An Essay — Under the pitch dark firmament, there were flashes galore, as signs of guidance for travellers. Romantic views for lovers. And mating signals between male and female fireflies. A girl was holding a jar, in an innocent and thoughtless attempt to collect fireflies. Unbeknownst to her, such a seemingly harmless act…

An Essay — I was sitting in front of my computer, scrolling through social media. Posts after posts, tweets after tweets. Pictures of conventionally attractive and photogenic women bathing in the sun, smiling, and enjoying glasses of a cocktail. The skies are always blue and the places are always exotic. It hurt. It…

This will be an ongoing list of geometry problems I have posted on medium. Feel free to give them a try. What Is The Length Inside The Square? A square with side length 1 has an inscribed semicircle along one of its edges as shown. The red line starts at the top…medium.com What Is The Area Of The Square? The circle has a radius 1. The diagonal of the square extends to be a tangent of the circle. The circle touches the…medium.com

The Fundamental Theorem Of Calculus — If you have taken high school calculus, you probably have computed a definite integral to find the area under a curve. But have you ever thought about the relation between the two, in particular, why the value of the definite integral gives us the area under the curve. Well, I…

Can You Find The Surface Area? 🔪🩸 — The diagram to the right shows a cube sliced in half. Find the total surface area of the sliced cube to the nearest integer. Give this problem a try before jumping in for the solution! Solution We will reconstruct the cube as shown below.

Think Carefully! — The red figure at the right is made of two hemispheres of equal radius. The blue cylinder at the left has the same radius and height as the red figure. Which shape has a larger surface area? Give this problem a try before jumping in for the solution! Solution We will…

Most People Got It Wrong! — Three 6-sided fair dice are rolled together. P(n) denotes the probability of obtaining a total sum of n. What is the relationship between P(9) and P(10)? Give this problem a try before jumping in for the solution! Solution If you have tried working through all the possible combinations of P(9) and…

Can You Solve It? — Evaluate the integral Give this problem a try before jumping in for the solution! Solution To start off, we will let I be our integral

Are You Smart Enough To Solve It? — Evaluate the integral Give this problem a try before jumping in for the solution! Solution We will start off with the following substitution