# Questions tagged [envelope]

In geometry, an Envelope of a family of curves is a curve that touches each member of that family at same family. Therefore it is the limiting curve of intersection of contiguous members the initial family.

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### First Order Condition with 1 decision variable and 2D state space

TL;DR: I'm trying to find the first-order condition (FOC) for an optimization problem with two state variables and one control variable. I don't want the value function $V$ to appear in the FOC but ...
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### Can a one parameter family of surfaces be only once-differentiable?

Reviewing this and that resource, I see that a one parameter family of curves has equation $$f(x,y,z,t)=0 \tag{1}$$ where $t$ is the parameter. And I see that the equation of the envelope of the ...
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### circle envelope tangent in another circle

As the picture shows, One big circle ,$(0,0)$ ,radius=R, there is a small circle in it, $(m,0)$ ,radius=r . G is on the big circle. From G ,we can do two tangent lines about the small circle. Get ...
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### How do you find the area of an egg shape formed from the union of circles whose diameters are horizontal chords of the unit circle? [closed]

This egg is the union of the red circles, whose diameters are horizontal chords of (the upper half of) the unit circle. How do you find its area? Some background information on this egg is shown ...
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### Solving the second example problem from the Wikipedia page on evelopes

While reading the Wikipedia page on Envelopes there are some examples given. In the second example a jump is made from a linear equation to $F(x,y,t)=0$ form. For context the transformation is made ...
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### Graph Envelope Constraint puzzles from The Witness game.

The computer game "The Witness" contains various puzzles based on a finite square grid graph arranged in the usual way. A path must be found from a given point on the edge to another. Each square can ...
Let $A$ and $B$ be two bugs lying on two distinct points $a_0, b_0$ on a fixed circle. They start to walk along the circle in the same direction such that at time $t$ their coordinates $a_t, b_t$ ...