MathLapse - Inscribed Angle Theorem


MathLapse - Inscribed Angle Theorem


Submitted by


Pavel Boytchev

MathLapse Festival 2016 Winner. Experiencing the Inscribed Angle Theorem.

The Inscribed angle theorem states that in a circle the measures of all inscribed angles subtending to the same arc are the same. 

Is it possible to feel this theorem and to experience a situation when this theorem manifests itself in a simple, yet effective way?

Imagine a round room with a door. While you walk next to the wall, the visible width of the door should remain the same. At least this is what the theorem makes us expect.

The most interesting thing is how two opposite effects cancel each other: the width of the door depends on the distance, but it also depends on the point of view. When we go further away from the door, it should be seen narrower, but at the same time we are reaching a more frontal point of view (we move along the wall of a round room!), thus the door should be seen wider. The final outcome is that the width remains constant.

Could you explain why the visible height of the door is not affected by this phenomena? 


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