Goals
Purpose
The purpose of this Geogebra book is to introduce students to the connections between the Fibonacci Sequence and the Golden Ratio through exploration with Golden Rectangles and Triangles.
Standards
CCSS.MATH.CONTENT.HSG.CO.A.5
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
CCSS.MATH.CONTENT.HSG.SRT.A.2
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
CCSS.MATH.CONTENT.HSS.ID.B.6
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
CCSS.MATH.CONTENT.HSS.ID.B.6.A
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
CCSS.MATH.CONTENT.HSS.ID.B.6.C
Fit a linear function for a scatter plot that suggests a linear association.
CCSS.MATH.CONTENT.HSS.ID.C.7
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Objectives
Students will be able to ...
- identify the Fibonacci Sequence within the constructions of Golden Rectangles,
- connect the Fibonacci Sequence algebraically and graphically to the Golden Ratio through a linear model of best fit,
- recognize recursion through rotations and dilation within constructions of Golden Rectangles and Triangles,
- develop an "eye" for recognizing shapes that are "Golden,"
- and apply previously learn concepts about similarity.