Knoji’s Equation Station – Your July Maths Challenge

Hello Mathletes! This July, we’re all about tangents.

When we’re chatting, a tangent is when what we say barely connects with the topic at hand.

When we’re talking maths, a tangent is a single point where two lines touch.

In calculus, a tangent line captures the curve’s direction at a single point, offering a momentary glimpse into its behaviour.

In this challenge, we explore the interplay between a straight line and an exponential curve

A quick history lesson

Long before calculus had a name, Pierre de Fermat was already thinking about how to find the slope of a curve at a single point. His early ideas about tangents—lines that just touch a curve without crossing it—paved the way for what we now call differentiation.

Real life applications

🧪 Physics & Engineering

Example: Car velocity at a point, stress points on a bridge

Use: Calculating speed, acceleration, forces at a moment

📊 Economics & Business

• Use: Finding max profit/min cost (optimisation)
• Example: Setting the ideal product price

🧠 Data Science & AI

• Use: Adjusting models using gradient descent
• Example: Training a machine learning model

🎮 Animation & Computer Graphics

• Use: Smoothing curves and movement paths
• Example: Animating natural motion in games or films

Maths challenge question:

• 🔎
• Solution!

Click “Solution!” to check your answers!