Wolfram Demonstrations Project

Given an equilateral triangle with side length 2, the radius

of any of the inscribed equal circles depends on the number of circles inscribed. Before reading Details, see if you can notice a pattern in the answer as you vary

Contributed by: Abraham Gadalla

Slider Zoom
Gamepad Controls
Automatic Animation

For a given

, the radius of a circle is

. The ratio of the total area of the circles to the area of the triangle is

, which approaches

approaches

This Demonstration is based on [1], problem 15, Chapter 11.

Reference

[1] J. Stewart, Calculus: Early Transcendentals, 5th ed., Belmont, CA: Brooks/Cole, 2007.

Abraham Gadalla

"Pool Circles"
http://demonstrations.wolfram.com/PoolCircles/
Wolfram Demonstrations Project
Published: July 18, 2011

- Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Download Demonstration as CDF »

Download Author Code »(preview »)

Files require Wolfram CDF Player or Mathematica.

Related Curriculum Standards

Common Core State Standards for Mathematics

RELATED RESOURCES

Mathematica » The #1 tool for creating Demonstrations and anything technical.	Wolfram\|Alpha » Explore anything with the first computational knowledge engine.	MathWorld » The web's most extensive mathematics resource.	Course Assistant Apps » An app for every course— right in the palm of your hand.
Wolfram Blog » Read our views on math, science, and technology.	Computable Document Format » The format that makes Demonstrations (and any information) easy to share and interact with.	STEM Initiative » Programs & resources for educators, schools & students.	Computerbasedmath.org » Join the initiative for modernizing math education.

Pool Circles

THINGS TO TRY

SNAPSHOTS

DETAILS

PERMANENT CITATION

Related Topics

Related Curriculum Standards