#### The Kanizsa Triangle: You Can't Believe Your Eyes

September 3rd, 2014

Mathematics is always thought to be difficult, abstract and far from everyday life. The following video (the view is strongly recommended in full screen) shows exactly the contrary, or at least, how mathematics relates to our daily life.

In the following lines, we would like to explain the interplay between the equations and the situations that appear in the video, respectively on the left and on the right. Who has never rolled a couple of dices or seen the weather forecasts?

**Lamp**. Waves (and therefore light) are mathematically described by the elementary mathematical functions of sine and cosine**Dices**. Probability is naturally associated to the roll of dices.**Snow**. Snowflakes have a fractal structure; the formula describes how to compute the area of a snowflake.**Spinning top**. The movement of a heavy gyroscope is described by the equations of a rigid body in classical mechanics.**Magnifying glass**. Equations of reflection in optics.**Compass**. The magnetic field and the Maxwell equations.**Coffee.**This is chemistry, but there are mathematical models for chemical reactions.**Clouds**. Weather forecasts use sophisticated mathematical models to predict results.**Computer**. The binary code is the language of a computer.**Plant**. An algorithm to build a fractal tree.**Finger prints**. Genetics use mathematics to compare different DNAs.**Sounds in the underground**. The wave equation and sounds.**Gas station**. The stock market is a classical stochastic model.**Rocket**. A mathematical model for aircraft flight dynamics.**Wires**. The role of mathematics in modern engineering

**References**:

Photo: Tom_Brown6117

mathematics, waves, optics, Maxwell equations, fractals, DNA, binary code