Conics sections in 3D world

A conic section is a curve obtained from a cone's surface intersecting a plane.

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Conic section in 2D space

A short experiment

​Reflection property of parabola

Reminder:
any point on the parabola is equidistant from the directrix and the focus.

We are going to discuss the 3D counterparts to our 2D conic sections.

Cylinder

Parabolic/Hyperbolic Cylinder

Sphere

Ellipsoid

• Please search the internet for anything or any structure that is in an elliptical paraboloid shape.

• Send me as quick as possible by AirDrop.

Radio telescope

Reflector installed in the lighthouse

is traditionally lit at Olympia, Greece, using a parabolic reflector concentrating sunlight

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The Olympic Flame

• Raise your hands and answer directly

Lee Valley VeloPark, Stratford, London

​​The James Evans house of 1960

• Please search the internet for anything or any structure that is in a hyperboloid shape.

• Either one-sheet or double-sheet

• Send me as quick as possible by AirDrop.

The Corporation Street Bridge in Manchester, England

Cooling tower of a nuclear power plant

Canton Tower, Guangzhou, China

National Stadium Singapore

​​Sonic boom

shock waves created when an object travels through the air faster than the speed of sound

• ​Conic sections are the plane section of the quadratic surfaces (e.g. cones) in 3 dimensional space

• The 3D surfaces can be obtained by rotating or translating the 2D conic sections along the axis of symmetry.

​More reference

https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/06%3A_Appendices/6.01%3A_A_Appendices/6.1.08%3A_A.8_Conic_Sections_and_Quadric_Surfaces

​More reference

https://calcworkshop.com/vectors-and-the-geometry-of-space/quadric-surfaces/