Waclaw Sierpinski Born in Warsaw, Poland in 1882. 1919- promoted to professor at Warsaw in mathematics and physics. 1920- founded math journal- Fundamenta.

Slides:

Advertisements

Similar presentations

40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Sequences Lesson: SEQ-L3 Drawing Fractal Patterns Drawing Fractal Patterns Learning Outcome.

Advertisements

1 st Place Post-Secondary Winner. 2 nd Place Post-Secondary Winner.

∞Exploring Infinity ∞ By Christopher Imm Johnson County Community College.

EXAMPLE 1 Finding Perimeter and Area SOLUTION Find the perimeter. P = 2l + 2w Write formula. = 2 ( 8 ) + 2( 5 ) Substitute. = 26 Multiply, then add. Find.

Problem Solving Process

6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles.

What is the probability that a I will randomly draw a girl’s name out of our math bucket?(only count those that are present today) What is the probability.

Sequences. Mathematical Patterns Suppose each student in your math class has a phone conversation with every other member of the class. What is the minimum.

Green text p.138 #s The length of the second side of a triangle is 2 inches less than the length of the first side. The length of the third.

Designed by David Jay Hebert, PhD

Fractals Nicole MacFarlane December 1 st, What are Fractals? Fractals are never- ending patterns. Many objects in nature have what is called a ‘self-

Arithmetic Sequences Explicit Formula.

Investigation 3: Inverse Variation

Investigation 3: Inverse Variation

11.5 = Recursion & Iteration. Arithmetic = adding (positive or negative)

This certificate is awarded to _____________________ on this 31 st day of May, _____________________.

21 March 2011 Warm UP– silently please 1 ) HOMEWORK DUE NEXT CLASS: pg. 493: include sketch, formula, substitution, math, units 2) WARM UP- Write.

FORMULAS FORMULAS Moody Mathematics. Let’s review how to “set up” a formula with the numbers in their correct places: Moody Mathematics.

FRACTALS FRACTALS The Geometry of Nature ϕ π Σ Π ξ ρ τ ω ψ Ξ Ω μ ε γ λ η ζ θ β α By Michael Duong.

Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.

Trigonometry – Right Angled Triangles By the end of this lesson you will be able to identify and calculate the following: 1. Who was Pythagoras 2. What.

Mathematics in Kindergarten Geometry OBJECTIVE FOR TODAY In Math a well-balanced mathematics curriculum for Kindergarten to Grade 2 need a primary.

Math 409/409G History of Mathematics

Fractals! Bullock Math Academy March 22, 2014 Brian Shelburne

Sierpinski Triangle Kendal, Matt, Heather, Caitlin.

 Life Expectancy is 180 th in the World.  Literacy Rate is 4 th in Africa.

Fractals What are fractals? Who is Benoit Mandlebrot? How can you recognize a fractal pattern? Who is Waclaw Sierpinski?

Area of a Parallelogram. What is a parallelogram? A parallelogram is a 4-sided shape formed by two pairs of parallel lines. Opposite sides are equal in.

BY ISRAEL COBEE DAVION GRANT.  This is a top view.

+ Lesson 3B: Geometric Sequences + Ex 1: Can you find a pattern and use it to guess the next term? A) 3, 9, 27, … B) 28, 14, 7, 3.5,... C) 1, 4, 9, 16,...

Patterns and Sequences Sequence: Numbers in a specific order that form a pattern are called a sequence. An example is 2, 4, 6, 8, 10 and 12. Polygon:

11-1 Mathematical Patterns Hubarth Algebra II. a. Start with a square with sides 1 unit long. On the right side, add on a square of the same size. Continue.

Math Pacing Special Products 3 5 3x – 5 6x + 3. Special Products 8-7 Multiplying Polynomials.

Fractals Lesson 6-6.

7-1C Areas and Perimeters of Similar Polygons What is the relationship between the perimeter ratios of similar figures and their similarity ratio? What.

st significant figure Significant figures Significant figures 1 st significant figure.

Arithmetic Recursive and Explicit formulas I can write explicit and recursive formulas given a sequence. Day 2.

Lesson 3A: Arithmetic Sequences Ex 1: Can you find a pattern and use it to guess the next term? A) 7, 10, 13, 16,... B) 14, 8, 2, − 4,... C) 1, 4, 9,

Unit 9: Sequences and Series. Sequences A sequence is a list of #s in a particular order If the sequence of numbers does not end, then it is called an.

Ch.9 Sequences and Series Section 1 - Mathematical Patterns.

Over Lesson 8–3. Splash Screen Special Products Lesson 8-4.

4-7 Arithmetic Sequences

12-1A Fractals What are fractals? Who is Benoit Mandlebrot?

What will the center number in Figure 6?

Finding Perimeter and Area

What will the center number in Figure 6?

9.2 Special Right Triangles EQ: What are the relationships between the sides on a triangle? Moody Mathematics.

3rd Grade Math Module 7 Lesson 8

BELL-WORK (x – 5)(x + 5) = x2 – 25 (b) (3x – 2)(3x + 2) = 9x2 – 4

Area and Perimeter (P3) Definition:

Title: Magic Square Challenge

School-Wide Achievement Mathematics

Warm Up 1st Term:_____ 1st Term:_____ 2nd Term:_____ 2nd Term:_____

Warm Up 1st Term:_____ 1st Term:_____ 2nd Term:_____ 2nd Term:_____

9.4 Solving Quadratic Equations

Grade one First term Second term Learning unit Learning unit

Paired Verbal Fluency 3 rounds 1st: Partner A then Partner B

4n + 2 1st term = 4 × = 6 2nd term = 4 × = 10 3rd term

Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.

True or False 1 2

Kinder Math Bee Counting Practice.

Kinder Math Bee Addition Practice.

Fractals What do we mean by dimension? Consider what happens when you divide a line segment in two on a figure. How many smaller versions do you get?

Write the recursive and explicit formula for the following sequence

Before and After Practice

4-7 Arithmetic Sequences

Lecture 8 Huffman Encoding (Section 2.2)

Presentation transcript:

Waclaw Sierpinski Born in Warsaw, Poland in promoted to professor at Warsaw in mathematics and physics founded math journal- Fundamenta Mathematica– specialized in set theory. Retired in 1960 and was given many awards. Died in 1969.

Sierpinski’s Carpet Go to g/interactivate/activiti es/carpet/index.html Go to g/interactivate/activiti es/carpet/index.html g/interactivate/activiti es/carpet/index.html g/interactivate/activiti es/carpet/index.html

Side Length & Area of Removed Square After 1 st iteration, what is the length of the removed square? What is the area of this square? After 2 nd iteration, what is the length of removed square? What is the area? After 3 rd,….? See any patterns? Write the formulas for side length & area of a removed square.

Number of Removed Squares After 1 st iteration, how many squares have been removed? After 2 nd iteration, how many squares have been removed? After 3 rd iteration, how many squares have been removed? See any patterns? Write down the formula for determining the number of removed squares.

Total Area Remaining  With no iterations, what is the area remaining of the figure.  After the 1 st iteration, how would you find the area remaining?  After the 2 nd iteration, what is the area remaining of the figure?  After the 3 rd,…?  What patterns do you see? Write down the explicit formula for the area remaining.

Area Removed How would we find the total area of the squares we removed? How would we find the total area of the squares we removed? What relationship is there between the area remaining and the area removed? What relationship is there between the area remaining and the area removed?

Limit of the Remaining Area  Using the formula of total area remaining, what is the limit if we send ‘n’ to infinity?

The End