Final products of the learning situation 'Approaching Infinity

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The concept of infinity (symbol: ∞) appears in various branches of mathematics, philosophy, and astronomy,1​ referring to a quantity without limit or end, contrasting with the concept of finiteness.

In mathematics, infinity appears in various forms: in geometry, the point at infinity in projective geometry and the vanishing point in descriptive geometry; in mathematical analysis, infinite limits; and in set theory as transfinite numbers.

Here, we present two final products generated in the learning situation where a construction was requested to provide a simple understanding of the concept of infinity.

The first one is a physical construction that you can observe in the following video:

Spanish video with English subtitles

Video in English

The second one is a graphic animation generated with GeoGebra, where a window is represented through which the various digits that make up the number π (pi) orderly pass. This number has an infinite number of digits, and the construction demonstrates that one of these digits is always passing through the window, regardless of the moment you look at it.

The construction can be seen at the following link.