Archive for the ‘Geometria differenziale’ Category

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The Asteroid is the envelope of a family of lines...

lunedì, Dicembre 21st, 2020

asteroid,curve,envelope
Fig. 1

Exercise

Determine the envelope of the lines on which the coordinate axes detach a segment of constant length a.


Solution
We write the equation of the generic line of the assigned family. For this purpose, let's look at the figure:


Here we denote by φ the angle that the aforementioned straight line forms with the x axis. His equation is therefore:


The family equation follows:


where


(altro…)



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How do you find the envelope of a family of curves?

lunedì, Dicembre 21st, 2020

How do you find the envelope of a family of curves?
Fig. 1

Exercise

Determine the envelope of the family of plane curves:


Solution
The system of equations that interests us is


where


for which


(altro…)



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