## Archive of posts with tag “from zhihu”

• ### Free trade (single good case)

I set up a simple model to determine the production and consumption in free trade between nations.

• ### Relationship between the Gini coefficient and the variance

Both the Gini coefficient and the variance are measures of statistical dispersion. We are then motivated to find the relationship between them. It turns out that there is a neat mathematical relationship between them.

• ### Distinguishing all the letters in handwritten math/physics notes

Personally, I have the demand of handwriting math/physics notes, but an annoying fact about this is that I usually cannot distinguish every letter that may be possibly used well enough. In this article, I will try to settle this problem.

何为手纸本?

• ### Introducing bra–ket notation to math learners

Bra–ket notation is a good-looking notation! I am sad that it is not generally taught in math courses. Let me introduce it to you.

• ### Even solutions to bound states in an odd number of $\delta$ potential wells

We try solving the even function solutions to the time-independent Schrödinger equation for the potential $V=-\alpha\sum_{j=-n}^n\delta(x-ja)$ such that $E<0$ (bound states).

• ### Defend our earth against aliens’ bullets!

The aliens intiated their attack to the earth! They shoot bullets with mass $m$ and speed $v$ from a far-awar planet. To defend, humans built a field $U=\alpha/r$ that can repel the bullets. What regions are safe? The answer turns out to be the interior of a circular paraboloid.

• ### How to construct mechanics in higher dimensions?

We can derive the equation of motion for mechanical systems in a Galileo universe with $\iota$ time dimensions and $\chi$ space dimensions by generalizing the principle of relativity and Hamilton’s principle.

Suppose a supersonic airplane has Mach number $M$. It flies horizontally. At some time, it flies past over your head at height $h$. Then, the distance between you and it when you have just heard it is $Mh$.
Sometimes the curvature radius of a curve can be found by using physical methods although it seems that you must use calculus to find it. In this article, the curvature radius of the curve $x^2=2py$ at the point where the curvature radius is smallest is found by using physical methods without using calculus (with only high school knowledge). The answer is that the smallest curvature is exactly $p$, and the point with smallest curvature is the vertex.