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In geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain ... more
A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more
A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more
A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more
Tortuosity is a property of curve being tortuous (twisted; having many turns). There have been several attempts to quantify this property. ... more
In geometry, the conic constant (or Schwarzschild constant, after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the ... more
Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more
Sight distance is dependent on the type of curve used and the design speed. For crest curves, sight distance is limited by the curve itself, as the curve ... more
Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more
In physics, the Young – Laplace equation, is a nonlinear partial differential equation that describes the capillary pressure difference sustained ... more
A lens is a transmissive optical device which affects the focusing of a light beam through refraction. A simple lens consists of a single piece of ... more
In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are well ... more
Centripetal force (from Latin centrum “center” and petere “to seek”) is a force that makes a body follow a curved path: its ... more
The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point. In a suitable coordinate system with three axes x, y, and z, it ... more
A bimetallic strip is used to convert a temperature change into mechanical displacement. The strip consists of two strips of different metals which expand ... more
In hyperbolic geometry, the law of cosines is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar ... more
The Plateau–Rayleigh instability, often just called the Rayleigh instability, explains why and how a falling stream of fluid breaks up into smaller packets ... more
The incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of ... more
The hyperbolic paraboloid (not to be confused with a hyperboloid) is a doubly ruled surface shaped like a saddle. In a suitable coordinate system, a ... more
The circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The center of this circle is ... more
Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.
A
... more
In science, buckling is a mathematical instability that leads to a failure mode.
When a structure is subjected to compressive stress, buckling may ... more
Two circles of non-equal radius, both in the same plane, are said to be tangent to each other if they meet at only one point.
Two circles are
... more
Spirograph is a geometric drawing toy that produces mathematical roulette curves as hypotrochoids and epitrochoids. A fixed outer circle of radius R is ... more
Spirograph is a geometric drawing toy that produces mathematical roulette curves as hypotrochoids and epitrochoids. A fixed outer circle of radius R is ... more
A hyperbola is a type of smooth curve, lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola ... more
The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point. In a suitable coordinate system with three axes x, y, and z, it ... more
Two circles of non-equal radius, both in the same plane, are said to be tangent to each other if they meet at only one point.
Two circles are
... more
In trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. ... more
Aside from momentum, when a vehicle makes a turn, two forces are acting upon it. The first is gravity, which pulls the vehicle toward the ground. The ... more
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