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Circle Area Formula

Supports the conceptual understanding of where the formula A=π*r² comes from.

Author: Nevil Hopley

Topic:  Mathematik

Tags  Kreisformeln ,  Fläche

The primary aim of this activity is to explain the formula for the area of a circle. Instead of presenting the formula as is, students can explore the limiting process of slicing a circle up into progressively more and more sectors.

Physically cutting up a circle with scissors into sectors and then rearranging these pieces has long been a traditional approach in the classroom, but often students only saw one example, and then had to generalise from that. This activity gives them access to all the other examples required to better appreciate and understand the extension of this idea.

Whilst it is easier - and often only necessary - for students to know how to process the formula πr², this activity applies knowledge of areas of rectangles, parallelograms and trapeziums to working out the area of a new shape, the circle.

The idea of a limit tending towards an exact answer will be required later in their mathematical careers, primarily in the topics of geometric series and calculus. This activity serves as an early introduction to this important mathematical technique.