Discover the general equation of the tangent line to the circumference $x^2 + y^2 - 2x + 4y + 1 = 0$ by the point $(3,4)$. NO CALCULUS. by the circumferen...

For example, if I need to find the equation of the line parallel to $$2x-3y=4$$ which passes through the point $(1,-5)$ I know how to do this by putting i...

I am going over a paper in which a theorem includes a condition that certain arcs are "properly-immersed geodesic arcs" in a surface $\Sigma$ with nonempt...

Why is it that, in calculus of variations (specifically Euler-Lagrange), we can take the derivative of a function with respect to a function $f$ and set t...

If I have a problem such as this: We need to enclose a field with a fence. We have 500m of fencing material and a building is on one side of the field and...

I know that it has something to do with Elliptic Curves in the Complex Plane but I don't have an intuitive sense as to what its there for. I understa...

Minton and Smith, in "Calculus" define the chain rule for full derivatives $\frac {dz} {dt}$ as it follows: Vretblad, however, in "Fourier Analysis and it...

I am studying the second partial derivative test and it says when determinant of the hessian matrix is $0$ then there is no conclusion. However I saw on a...

I just did the classification of the isometries of the Euclidean Plane using some results of linear algebra and euclidean geometry, guiding myself through...

Assume $A$ is an arbitrary $m\times n$ real matrix. Is $\det(AA^T)$ always positive? Is it non-negative or it can have any value? Edit: It seems I have to...