# Endless Snowflake

Hard

Have you ever wondered if it's possible to create a shape with an infinite perimeter but a finite area? With this project, you can explore the possibilities of fractals and power series to construct a snowflake and discover new families of curves with infinite perimeters and finite areas.

## Hypothesis

The hypothesis is that it is possible to construct shapes with infinite perimeters but finite areas.

## Method & Materials

You will use the Geometer's Sketchpad program and a Koch curve to construct a snowflake and calculate its area.

You will need the Geometer's Sketchpad program and a Koch curve.

## Results

This project reveals that it is possible to construct shapes with infinite perimeters but finite areas. Using the idea of convergent series, it is possible to add ever-smaller increments of area such that while the perimeter grows to infinity, the sum of the areas remains finite.

## Why do this project?

This science project is unique because it explores the possibilities of fractals and power series to construct a snowflake and discover new families of curves with infinite perimeters and finite areas.

## Also Consider

Experiment variations to consider include exploring the possibility of generalizing this approach to three dimensions, producing a shape of infinite surface area and finite volume, and constructing a snowflake with a different shape than the traditional triangular Koch curve.

## Full project details

You can find additional information and details for this science fair project here. Have fun exploring!Share this Science Project:

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