Hey wilbsy.
Have you taken a calculus course? If you know calculus you can solve this through an optimization problem.
two questions, on the same vein...
the radius of the red circle is given, and its center point is always at 0,0.
point A moves, tracing the path of the red circle.
given point A, how would you calculate the remaining point coordinates to form the largest possible square within the red circle?
given point A, how would you calculate the remaining point coordinates to form the largest possible equilateral triangle within the red circle?
thanks!
Because this is posted in the trigonometry sub-forum it can be done without calculus.
If is any point on a circle centered at with radius there is unique equilateral triangle inscribed in the circle with a vertex at .
Suppose that then
The angle is the angle makes with the positive x-axis.
The coordinates of can now be written as
Here are the coordinates of the other vertices: .
In case of the square, do the exact same steps using
i took some pre-cal years ago, but even in that my working knowledge is definitely sub-par. i'd be curious to know the calculus approach to this problem... i'm using these equations in a program, so it's always good to know all the potential methods in order to optimize the code.
would it be appropriate to continue on this thread? or should we move it over to the calculus sub-forum?
thanks!
If you rotate a point (x, y) by radians counterclockwise around the origin (in the case of the triangle, and for the square ), the new coordinates are and . In matrix form,
.
Some languages have libraries for 2D drawing that include transformations, in particular, rotation. For example, in Java there is a class AffineTranformation and a function that returns an object of this class that performs rotation. You can use this object to transform individual points, shapes or the entire canvas. This way, you don't necessarily have to understand how matrices inside AffineTranformation work.
Here calculus can be used only to make sure that the vertices of the largest triangle lie on the circle, which is obvious anyway.
Hello, wilbsy!
The radius of the circle is given, and its center point is at (0,0).
Given point A, how would you calculate the remaining point coordinates
to form the largest possible square within the circle?
With a square, no trigonometry or calculus is needed.
Suppose vertex is in Quadrant I with coordinates
Then the other vertices are easily located.
Code:| D * * * (-q,p)o | * * | * A * | o(p,q) | * | * - - * - - - - + - - - - * - - * | * | (-p,-q)o | * C * | * * | o(q,-p) * * * B |
Whereas I think that Soroban should have provided a method or at least hints to get to his solution we can calculate that the quadrilateral has two pairs of parallel sides, the sides all meet at right angles, and all sides have the same length...these points form a square.
-Dan