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  2. Parabola - Wikipedia

    en.wikipedia.org/wiki/Parabola

    The point F is the foot of the perpendicular from the point V to the plane of the parabola. [c] By symmetry, F is on the axis of symmetry of the parabola. Angle VPF is complementary to θ, and angle PVF is complementary to angle VPF, therefore angle PVF is θ. Since the length of PV is r, the distance of F from the vertex of the parabola is r ...

  3. Conic section - Wikipedia

    en.wikipedia.org/wiki/Conic_section

    The type of the conic is determined by the type of cone, that is, by the angle formed at the vertex of the cone: If the angle is acute then the conic is an ellipse; if the angle is right then the conic is a parabola; and if the angle is obtuse then the conic is a hyperbola (but only one branch of the curve). [27]

  4. Geometrical-optical illusions - Wikipedia

    en.wikipedia.org/wiki/Geometrical-optical_illusions

    The widely accepted interpretation of, e.g. the Poggendorff and Hering illusions as manifestation of expansion of acute angles at line intersections, is an example of successful implementation of a "bottom-up," physiological explanation of a geometrical–optical illusion. Ponzo illusion in a purely schematic form and, below, with perspective clues

  5. Menaechmus - Wikipedia

    en.wikipedia.org/wiki/Menaechmus

    Menaechmus (Greek: Μέναιχμος, c. 380 – c. 320 BC) was an ancient Greek mathematician, geometer and philosopher [1] born in Alopeconnesus or Prokonnesos in the Thracian Chersonese, who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube using the ...

  6. Convex curve - Wikipedia

    en.wikipedia.org/wiki/Convex_curve

    It is an example of a hedgehog, a type of curve determined as the envelope of a system of lines with a continuous support function. The hedgehogs also include non-convex curves, such as the astroid , and even self-crossing curves, but the smooth strictly convex curves are the only hedgehogs that have no singular points.

  7. Gabriel's horn - Wikipedia

    en.wikipedia.org/wiki/Gabriel's_horn

    Graph of = /. Gabriel's horn is formed by taking the graph of =, with the domain and rotating it in three dimensions about the x axis. The discovery was made using Cavalieri's principle before the invention of calculus, but today, calculus can be used to calculate the volume and surface area of the horn between x = 1 and x = a, where a > 1. [6]

  8. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    Angle trisection is the construction, using only a straightedge and a compass, of an angle that is one-third of a given arbitrary angle. This is impossible in the general case. For example, the angle 2 π /5 radians (72° = 360°/5) can be trisected, but the angle of π /3 radians (60°) cannot be trisected. [8]

  9. Projectile motion - Wikipedia

    en.wikipedia.org/wiki/Projectile_motion

    The only force of mathematical significance that is actively exerted on the object is gravity, which acts downward, thus imparting to the object a downward acceleration towards Earth's center of mass. Due to the object's inertia, no external force is needed to maintain the horizontal velocity component of the object's motion.