Share <Embed>

FREE Shipping on orders over $25.00 shipped by Amazon or get Fast, Free Shipping with Amazon Prime

Arrives: Wednesday, Jan 6 Details

Only 4 left in stock - order soon.
As an alternative, the Kindle eBook is available now and can be read on any device with the free Kindle app.

Secure transaction

Ships from	Amazon.com
Sold by	Amazon.com

Details

Ships from

Amazon.com

Sold by

Amazon.com

Add a gift receipt with prices hidden

+ $3.99 shipping

Used: Acceptable | Details

Sold by goodwillswmi

Have one to sell?

Sell on Amazon

Flip to back Flip to front

Listen Playing... Paused You're listening to a sample of the Audible audio edition.
Learn more

See all 2 images

Follow the Author

Wacław Sierpiński

Pythagorean Triangles (Dover Books on Mathematics) Paperback – Illustrated, November 2, 2011

by Waclaw Sierpinski (Author)

6 ratings

Part of: Dover Books on Mathematics (210 Books)

See all formats and editions Hide other formats and editions

Price

New from

Used from

Kindle

"Please retry"

$12.30

—

Hardcover

"Please retry"

$72.69

—

$72.69

Paperback, Illustrated

"Please retry"

$12.95

$8.95

$2.90

The Pythagorean Theorem is one of the fundamental theorems of elementary geometry, and Pythagorean triangles — right triangles whose sides are natural numbers — have been studied by mathematicians since antiquity. In this classic text, a brilliant Polish mathematician explores the intriguing mathematical relationships in such triangles.
Starting with "primitive" Pythagorean triangles, the text examines triangles with sides less than 100, triangles with two sides that are successive numbers, divisibility of one of the sides by 3 or by 5, the values of the sides of triangles, triangles with the same arm or the same hypotenuse, triangles with the same perimeter, and triangles with the same area. Additional topics include the radii of circles inscribed in Pythagorean triangles, triangles in which one or more sides are squares, triangles with natural sides and natural areas, triangles in which the hypotenuse and the sum of the arms are squares, representation of triangles with the help of the points of a plane, right triangles whose sides are reciprocals of natural numbers, and cuboids with edges and diagonals expressed by natural numbers.

Print length

128 pages
Language:

English
Publisher

Dover Publications
Publication date

November 2, 2011
Dimensions

4.92 x 0.3 x 8.54 inches
ISBN-10

0486432785
ISBN-13

978-0486432786
See all details

Customers who bought this item also bought

Page 1 of 1 Start overPage 1 of 1

This shopping feature will continue to load items when the Enter key is pressed. In order to navigate out of this carousel please use your heading shortcut key to navigate to the next or previous heading.

H. S. M. Coxeter

25

Paperback
$12.39
Only 5 left in stock (more on the way).
George Oliver

2

Paperback
$12.92
Usually ships within 3 days.

Special offers and product promotions

Amazon Business : For business-only pricing, quantity discounts and FREE Shipping. Register a free business account

Product details

Publisher : Dover Publications (November 2, 2011)
Language: : English
Paperback : 128 pages
ISBN-10 : 0486432785
ISBN-13 : 978-0486432786
Item Weight : 5 ounces
Dimensions : 4.92 x 0.3 x 8.54 inches

Best Sellers Rank: #1,705,511 in Books (See Top 100 in Books)
- #338 in Trigonometry (Books)
- #1,644 in Geometry & Topology (Books)

Customer Reviews:
6 ratings

Start reading Pythagorean Triangles (Dover Books on Mathematics) on your Kindle in under a minute.

Don't have a Kindle? Get your Kindle here, or download a FREE Kindle Reading App.

Customer reviews

5 star		45%
4 star		44%
3 star		11%
2 star 0% (0%)		0%
1 star 0% (0%)		0%

How are ratings calculated?

Top reviews from the United States

There was a problem filtering reviews right now. Please try again later.

Amazon Customer

Cool book. Couldn't put it down.

Reviewed in the United States on October 21, 2019

Verified Purchase

Elemantary facts about Pythagorean triangles (C-squared = A-squared + B-squared), A,B,C integers,
developed by the famous topologist Waclaw Sierpinski, known for the Sierpinski gasket, the Sierpinski carpet,
and other wonders. An understanding of high-school algebra is all you need to read this book.
Book arrived promptly, clean and intact.

One person found this helpful

Helpful

watzizname

A Compendium of Facts about Pythagorean Triangles

Reviewed in the United States on September 4, 2010

Verified Purchase

A pythagorean triangle (PT) is a right triangle (i. e. a triangle which has a right angle) the lengths of the sides of which are all 'natural numbers' (i.e. positive integers) The smallest and best known PT is (4, 3, 5).

Chapter 1, section 1.2 begins: In a pythagorean triangle (as in any right triangle) the biggest side is obviously the hypoteneuse; the other two sides, called arms, contain the right angle. If these (i. e. their lengths) are x and y and the hypoteneuse is z, then by the theorem of Pythagoras,

. . x^2 + y^2 = z^2

[Sierpinski used superscripts, but Amazon's text box doesn't provide for them]

Many (I think most) Americans are used to calling the shorter sides of a right triangle legs, not arms, and we might be more comfortable with 'called' instead of 'obviously.' Also, we are used to naming the legs a and b and the hypoteneuse c, rather than x, y, and z. While differences such as these make this book require a bit more effort to read, the effort is worth it for the many interesting facts you will find here.

For example, on page 16 we learn that if the lengths of the two legs of a PT are consecutive numbers, b = a + 1, then (3a + 2c + 1, 3a + 2c + 2, 4a + 3c + 2) is another PT, On page 17 he lists the first six such triangles: (4, 3, 5), (20, 21, 29), (120, 119, 169), (696, 697, 985), (4060, 4059, 5741), and (23660, 23661, 33461). Perhaps because it is so obvious, Sierpinski doesn't mention that therefore PTs exist with acute angles arbitrarily close (but never =) to 45 degrees.

While extensive, the information about PTs in this slim volume (107 pages) is not exhaustive. In addition to the omission cited above, Sierpinski says nothing about infinite matrices of PTs, of which there are two that I know of. One is based on x=2r-1, y=2k, where r is the row number and k is the column number, and
a(r,k) = 2xy,
b(r,k) = y^2 - x^2,
c(r,k) = y^2 + x^2.
This has the advantage of formulaic simplicity, compared to:
a(r,k) = 4rk+2k(k-1),
b(r,k) = 4r(r+k-1) - 2k + 1,
c(r,k) = 4r(r+k-1) + 2k(k-1) + 1.
However, the latter gives a matrix in which every row is an infinite family of PTs in each of which c exceeds a by the square of the rth odd number (1, 9, 25, 49, . . .)
and every column is an infinite family in each of which c exceeds b by twice the square of k (2, 8, 18, 32, . . .).

watziznayme@gmail.com

11 people found this helpful

Helpful

Scott Krumwiede

Five Stars

Reviewed in the United States on August 21, 2017

Verified Purchase

Helps me in my personal study of Math's various areas!! Enjoy studying Pythagoras Theorem

Helpful

Joan Antoni

Number Theory essay

Reviewed in the United States on March 1, 2018

It's an essay on differents relationship between lot of parts (lengs, area, perimetre,...) of the rectangle triangle with integer sides, the so called Pythagorean Triangles.
Don't you expect any drawings inside it. The only figures in book they are on cover and sec. 11.7
Only for Number Theory lovers.

2 people found this helpful

Helpful

Top reviews from other countries

Andrew Allison

A well written book, on an interesting topic, by a famous author

Reviewed in Australia on July 23, 2014

Verified Purchase

Waclaw Sierpinski may not be a household name amongst non-mathematicians, but in the world of mathematics he is highly regarded. He writes well about this particular Diophantine problem, of integral Pythagorean triples. I particularly like his derivation of the formula in Euclid: A= 2*m*m, B= m^2-n^2, and C= m^2+n^2. He goes on to consider a number of more advanced problems, including pythagorean 3D-boxes.

I use his material in planning text and examination problems for Electrical Engineering. All the voltages and currents are Pythagorean triples, in the phasor-domain. For me, this book is beautiful and practical and affordable.

See all reviews

Buy used: $2.90

Follow the Author

Similar authors to follow

Pythagorean Triangles (Dover Books on Mathematics) Paperback – Illustrated, November 2, 2011

Customers who bought this item also bought

Special offers and product promotions

Product details

Customer reviews

Top reviews from the United States

There was a problem filtering reviews right now. Please try again later.

Top reviews from other countries

Buy used:

$2.90