Mathematical Quilts

in aRadical Way

04/19/2023Kathleen M. Sylla

Summmer Institute 2007

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Objectives

• The students will investigate the mathematical patterns found in quilts.

• The students will investigate special right triangles through measurement and the use of the Pythagorean Theorem.

• The students will investigate special right triangles using radicals.

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Friendship Star Quilt

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

In a Radical Way

Pythagoras of Samos lived from about 569 BC to about 475 BC

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

In a Radical Way

Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it.

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Pythagorean Theorem Building squares on the sides of a right triangle.

Pythagoras' Theorem states that the sum of (the areas of) two small squares equals (the area of) the big one.

In algebraic terms, a2 + b2 = c2 where c is the hypotenuse while a and b are the legs of the triangle.

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Let’s Investigate

Quilt

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

A Second Look

What is the length of the hypotenuse?

222 cba

222 ca

ca 2

222 caa

222 ca

ac /2

41.12

2/ leghypotenuse45, 45, 90

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Square Root of 2

• The square root of 2 is the length of the hypotenuse (longest side) of a right triangle whose other two sides are each one unit long.

• The square root of 2 has the approximate value 1.41421356

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

More Quilts

GeoGebra

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

30, 60, 90

222 2aba

222 cba

222 4aba 22 3ab 22 3ab

3ab

3/ ab

2

11

60

30 30

60 60

3 / short long

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

More Quilts

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Behold Quilt

Behold

What is the ratio of the area of the white square to whole square?

What is the side length of the white square?

What are the length of the legs of the triangles?

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Making New Designs

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Behold a Bigger Quilt

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Lets make a Quilt

• Open to Geogebra

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Sunshine State Standards

• Number Sense, Concepts and Operations Benchmarks– MA.A.1.4.4 Students apply their understanding that

numbers can be represented in a variety of equivalent forms.

– MA.A.3.4.3 Students evaluate the hypotenuse and leg length of a triangle using the 45,45,90 degree Triangle Theorem.

• Geometry and Spatial Sense Benchmark– MA.C.1.4.1 Students understand and prove the

properties of 45, 45, 90 and 30, 60, 90 degree triangles.

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Algebra- Prentice Hall

• Introduce inSection 10-3• Finding and Estimating Square Roots

• 11-1 Simplifying Radicals• 11-2 The Pythagorean Theorem• 11-4 Operation with Radical

Expressions• 11-5 Solving Radical Equations

04/19/2023 Kathleen M. Sylla Summmer Institute 2007

Geometry Lesson

• Geometry, Prentice Hall • Section 7-3• Special Right Triangle