The Golden Curve Maths, art and nature. It’s surprising who uses maths Many of the writers for The Simpsons have maths degrees.

Slides:

Advertisements

Similar presentations

By Christophe Dufour & Ming Au. Finding φ. The property that defines the golden ratio is: L = L+1 1 L a. Cross multiplying and rearranging the equation.

Advertisements

Chapter 5 Number Theory © 2008 Pearson Addison-Wesley. All rights reserved.

Original Question: How fast rabbits can rabbits breed in ideal circumstances? Suppose a newly-born pair of.

The Golden Ratio BY MS. HANCOCK

Basic Practice of Statistics - 3rd Edition

Digital Design: Fibonacci and the Golden Ratio. Leonardo Fibonacci aka Leonardo of Pisa 1170 – c

A Ratio That Glitters Exploring Golden Ratios. Golden Ratio in Architecture The Pyramid of Khufu has the Golden Ratio in the ratio of the height of the.

 Pythagoras was especially interested in the golden section, and proved that it was the basis for the proportions of the human figure. He showed that.

Golden Ratio Phi Φ 1 : This could be a fun lesson. Fibonacci was inspired by how fast rabbits could breed in ideal circumstances,

Why is art important? In what ways can math explain art? (Helps the slides look less boring)

Fibonacci Spiral Richard Kwong MAT 385

The Golden Ratio Math in Beauty, Art, and Architecture.

Maths in Nature By Keith Ball.

SECTION 5-5 The Fibonacci Sequence and the Golden Ratio Slide

The Golden Ratio. Background Look at this sequence… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,... Can you tell how it was created? SStart with the numbers.

The Mathematical Formula of Art

GOLDEN MEAN AUKSO PJŪVIS. Definition of the Golden Rectangle The Golden Rectangle is a rectangle that can be split into a square and a rectangle similar.

The Golden Ratio and Fibonacci Numbers in Nature

The Golden Ratio Lynn DeRosa Carole McMahon Carol Herb.

Geometry: Similar Triangles. MA.912.D.11.5 Explore and use other sequences found in nature such as the Fibonacci sequence and the golden ratio. Block.

Aims and Objectives Correctly identify properties in each of a range of 2D shapes. Correctly recognise and identify different types of angles and their.

The Golden Ratio Is your body golden?.

The Golden Section The Divine Proportion The Golden Mean

Investigation 11 Golden Ratio.

INTRODUCTION TO THE GOLDEN MEAN … and the Fibonacci Sequence.

MATHS IN NATURE AND ARTS FIBONACCI’S SEQUENCE AND GOLDEN RATIO.

Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues.

MATHLETES Fibonacci Numbers and “The Golden Ratio”

MATH 2160 Sequences. Arithmetic Sequences The difference between any two consecutive terms is always the same. Examples: 1, 2, 3, … 1, 3, 5, 7, … 5, 10,

Phi:The GФldФn RatiФ Suki Kaur. Phi in Nature Sunflower If you count the pedals on one side of a sunflower, then count the number of pedals on the other.

Which rectangle do you like most?

The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.

Objectives To identify similar polygons. To apply similar polygons.

By Steven Cornell.  Was created by Leonardo Pisano Bogollo.  It show’s the growth of an idealized rabbit population.

The Fibonacci sequence occurs throughout nature. Where does the Fibonacci sequence occur on the human body and in animals?

Pure maths:  Axioms  Theorems Applied maths:  What you know  What is used in other disciplines.

Similar Polygons 7-2 Geometry. Warm-Up (5 min) Homework Review (5 min)

Golden Ratio Aka Golden rectangle, Divine ratio. Beautiful?

 Pythagoras was especially interested in the golden section, and proved that it was the basis for the proportions of the human figure. He showed that.

Interesting Math Discrete Math Mr. Altschuler. What Interests You? Write on a small piece of paper, a subject of endeavor that interests you. I will try.

The Golden Ratio Math in Beauty, Art, and Architecture

Year 7: Length and Area Perimeter The perimeter of a shape is the total distance around the edge of a shape. Perimeter is measured in cm A regular shape.

 2012 Pearson Education, Inc. Slide Chapter 5 Number Theory.

The Golden Mean. The Golden Mean (or Golden Section), represented by the Greek letter phi, is one of those mysterious natural numbers, like e or pi, that.

“The two highways of the life: maths and English”

By Jamie Harvey.  The golden ratio is ….  The golden ratio is the most esthetically pleasing to the eye  The golden rectangle  Fibonacci Sequence.

Golden Spirals or ‘Whirling squares’ These are mathematical constructions which appear in many places.

How maths can prove that you too are beautiful. Fibonacci & Rabbits

PERIMETERS What is the Perimeter of a shape. What is the Perimeter of this rectangle? What is the Perimeter of this rectangle? 5cm 15cm.

Mathematical Connections.

The Fibonacci Number Sequence

What makes things Beautiful?

STEAM patterns.

Chapter 5 Number Theory 2012 Pearson Education, Inc.

NUMBER PATTERNS What are the next 2 numbers in each pattern?

What Have These Got in Common?

Warm up The rectangles are similar. Find x. x

Investigation 11 Golden Ratio.

Parallelogram Rectangle Rhombus Square Trapezoid Kite

Mr Barton’s Maths Notes

2D shape properties- PowerPoint months

Similar Figures.

2D shape properties- PowerPoint months

STEAM patterns.

All About Shapes! Let’s Go!.

SHAPES By: Ms. Conquest.

The Golden Ratio and Other Applications of Similarity

Surprising Connections in Math: From the Golden Ratio to Fractals

Presentation transcript:

The Golden Curve Maths, art and nature

It’s surprising who uses maths Many of the writers for The Simpsons have maths degrees.

Maths helps us… Design

DesignPlan

DesignPlanUnderstand

Where’s the maths?

Where’s the maths? (1)

Where’s the maths? (2)

Where’s the maths? (3)

Where’s the maths? (4)

The “Golden Curve”

The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, …. What comes next? = = = = 233

The ratios of the sequence 1 ÷ 1 = 11 ÷ 1 = 1 2 ÷ 1 = 22 ÷ 1 = 2 3 ÷ 2 = 1.53 ÷ 2 = ÷ 3 = …5 ÷ 3 = … 8 ÷ 5 = 1.68 ÷ 5 = ÷ 8 = ÷ 8 = ÷ 13 = …21 ÷ 13 = …

The ratios of the sequence… 8 ÷ 5 = 1.68 ÷ 5 = ÷ 8 = ÷ 8 = ÷ 13 = …21 ÷ 13 = … 34 ÷ 21 = …34 ÷ 21 = … 55 ÷ 34 = …55 ÷ 34 = … 89 ÷ 55 = …89 ÷ 55 = …

The ratios tend to a number!

The golden ratio The number that these ratios tend towards is called the golden ratio:The number that these ratios tend towards is called the golden ratio: …

Why golden? It has lots of special propertiesIt has lots of special properties People have studied it for over 2000 yearsPeople have studied it for over 2000 years It occurs in art, architecture and natureIt occurs in art, architecture and nature

Golden rectangles A golden rectangle has one side which is … times the length of the otherA golden rectangle has one side which is … times the length of the other The United Nations building in New York has this shapeThe United Nations building in New York has this shape

People like golden rectangles Too long? Too short? Just right!Too long? Too short? Just right!

Nature and the golden ratio Sunflowers use the Fibonacci sequenceSunflowers use the Fibonacci sequence

Shells and the golden curve The shell of a nautilus (sea creature)The shell of a nautilus (sea creature)