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
THINGS TO TRY
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
This Demonstration is based on , problem 15, Chapter 11.
 J. Stewart,
Calculus: Early Transcendentals
, 5th ed., Belmont, CA: Brooks/Cole, 2007.
Wolfram Demonstrations Project
Published: July 18, 2011
Embed Interactive Demonstration
More details »
Download Demonstration as CDF »
Download Author Code »
More by Author
Fraction of a Circle Covered by Arcs of a Given Length
Problems on Circles XIII: Common Area of Two Circles
Minimum Area between a Semicircle and a Rectangle
Coverage of a Unit Square by Random Discs
Optimal Rectangles for Circles
Ed Pegg Jr
Area between a Line and the Graph of a Function
The Area between Two Circles
Making the Three Areas Defined by Congruent Overlapping Circles Equal
Kenneth E. Caviness and Eugene Stewart
Largest Isosceles Triangle Inscribed in a Circle
Cumulative Area under a Cycloid versus the Area of Its Rolling Circle
Browse all topics
Related Curriculum Standards
US Common Core State Standards, Mathematics
The #1 tool for creating Demonstrations
and anything technical.
Explore anything with the first
computational knowledge engine.
The web's most extensive
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
STEM Initiative »
Programs & resources for
educators, schools & students.
Join the initiative for modernizing
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
© 2016 Wolfram Demonstrations Project & Contributors |
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have