Celestial Circles Slides Celestial Circles
THE GEOMETRY OF THE HEAVENS
A Geometric Design Project
The Mission
Design
Create an original "Star Chart" or celestial map using geometric constructions within circles.
Prove
Demonstrate mastery of 5 circle theorems by calculating and proving the angles in your design.
Theorem Toolkit
PART 01
Inscribed Angle Theorem
2x x
Center angle is double the circumference angle.
Angles in a Semicircle
The angle in a semicircle is always 90° .
Theorem Toolkit
PART 02
Cyclic Quadrilaterals
A B
Opposite angles sum to 180° .
Tangent-Radius
A tangent is perpendicular to the radius.
Theorem Toolkit
PART 03
Two-Tangent Theorem
= =
Tangents from a common external point are equal in length .
Advanced Maneuvers
You may also use the Alternate Segment Theorem or Angle at Circumference (Same Arc) to fulfill your 5-theorem requirement.
Project Requirements
At least 3 main circles of varying sizes.
Incorporate 5 different theorems in your design.
A Proof Log identifying every theorem used.
Full color, aesthetic layout with celestial theme.
Design Inspiration
Phase Charts
Solar Paths
Astrolabes
Initializing Space Program...
Star Chart Project Guide Celestial Star Chart
Project Mission Guide
Explorer: ____________________
Date: ________________________
The Mission
Design a modern Celestial Star Chart . Your design must incorporate at least 3 main circles and 5 different circle theorems . You will label 12 unique angles and complete a rigorous calculation log for your final submission.
Design Checklist
Ruler & Compass construction
Themed coloring & layout
Minimum 3 interlocking circles
Math Checklist
5 unique circle theorems
12 labeled angles
Calculation Log (Full Proofs)
Rough Draft Blueprint
Construct your primary interlocking circles and chords in this space first.
The Calculation Log
Provide proof for Theorems 01, 02, and 03.
LOG ENTRY #01 SCORE: ___ / 10
Theorem Applied:
Target Angle(s):
Calculation Steps:
LOG ENTRY #02 SCORE: ___ / 10
Theorem Applied:
Target Angle(s):
Calculation Steps:
LOG ENTRY #03 SCORE: ___ / 10
Theorem Applied:
Target Angle(s):
Calculation Steps:
The Calculation Log
Provide proof for Theorems 04 and 05.
LOG ENTRY #04 SCORE: ___ / 10
Theorem Applied:
Target Angle(s):
Calculation Steps:
LOG ENTRY #05 SCORE: ___ / 10
Theorem Applied:
Target Angle(s):
Calculation Steps:
Explorer Reflection
Which theorem was the most challenging to incorporate into your star chart design? Why?
Mission Control Teacher Guide Mission Control
Teacher's Guide: Celestial Circles
Grade Level
9 - 11
Subject
Geometry
Duration
3 - 5 Days
Lesson Objectives
Apply circle theorems to construct complex geometric designs.
Verify angle and segment relationships using mathematical proofs.
Communicate geometric reasoning through a structured "Calculation Log".
Project Timeline
Day 1
Introduction & Ideation
Review theorems via slides. Students sketch rough drafts and choose their 5 theorems.
Day 2-3
Construction & Verification
Students create final designs using compass/ruler. Concurrent math checks for accuracy.
Day 4-5
Final Proofs & Presentation
Students complete the Calculation Log and finalize the aesthetic details.
Grading Rubric
Criteria Mastery (4) Proficient (3) Basic (2) Math Accuracy All calculations are 100% correct. Theorems applied perfectly. Minor arithmetic errors. Logic is sound. Significant errors in application of theorems. Proof Quality Proofs are rigorous, labeled, and use formal notation. Most proofs are clear but may lack formal notation. Proofs are incomplete or confusing. Design & Theme Visually stunning. Celestial theme is evident and creative. Clean design. Theme is present but standard. Design is messy or theme is missing.
