11165
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Pythagorean Triangles with the Same Area
Explore Pythagorean triangles with the same area. They appear in sets of three because the legs (
a
and
b
) and the hypotenuse (
c
) can be written in three different ways in terms of parameters
r
and
s
.
Contributed by:
Enrique Zeleny
THINGS TO TRY
Automatic Animation
SNAPSHOTS
DETAILS
The lengths of the legs
and
and the hypotenuse
can be written in terms of integers
and
as
,
,
that have three sets of solutions for
and
given by
,
;
,
;
,
.
RELATED LINKS
Pythagorean Triple
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Pythagorean Triangles with the Same Area
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/PythagoreanTrianglesWithTheSameArea/
Contributed by:
Enrique Zeleny
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 Demonstrations
More by Author
Pythagorean Triples Star
Enrique Zeleny
Primitive Pythagorean Triples on a Curvilinear Grid Defined by Euclid's Formula
Enrique Zeleny
Plotting Pythagorean Triples
Enrique Zeleny
Enumerating Pythagorean Triangles
Jaime Rangel-Mondragon
Twin Pythagorean Triples
Alvaro Jose Ibarra Rivas (Institucion Educativa Santa Fe Santiago de Cali,Colombia)
Pythagorean Primitive Triples Using Primes
Robert L. Brown
Twin and Nearly Twin Pythagorean Triples
Robert L. Brown
Dudeney's Proof of the Pythagorean Theorem
Izidor Hafner
An Intuitive Proof of the Pythagorean Theorem
Yasushi Iwasaki
Euclid's Formula and Properties of Pythagorean Triples
Kenneth E. Caviness and R. Lewis Caviness
Related Topics
Greek Mathematics
Number Theory
Plane Geometry
Triangles
High School Finite Mathematics
High School Geometry
High School Mathematics
Browse all topics
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
Mathematica Player
or
Mathematica 7+