I found this geometric reasoning (or proof) of a derivative of a Tangent function in Tristan Needham’s book on Visual Differential Geometry and it struck me as something really intuitive, simple and beautiful. I wanted to do similar derivations for other simple trigonometric functions, namely, Sine and Cosine of an angle. Although I was able to get the answers, it was not that succint or elegant as the proof of the Tan function....
The Monty Hall problem is an interesting puzzle in probability which has a counter-intuitive answer. In fact, it is documented that many people got the answer wrong and many people continue to get the answer wrong. The problem The problem goes somewhat like this: Imagine a game show. There are 3 doors and behind one door there is a car and behind the other 2, goats. The player picks a door hoping to win a car that’s behind the door....
Life needs energy to survive. Energy is needed to perform basic life functions like movement, hunting and gathering, protecting from prey and natural elements. It is converted from one form to another. Eventually, the energy within the living organism is expelled from the organism while useful work is performed. Why and how energy for life? Work is done when there is change in energy. In other words, energy has to go somewhere, so work gets done....
Emacs org-mode is an emacs major mode used for note keeping, project planning and for creating documents and articles. It has many export options from markdown to pdf to latex. While all this is great for document generation, it can also be used for creating presentations with org-reveal. Still, this needs a browser and sometimes you really have more text than a few bullet points and want a simpler option to just focus on the text under each heading by narrowing to each heading as you present....
While I was refreshing some concepts in statistics, I came up with a problem I thought I could ask ChatGPT (talk about attention deficit). I am still using the cheap ChatGPT3.5, so what I am about to show may not work on the expensive ChatGPT4.0. Here’s an example on how it can mislead while solving math problems and one should already have an inkling how to solve the problem (or atleast have an estimate of the answer) to do some prompt engineering to finally get to a solution....
Mosquito bats work great for killing mosquitoes and flies. Until they don’t work! They hardly last one mosquito generation. It turns out that the rechargeable battery in them go bad fairly quickly. So as a small hack, I took out the cheap battery they come with and replaced it with a decent rechargeable LiIon 3.7v 2200mah one. You have to modify the battery housing a little bit by carving out some extra bits of plastic to make the 18650 type battery to fit....
The Marangoni effect is a phenomenon in fluid dynamics where a change in surface tension along the interface of two fluids causes the movement of liquid (Ref. 1). This effect can be demonstrated using a toy boat with soap or camphor mounted at the center/rear of the boat touching the water. The dissolved soap or camphor causes a reduction of surface tension of water at the back of the boat compared to the surface tension of water at the front....