What Are These Curves?
This picture was taken in a hotel. A light is installed against the wall, and it casts beautiful shadow curves on the wall. What kind of curves are these from a mathematical perspective?
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AI GeneratedMay contain errors
Video Summary
AI GeneratedThe speaker describes discovering mathematical patterns in everyday life after noticing the curved shadows cast by a hotel wall light. By applying the definitions of conic sections, the speaker concludes that the resulting shadow curves are likely hyperbolas, as the wall acts as a section plane for the light source.
I took this picture in a hotel. A light is installed against the wall and it casts
beautiful shadow curves on the wall. I started wondering what kind of curves these are
from a mathematical perspective. I double-checked the definition of conic sections.
There are four types, circles, ellipse, parabolas, and hyperbolas. Based on the definition,
the shadow curve should be very close to a hyperbola. Please see the explanation here.
Assuming the light is a point light, the vertical wall is like a section plane.
Isn't it interesting to find the final math in your daily lives?