Musical Geometry

Project Overview:

Geometry constructions allow us to create interesting and detailed art using the most basic tools; a straightedge and compass. In this project, you will be creating an art piece using what you know about geometric constructions.

Essential Questions:

-What types of patterns and symmetry do humans find beautiful?

-How can we use Geometric Transformations to make music?

Deliverables:

• A song that uses 8 Geometric Transformations

• A visual representation

• A written explanation of how you used each transformation

Steps

1- Bring expert in.

2 - Read the Geometric Art Project Description.

3 - Watch and take notes on videos below.

4 - Get Critique on Geometric art.

5 - Make Construction by hand.

6 - Take Quizzes.

- Constructions Quiz.

- Geometric Transformation Quiz.

- Triangles and Pythagorean Theorem Quiz.

Song Requirements:

For this project, you will need to meet some basic construction requirements. Your construction needs a minimum of one thing from each category below. Additionally, you need a total minimum of 8 different things below. Since you can not draw out these Geometric Transformations, you will have to be creative in how to use each. For example, you could use a Line Bisector by inserting a new beat or rhyme perpendicular and in the middle of a different line.

Intro to Geometry - Definitions

Angle: A shape, formed by two lines or rays diverging from a common point (the vertex).

Circle: A line forming a closed loop, every point on which is a fixed distance from a center point.

Perpendicular Line: A line is perpendicular to another if it meets or crosses it at right angles (90°).

Parallel Line: Lines are parallel if they lie in the same plane, and are the same distance apart over their entire length

Line segment: A part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

Investigate... Rotations and Reflections that map a rectangle, parallelogram, trapezoid, regular polygon onto itself.

Transformations in the plane: functions that take points in the plane as inputs and ice other points as outputs. Some preserve distance and angle and some do not.

Rigid Motion: transformations that preserve both

the length of a line segment, and the measure of an angle.

Congruence: A congruence between two geometric objects is a rigid motion of the plane that maps one of the objects onto the other. When two objects are congruent, we can then pose the problem of finding all of the rigid motions of the plane that establish this congruence.

Rotation: A Rotation is a transformation that turns a figure about a fixed point.

Reflection: A transformation where each point in a shape appears at an equal distance on the opposite side of a given line - the line of reflection.

Translation: Translation is a transformation that "slides" an object in a fixed distance and in a given direction. The original object and its translation have the same shape and size, and they face in the same direction.

Congruent triangles: If two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they will be there.

CPCTC: CPCTC states that if two or more triangles are proven congruent by any method, then all of their corresponding parts are congruent as well

Congruent triangles: It can be proved that triangles are congruent if they have the following relationships: ASA, SAS, SSS, AAS.