Motivation — My favourite song is Legends Never Die from League of Legends. I don’t play the game anymore. But their music always motivates me to keep going in life. What I love most about Legends Never Die is the mentality and grit the song imbues in all of us. Legends Never…

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…

Seneca said every night before bed, we should tell ourselves that our lives have ended and we have come back to life. Everything is extra. This is all bonus time. I very much agree with it. We have done everything that we wanted in our past lives. And this is…

Can You Solve It? — Two cotangent circles are constructed such that AB is a straight line as shown. The dashed lines are tangent to the smaller circle. Find the missing angle. Give the problem a try before jumping in for the solution! Solution 1

Sangaku — A circle is constructed within an equilateral triangle of side length 2 using three congruent sectors as shown. What is the area of the circle? Give this problem a go before jumping in for the solution! Solution 1 We will construct a 30, 60, 90 triangle as follows.

Geometry Challenge — The sides of an equilateral unit triangle are used to construct three squares with Svertices that touch a circle as shown. Find the area of the circle. Give the problem a go before jumping in for the solution! Solution 1 We know that the centres of the circle and the triangle are…

Can You Solve Them? — Problem 1 Let x be a real number. What is the minimum value of the following expression?

Geometry Problem — A point P is chosen at random inside a square QRST. What is the probability angle RPQ is acute? Give the problem a go before jumping in for the solution! Solution From knowledge of circle geometry, we know that if the angle RPQ is 90 degrees, then P lies on a…

Three Squares — The black triangle is drawn, and a square is drawn on each of its edges. The three shaded triangles are then formed by drawing three lines which join vertices of the squares and a square is now drawn on each of these three lines. The total area of the original…