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. …

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…