Value is 1 Let x = FIBO(n-1)Let y = FIBO(n-2)x + y endbegin n > 2 n =1 or 2 RTN for Fibonacci numbers FIBO(n) begin Value is 1 Let y = FIBO(n-2)x + y.

Slides:

Advertisements

Similar presentations

Power Series Definition of Power Series Convergence of Power Series

Advertisements

Circles Sheila Roby April 22, What is a circle? A circle is the set of all points in a plane equidistant from a fixed point. Equi means same, so.

9 x9 81 4/12/2015 Know Your Facts!. 9 x2 18 4/12/2015 Know Your Facts!

Recursion October 5, Reading Read pp in the text.

§3 Dynamic Programming Use a table instead of recursion 1. Fibonacci Numbers: F(N) = F(N – 1) + F(N – 2) int Fib( int N ) { if ( N

1 x0 0 4/16/2015 Know Your Facts!. 1 x8 8 4/16/2015 Know Your Facts!

3 x0 0 7/18/2015 Know Your Facts!. 4 x3 12 7/18/2015 Know Your Facts!

Tangents and Circles. Tangent Definition A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point.

Notes Over 10.3 r is the radius radius is 4 units

Lesson 7-3 The Sine and Cosine Functions. Objective:

Advanced Algebra Trigonometry Appendix B

Lesson 16: The Most Famous Ratio of All

Recursion. Recursive Definitions In recursive definitions, we define a function, a predicate, a set, or a more complex structure over an infinite domain.

Construct a Regular Hexagon Scribe circumscribing circle.

More Practice with Trigonometry Section 4.3b. Let’s consider… Quadrantal Angle – angles whose terminal sides lie along one of the coordinate axes Note:

Radian Measure A central angle has a measure of 1 radian if it is subtended by an arc whose length is equal to the radius of the circle. Consider the circle.

CIRCUMFERENCE OF A CIRCLE LEARNING TARGET 4: I CAN SOLVE PROBLEMS USING AREA AND CIRCUMFERENCE OF A CIRCLE.

10.6 Equations of a Circle Standard Equation of a Circle Definition of a Circle.

Geometry Equations of a Circle.

GeometryGeometry Lesson 75 Writing the Equation of Circles.

Writing the Equation of a Circle We will be using the completing the square method for this, so lets remember…

Equations of Circles 10.6 California State Standards 17: Prove theorems using coordinate geometry.

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. The radius is 3 and the center is at the origin. x 2 + y 2 = r 2 x 2 +

10.6 Equations of Circles Advanced Geometry. What do you need to find the equation of a circle? Coordinates of the Center of the circle. Radius – Distance.

Standard Form for the Equation of the Circle

15-1 Chapter-18: Recursive Methods –Introduction to Recursion –Solving Problems with Recursion –Examples of Recursive Methods.

1 Circles. 2 3 Definitions A circle is the set of all points in a plane that are the same distance from a fixed point called the center of the circle.

10.1 Circles. Definition: Although all circles have the same shape, their sizes are determined by the measures of their radii. Two or more coplanar circles.

Lecture#16 Discrete Mathematics. Recursion Now, 1 is an odd positive integer by the definition base. With k = 1, = 3, so 3 is an odd positive integer.

4 x1 4 10/18/2015 Know Your Facts!. 5 x /18/2015 Know Your Facts!

3 x0 0 10/18/2015 Know Your Facts!. 11 x /18/2015 Know Your Facts!

Lesson 7-2 Circumference and Area of Circles. Definitions Circle - A set of points in a plane that are the same distance away from a given point in the.

Circumference & Area of a Circle

Uniform Circular Motion (UCM) The object travels in a circular path with a constant speed. Its velocity is tangent to the circle and is changing due to.

Orchard Hideout Circles – terms and definitions circle:Set of points that are equidistant from a given point, which is know as the center. center.

Square both sides to find the standard equation of a circle with radius r and center (h, k). Finding Equations of Circles You can write an equation of.

Unit 5 – Series, Sequences, and Limits Section 5.2 – Recursive Definitions Calculator Required.

12.6 Surface Area and Volume of a Sphere

Section 1.5: Circles Definition circle: Set of points a fixed distance from a center point. Definition radius: Distance from center to any point.

Conics Conics Review. Graph It! Write the Equation?

Infinite Geometric Series Recursion & Special Sequences Definitions & Equations Writing & Solving Geometric Series Practice Problems.

Equations of Circles. Vocab Review: Circle The set of all points a fixed distance r from a point (h, k), where r is the radius of the circle and the point.

Warm-Up What is the distance between the two trees? If you wanted to meet a friend halfway, where would you meet.

10-3 Circles Learning Target: I can use equations of circles to model and solve problems Goal 2.09.

Warm Up. EQUATION OF A CIRCLE Geometry How can we make a circle? What are the most important aspects when drawing a circle?

The Circle. Examples (1) – (5) Determine the center and radius of the circle having the given equation. Identify four points of the circle.

10-6 Equations of Circles Equations of Circles AB 2 = AC*AD AE 2 = AC*AD AB = AE.

9.6 Circles in the Coordinate Plane Date: ____________.

Trigonometric Functions: The Unit Circle Section 4.2.

[10.3] Tangents Circle Vocab. [10.3] Tangents Circle Vocab.

Equations of Circles. You can write an equation of a circle in a coordinate plane, if you know: Its radius The coordinates of its center.

THERE ARE MANY INTERESTING & EASY WAYS FOR MULTIPLICATION OF NUMBERS. LET’S SEE ONE OF THE INTERESTING METHOD………..

Equation of a Circle. Equation Where the center of the circle is (h, k) and r is the radius.

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. SOLUTION The radius is 3 and the center is at the origin. x 2 + y 2 = r.

Circles A review?. Let's review what we already know about circles. Definition: A circle is a locus (set) of points in a plane equidistant from a fixed.

  Where the center of the circle is (h, k) and r is the radius. Equation.

10-8 Equations of Circles 1.Write the equation of a circle. 2.Graph a circle on the coordinate plane.

The circumference & the circle. Elements of the circumference Centre (UK) / center (US)

Concentric Circles 1. Draw 4 circles on paper.

Fibonacci Fibonacci series 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 Definition:

Learn Your 2x Facts.

Page 12 Directions: C’ B B’ C A A’

Standard Equation of a Circle Definition of a Circle

Standard Equation of a Circle Definition of a Circle

Presentation transcript:

Value is 1 Let x = FIBO(n-1)Let y = FIBO(n-2)x + y endbegin n > 2 n =1 or 2 RTN for Fibonacci numbers FIBO(n) begin Value is 1 Let y = FIBO(n-2)x + y end n > 2 n =1 or 2 FIBO(n) n = 4 Let x = FIBO(n-1) begin Let x = FIBO(n-1) Let x = FIBO(3)

RTN for Fibonacci numbers begin Value is 1 Let y = FIBO(n-2)x + y end n > 2 n =1 or 2 FIBO(n) n = 3 Let x = FIBO(n-1) Let x = FIBO(n-1) Let x = FIBO(2) begin Value is 1 Let y = FIBO(n-2)x + y end n > 2 n =1 or 2 FIBO(n) n = 2 Let x = FIBO(n-1) Value is 1 end begin Result = 1

RTN for Fibonacci numbers begin Value is 1 Let y = FIBO(n-2)x + y end n > 2 n =1 or 2 FIBO(n) n = 3 begin Value is 1 Let y = FIBO(n-2)x + y end n > 2 n =1 or 2 FIBO(n) n = 2 Let x = FIBO(n-1) end Result = 1 Let x = FIBO(n-1) Let x = 1 Let y = FIBO(n-2) Let y = FIBO(1)

RTN for Fibonacci numbers begin Value is 1 Let y = FIBO(n-2)x + y end n > 2 n =1 or 2 FIBO(n) n = 3 begin Value is 1 Let y = FIBO(n-2)x + y end n > 2 n =1 or 2 FIBO(n) n = 1 Let x = FIBO(n-1) Let x = FIBO(n-1) Let x = 1 Let y = FIBO(n-2) Let y = FIBO(1) begin Value is 1 end Result = 1

Let y = FIBO(n-2) Let y = 1 RTN for Fibonacci numbers begin Value is 1 x + y end n > 2 n =1 or 2 FIBO(n) n = 3 begin Value is 1 Let y = FIBO(n-2)x + y end n > 2 n =1 or 2 FIBO(n) n = 1 Let x = FIBO(n-1) Let x = FIBO(n-1) Let x = 1 Let y = FIBO(n-2) Let y = 1 end Result = 1 x + y end Result = 2

Value is 1 Let x = FIBO(n-1)Let y = FIBO(n-2)x + y endbegin n > 2 n =1 or 2 RTN for Fibonacci numbers FIBO(n) begin Value is 1 Let y = FIBO(n-2)x + y end n > 2 n =1 or 2 FIBO(n) n = 4 Let x = FIBO(n-1) Let x = 2 Let x = FIBO(n-1) Let x = FIBO(3) Let x = FIBO(n-1) Let x = 2 Let y = FIBO(n-2) Let y = FIBO(2)

RTN for Fibonacci numbers begin Value is 1 Let y = FIBO(n-2)x + y end n > 2 n =1 or 2 FIBO(n) n = 2 Let x = FIBO(n-1) Value is 1 end begin Result = 1

Value is 1 Let x = FIBO(n-1)Let y = FIBO(n-2)x + y endbegin n > 2 n =1 or 2 RTN for Fibonacci numbers FIBO(n) begin Value is 1 x + y end n > 2 n =1 or 2 FIBO(n) n = 4 Let x = FIBO(n-1) Let x = 2 Let y = FIBO(n-2) Let y = 1 Let y = FIBO(n-2) Let y = FIBO(2) Let y = FIBO(n-2) Let y = 1 x + y

Value is 1 Let x = FIBO(n-1)Let y = FIBO(n-2)x + y endbegin n > 2 n =1 or 2 RTN for Fibonacci numbers FIBO(n) begin Value is end n > 2 n =1 or 2 FIBO(n) n = 4 Let x = FIBO(n-1) Let x = 2 Let y = FIBO(n-2) Let y = end 3 FIBO(4) = 3

Recursive definitions vs circular definitions This is the crucial fact [that] distinguishes recursive definitions from circular ones. There is always some part of the definition [that] avoids self-reference. GEB, p.133 Study Question 8 B. To make a series of concentric circles, draw a circle with a radius of one unit, then draw other circles with the same center and a radius of one unit greater than that of the previous circle. How to make this circular?

Recursive definitions vs circular definitions This is the crucial fact [that] distinguishes recursive definitions from circular ones. There is always some part of the definition [that] avoids self-reference. GEB, p.133 Study Question 8 C. To understand a sentence: (a) Read the first unread word in a sentence, (b) understand its meaning, (c) go back to step (a). How to make this circular?