tautochrone problem
E923653
The tautochrone problem is a classic question in physics and calculus of variations that seeks the curve along which a bead sliding under gravity reaches the lowest point in the same time regardless of its starting position, whose solution is a cycloid.
All labels observed (1)
| Label | Occurrences |
|---|---|
| tautochrone problem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11398739 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: tautochrone problem Context triple: [brachistochrone problem, relatedConcept, tautochrone problem]
-
A.
brachistochrone problem
The brachistochrone problem is a famous challenge in the calculus of variations that asks for the curve along which a particle will descend between two points in the shortest time under gravity, whose solution is a cycloid.
-
B.
Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
-
C.
Hamilton–Jacobi equation
The Hamilton–Jacobi equation is a fundamental partial differential equation in classical mechanics that reformulates dynamics in terms of a generating function, providing a powerful bridge to quantum mechanics and modern analytical methods.
-
D.
Tusi couple
The Tusi couple is a geometric device from medieval Islamic astronomy that generates linear motion from the sum of two circular motions, later influencing Copernican models of planetary motion.
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E.
Chaplygin R
Chaplygin R is a small satellite impact crater on the Moon located near the larger Chaplygin crater on the lunar far side.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: tautochrone problem Target entity description: The tautochrone problem is a classic question in physics and calculus of variations that seeks the curve along which a bead sliding under gravity reaches the lowest point in the same time regardless of its starting position, whose solution is a cycloid.
-
A.
brachistochrone problem
The brachistochrone problem is a famous challenge in the calculus of variations that asks for the curve along which a particle will descend between two points in the shortest time under gravity, whose solution is a cycloid.
-
B.
Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
-
C.
Hamilton–Jacobi equation
The Hamilton–Jacobi equation is a fundamental partial differential equation in classical mechanics that reformulates dynamics in terms of a generating function, providing a powerful bridge to quantum mechanics and modern analytical methods.
-
D.
Tusi couple
The Tusi couple is a geometric device from medieval Islamic astronomy that generates linear motion from the sum of two circular motions, later influencing Copernican models of planetary motion.
-
E.
Chaplygin R
Chaplygin R is a small satellite impact crater on the Moon located near the larger Chaplygin crater on the lunar far side.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
physics problem
ⓘ
problem in the calculus of variations ⓘ |
| alsoKnownAs | isochronous curve problem NERFINISHED ⓘ |
| application |
design of isochronous pendulum clocks
ⓘ
understanding timekeeping accuracy ⓘ |
| assumes |
frictionless motion
ⓘ
motion constrained to a fixed curve in a vertical plane ⓘ uniform gravitational field ⓘ |
| category |
classical variational problem
ⓘ
isochronous systems ⓘ |
| curveEquationForm | cycloid generated by a circle rolling along a straight line ⓘ |
| definition | problem of finding a curve along which a bead sliding under gravity reaches the lowest point in the same time regardless of starting position ⓘ |
| field |
calculus of variations
ⓘ
classical mechanics ⓘ mathematical physics ⓘ |
| historicalPeriod | 17th century ⓘ |
| inspiredDevelopment |
advances in the theory of cycloids
ⓘ
development of the calculus of variations ⓘ |
| involvesConcept |
Euler–Lagrange equation
NERFINISHED
ⓘ
conservation of energy ⓘ differential equations ⓘ isochronous motion ⓘ parametric representation of curves ⓘ time of descent under gravity ⓘ |
| keyProperty | time of descent is independent of starting point along the curve ⓘ |
| mathematicalFormulation | variational problem minimizing time of descent with isochrony constraint ⓘ |
| physicalModel | bead sliding on a wire in a vertical plane under gravity ⓘ |
| relatedTo |
brachistochrone problem
ⓘ
cycloid ⓘ pendulum theory ⓘ simple harmonic motion ⓘ |
| requires |
neglect of air resistance
ⓘ
no rolling or rotational kinetic energy of the bead ⓘ |
| solutionCurve | cycloid ⓘ |
| solutionMethod |
imposition of isochrony condition to determine curve shape
ⓘ
integration of time element along the curve ⓘ use of energy conservation to express velocity as a function of height ⓘ |
| solutionProperty | the cycloidal pendulum has a period independent of amplitude for small oscillations ⓘ |
| solutionUniqueness | the cycloid is the unique solution under standard assumptions NERFINISHED ⓘ |
| studiedBy |
Christiaan Huygens
NERFINISHED
ⓘ
Gottfried Wilhelm Leibniz NERFINISHED ⓘ Isaac Newton NERFINISHED ⓘ Johann Bernoulli NERFINISHED ⓘ |
| timeIndependenceCondition | descent time is constant for all starting points above the lowest point ⓘ |
| typicalAssumption |
point mass bead
ⓘ
rigid wire or track ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: tautochrone problem Description of subject: The tautochrone problem is a classic question in physics and calculus of variations that seeks the curve along which a bead sliding under gravity reaches the lowest point in the same time regardless of its starting position, whose solution is a cycloid.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.