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### Euclid's Elements

Description

Euclid’s Elements is a remarkable geometry course centered around the propositions of Euclid’s Elements.

In the first half of each class students will present prepared talks to explain and demonstrate a geometric proof to the group. Students will learn to make presentations, critically think, and build their confidence as they go through this yearlong course. Students become the teachers of other students!

The second half of each class will have students work through QED™ designed activities to

Euclid's Elements was the first logical presentation of mathematics as designed from a set of first principles. Until publication of modern text books in the 20th century, the Elements was the standard geometry text for all advanced mathematics students. Our course reintroduces this tradition striving to foster excellence in geometry, logic, critical thinking, and public speaking.

Sequence

The Fundamentals
An exciting introduction to Euclid's classic "The Elements". Students will learn logical flow, presentation skills, and the fundamentals of geometry from Euclid's first and second book.

mathematics: triangle types, line properties, line types, congruence, angles, bisecting, perpendicularity, side-angle relationships, quadrilateral types, Pythagorean's Theorem, geometric algebra, angle types.

science: students will learn construction methods for simple tools and devices.

Figures & Solids
Students will focus their geometric studies to those of circles, polygons, and 3-d solids. Students will be working through books 3,4,5,6,11,12,13.

mathematics: proportions, similar figures, proportional figures,  theory of circles, inscription and circumscription, solid geometry, measurement of figures, regular solids.

science: students will learn construction methods for various 2-D and 3-D objects.

Number Theory
In this last quarter, students will be amazed by how geometry can actually build up an entire theory of numbers on its own! Students will work through books 7,8,9,10.

mathematics: fundamentals of number theory, prime numbers, composite numbers, rational numbers, exponentials, irrational numbers, binomials.

science: students will work with a range of physical problems to determine ideas of measurement, accuracy, and precision.

Information

Each course in Euclid's Elements is a 30-hour workshop for a total of 90 hours of in-class material. Academic year sequences are held in 10 week classes each 3 hours long. Summer camps are held in a single week and cover 30 hours of material.

Each student will receive a full copy of Euclid's Elements. Students are expected to be prepared each week to make a presentation to their classmates.

Classes consist of hands-on activities, lecture, and practice problems. Academic year students are required to complete a minimal amount of practice problems.

#### Prerequisites

Students should have completed Algebra and should be reading at an 8th grade level.

#### CDE Geometry Standards

1.0 understanding concepts of definitions, axioms, theorems, inductive and deductive reasoning
2.0 write proofs
3.0 assess and judge validity of logic
4.0 prove theorems regarding congruence and similarity
5.0 CPCTC Theorem
6.0 triangle inequality theorem
7.0 theorems involving parallel lines cut by transversal
8.0 derive perimeter, circumference, area, volume, lateral area, surface area of common geometric figures
9.0 volumes and surface areas of prism, pyramid, cylinder,cone, sphere
10.0 areas of rectangle, scalene triangle, equilateral triangle, rhombi, parallelogram, trapezoid
11.0 dimensional analysis
12.0 triangle interior and exterior angles
13.0 relationships between angles in polygons
14.0 Pythagorean theorem
15.0 Pythagorean theorem application
16.0 construct angle bisector, perpendicular bisector, line parallel to given line through point off the line
17.0 midpoint formula, distance formula, line and circle equation
18.0 basic trigonometry functions
19.0 solving right triangles
20.0 30-60-90 and 45-45-90 triangles
21.0 chords, secants, tangents, inscribed angles, inscribed and circumscribed polygons of circles
22.0 rotations, translations, and reflections