., |A3| ≥ |A|1+ε
László_Pyber
Technique to compress data
L} is the maximum length of a codeword. No algorithm is known to solve this problem in O ( n ) {\displaystyle O(n)} or O ( n log n ) {\displaystyle
Huffman_coding
Argument for the existence of God
be God." The argument from contingency is formulated as the Third Way (Q2, A3) in the Summa Theologica. It may be expressed as follows: There exist contingent
Cosmological_argument
Underground railway cars
electricity. A3 trains have begun refurbishment for A3-64 and A3-66 from 2003 to 2006, known as A3E, but 8 trains were scrapped in 2000. Based on the A3, the
Berlin_U-Bahn_rolling_stock
Object-oriented software design pattern
subcategorized as a creational pattern. The factory method design pattern solves problems such as: How can an object's subclasses redefine its subsequent and
Factory_method_pattern
American cryptographer (born 1947)
partial words in documents; he later published this work as a journal paper.[A3] His research from this time on self-organizing lists[A4] became one of the
Ron_Rivest
Chess opening
and World Chess Championship 1985. Another option after 11...Bf8 is 12.a3. With a3, White controls the b4-square further, preventing Nc6–Nb4 ideas, and
Ruy_Lopez,_Zaitsev_Variation
Angers Critics of the Military". The New York Times. Reuters. 1989-10-09. p. A3. Retrieved 2021-06-24. "Strange case of kidnapping". The Independent. April
List of solved missing person cases (1970s)
List_of_solved_missing_person_cases_(1970s)
1986 American public fundraising event
hands held state together", Wilmington Morning News, May 26, 1986, page A3. Ciliberti, Dino. "Divers bridge gap in hands across the Susquehanna", Wilmington
Hands_Across_America
American talk radio host (1934–2022)
and began chatting with callers. He got the reputation of being a problem-solver, and comedian Mort Sahl, a big fan of his, jokingly called him "the
Michael Jackson (radio commentator)
Michael_Jackson_(radio_commentator)
Chess opening
queen's knight does little to utilize White's advantage of the first move. On a3, the knight does not control central squares, and White would have to move
Durkin_Opening
Chinese automobile manufacturing company
outside the Anhui province for several years. During that period, Chery solved the problem by piggybacking on a SAIC Motor license until 2003. In this period
Chery
American serial rapist and serial killer (born 1945)
California and has been called second only to Virginia's in effectiveness in solving cold cases. In an attempt to increase awareness, crime writer Michelle
Joseph_James_DeAngelo
Hemoglobin with ferric iron unable to carry oxygen
cyanide adduct is to prevent the binding of free cyanide to the cytochrome a3 group in cytochrome c oxidase. Methemoglobin is expressed as a concentration
Methemoglobin
pieces, see Fairy chess piece; terms specific to chess problems, see Glossary of chess problems; named opening lines, see List of chess openings; chess-related
Glossary_of_chess
Chess opening
seek counterplay on the kingside. 7...a6 Black forces White's knight back to a3. 8.Na3 The immediate 8.Bxf6 forces 8...gxf6, when after 9.Na3, Black can transpose
Sicilian Defence, Sveshnikov Variation
Sicilian_Defence,_Sveshnikov_Variation
Chinese automobile manufacturer
Chuanfu, Chairman and President of BYD Company, released "Xuanji A3" (Chinese: 璇玑A3), BYD's 567th automobile-grade chip and first in-house developed assisted
BYD_Auto
Use of a GPU for computations typically assigned to CPUs
algorithm solving the resource-constrained project scheduling problem is freely available on GitHub; the GPU algorithm solving the nurse scheduling problem is
General-purpose computing on graphics processing units
General-purpose_computing_on_graphics_processing_units
2010s diesel emissions scandal involving Volkswagen
the scientific humor magazine Annals of Improbable Research for "solving the problem of excessive automobile pollution emissions by automatically, electromechanically
Volkswagen_emissions_scandal
Chess opening
Qc2 Bb7 10.Bd2 Ra7 11.Rc1 Be4 12.Qb3 Nc6 13.e3 Qa8 14.Qd1 Nb8 15.Ba5 Rc8 16.a3 Bd6 17.Nbd2 Bd5 18.Qf1 Nbd7 19.b4 e5 20.dxe5 Bxe5 21.Nxe5 Nxe5 22.f3 Nc4 23
Catalan_Opening
Propaganda term for WWII German weapons programmes
term Wunderwaffe now generally refers to a universal solution which solves all problems related to a particular issue, mostly used ironically for its illusionary
Wunderwaffe
American activist (born 1973)
Tonight with John Oliver, where they discussed the importance of solving the problem of public shaming and how her situation may have been different if
Monica_Lewinsky
German mathematician (1882–1935)
invariant theory was to solve the "finite basis problem". The sum or product of any two invariants is invariant, and the finite basis problem asked whether it
Emmy_Noether
Chess test suite
Bc2 Kf3 a3 bxa3 Bxa3 g6 Bxg6 Bxb3 Kf8 Ke2 Bf5 f3 Bd7 Bc4 Bc1 Kf2 Ba4 FEN r1b2rk1/1p1nbppp/pq1p4/3B4/P2NP3/2N1p3/1PP3PP/R2Q1R1K w - - 0 15 Problem 10 Van
Nolot
Chess opening
on White's knight, which often ends up driven to the edge of the board on a3. The theoretically critical next move is 6.Ndb5, threatening Nd6+. All other
Sicilian_Defence
Cubic polynomials defined from a monic polynomial of degree four
cubic is defined only when P(x) is a quartic in depressed form—that is, when a3 = 0. Note that the fourth and fifth definitions below also make sense and
Resolvent_cubic
Chess opening
problem glossary joke chess Chess prodigy Elo rating system Mechanical Turk Simultaneous exhibition Tie-breaking in Swiss-system tournaments Solving chess
Barnes_Opening
Canadian politician (born 1979)
defended his investments, saying that he and his wife are "helping solve the problem by providing affordable rental accommodations to two deserving families"
Pierre_Poilievre
United States historic place
2005). "Time Capsule of Hawaiian King Located". The Victoria Advocate. p. A3. "Radar quickly pinpoints site of Kamehameha V capsule". Honolulu Star-Bulletin
Aliʻiōlani_Hale
Electric convertible sports car (2008–2012)
now we just need some cars". Pogue, David (April 5, 2007). "Solving the Car Propulsion Problem". The New York Times. Motors, Tesla (May 15, 2008). "Program
Tesla Roadster (first generation)
Tesla_Roadster_(first_generation)
Chess opening
problem glossary joke chess Chess prodigy Elo rating system Mechanical Turk Simultaneous exhibition Tie-breaking in Swiss-system tournaments Solving chess
Zukertort_Opening
American actor (1928–1994)
A3. Retrieved April 29, 2025 – via Newspapers.com. "George Peppard, Elizabeth Ashley Granted Divorce". Los Angeles Times. February 28, 1972. p. A3. Retrieved
George_Peppard
Advantage of White over Black in chess
Dorfman, Ron (28 October 2007). "The 'Bilbao Draw' – how it doesn't solve the problem". chessbase.com. ChessBase. Retrieved 21 January 2024. Friedel, Frederic
First-move_advantage_in_chess
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
Male
Greek
(Οἰδίπους) Greek name composed of the elements oid "knew" and pous "feet," probably with the intended OIDIPOUS means "he who knew the Sphinx's riddle of the feet." In mythology, this is the name of a king of Thebes who unknowingly killed his father and married his mother after solving the riddle of the Sphinx.Â
Surname or Lastname
English
English : variant of Preble.
Boy/Male
Tamil
Born during the rainy season, Money
Girl/Female
Muslim/Islamic
Away from all Problems
Boy/Male
Hindu
Born during the rainy season, Money
Boy/Male
Hindu, Indian
Problem
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Boy/Male
African, Australian, Hindu, Indian
Flowers
Boy/Male
Muslim
Problem solver
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Surname or Lastname
English
English : variant of Preble.
Boy/Male
Indian, Tamil
People with this Name are Preferably Intelligent and Very Generous; Highly Knowledgeable in Problem Solving Skills
Girl/Female
Indian, Telugu
Destroyer of Problems
Surname or Lastname
English
English : unexplained. It may be a variant of a medieval name, Preville, a habitational name from a Norman place named with the elements pré ‘meadow’ + ville ‘settlement’. However, this theory is not supported by evidence of early forms.
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
Girl/Female
Indian
Boy/Male
Muslim
One has many followers
Boy/Male
Tamil
(Maternal uncle of Krishna who usurped the throne from his father, Ugrasena. He was killed by Krishna. Details of his life are found in the Bhagavata Purana.)
Girl/Female
Arabic, Muslim
Pure; True; Clear; Real
Girl/Female
Tamil
Wise
Female
Egyptian
, the wife of Smen.
Male
Hebrew
 Variant spelling of Hebrew Emmet, EMMETT means "truth." Compare with another form of Emmett.
Girl/Female
American, Anglo, Australian, Danish, French, German, Irish, Latin
Alive; Lively; Full of Life; Vibrant; Form of Vivi
Boy/Male
Bengali, Indian
Beautiful
Male
Egyptian
, Mer-ba.
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
n.
One who proposes problems.
n.
Prowler; thief.
n.
The act or process of solving; solution; as, the resolution of an equation or problem.
n.
Same as Proleg.
n.
Proem.
a.
Having the nature of a problem; not shown in fact; questionable; uncertain; unsettled; doubtful.
imp. & p. p.
of Probe
v. t.
To propose problems.
v. t.
To examine, as a wound, an ulcer, or some cavity of the body, with a probe.
n.
A question proposed for solution; a matter stated for examination or proof; hence, a matter difficult of solution or settlement; a doubtful case; a question involving doubt.
n.
To begin to deal with; as, to tackle the problem.
n.
Same as Proleg.
n.
A problem to be solved, or an example to be wrought out.
n.
Anything which is required to be done; as, in geometry, to bisect a line, to draw a perpendicular; or, in algebra, to find an unknown quantity.
n.
A problem of more than usual difficulty added to another on an examination paper.
n.
The quantities or relations which are assumed to be given in any problem.
a.
Not solvable; insoluble; admitting no solution or explanation; as, an insolvable problem or difficulty.
n.
Something not easily solved; an intricacy; a difficulty; a perplexity; a problem.
v. i.
To work, as at a puzzle; as, to puzzle over a problem.
n.
One of the fleshy legs found on the abdominal segments of the larvae of Lepidoptera, sawflies, and some other insects. Those of Lepidoptera have a circle of hooks. Called also proped, propleg, and falseleg.