Created by Dave Richeson.

Science and Math
Science and Math World

(From 11/ 2013 to 11/2017): It has been 4 years since, I created my blog on Tumblr: Spring of Mathematics. I remember that: Geometry in daily life (Herb pot) is my first post on Tumblr.

Currently, I am also very happy for teaching mathematics and research. After a long time, I have been working with the lecture hall. My mathematical passion hasn’t diminished.

Thank you everyone and the Tumblr math community! I’ve learned so many things and had lots of fun. Thank you all 🙂

**Brachistochrone Problem & cycloid. **

GIF:Source is Vsauce / The Brachistochrone :https://www.youtube.com/watch?v=skvnj67YGmw.

**Which is the quickest path?** …. The cycloidis is the curve which yields the quickest descent.

Suppose there is an incline such as that shown in Figure 1. When a ball rolls from A to B, which curve yields the shortest duration? Let’s assume that we have three hypotheses: a straight line, a quadratic, and a cycloid. The shortest path from A to B is the straight line, so one might think that the straight path is the fastest, but in fact it is surprisingly slow. It’s better to select a path which has a downward drop in order to accelerate the ball in the first phase, so that it rolls quickly. The ball arrives earlier on the quadratic path than on the straight line path. However, increasing the degree of the function causes the ball to travel more slowly on the flat section.

It is said that Galileo (1564-1642) first presented this problem. It is also known that the cycloid is the curve which yields the quickest descent. This time I will discuss this problem, which may be handled under the field known as the calculus of variations, or variational calculus in physics, and introduce the charming nature of cycloid curves.

See more atThe Brachistochrone Curve: The Problem of Quickest Descent by Yutaka Nishiyama- PDF.

** (**Written by** poet ****Lilia Rose )**

*Shapes of the Past.Numbers of the PresentVariables of the Future.*

*Shapes are different for every little hand drawing them,every grown-up touching them.Sometimes they miss a point,only later to remember and disappoint,in finding it too late to mend,that broken shape.*

*Numbers are the same every time you see them,a constant in problems and mazes of wits.Yet, with 1 careless mistake,it changes, never to be fixed again,because you wrote in pen,with the confidence of a youth, the bane and talent of adolescence.*

*Variables change every time you try to simplify them.Yet they never change their appearance,staying the same throughout.Until that moment, reaching the last step,they just become additional numbers,that might be the right or wrong solution,later confirmed with substitution. *

Wow! 🙂

[https://soundcloud.com/huyn-n-y/shining-the-morning-cd1-morning]

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