Taxonomy Distribution Report

Overview

• Total Concepts: 200
• Number of Taxonomies: 12
• Average Concepts per Taxonomy: 16.7

Distribution Summary

Category	TaxonomyID	Count	Percentage	Status
AREA	AREA	34	17.0%	✅
TRI	TRI	28	14.0%	✅
SIM	SIM	20	10.0%	✅
CIRC	CIRC	20	10.0%	✅
LOGIC	LOGIC	19	9.5%	✅
POLY	POLY	16	8.0%	✅
ANGLE	ANGLE	14	7.0%	✅
LINES	LINES	13	6.5%	✅
Foundation Concepts - Prerequisites	FOUND	12	6.0%	✅
TRANS	TRANS	10	5.0%	✅
CONST	CONST	8	4.0%	✅
APP	APP	6	3.0%	✅

Visual Distribution

AREA   ████████  34 ( 17.0%)
TRI    ███████  28 ( 14.0%)
SIM    █████  20 ( 10.0%)
CIRC   █████  20 ( 10.0%)
LOGIC  ████  19 (  9.5%)
POLY   ████  16 (  8.0%)
ANGLE  ███  14 (  7.0%)
LINES  ███  13 (  6.5%)
FOUND  ███  12 (  6.0%)
TRANS  ██  10 (  5.0%)
CONST  ██   8 (  4.0%)
APP    █   6 (  3.0%)

Balance Analysis

✅ No Over-Represented Categories

All categories are under the 30% threshold. Good balance!

Category Details

AREA (AREA)

Count: 34 concepts (17.0%)

Concepts:

• 1. Area of Rectangle
• 1. Area of Square
• 1. Area of Parallelogram
• 1. Area of Triangle
• 1. Area of Trapezoid
• 1. Area of Rhombus
• 1. Area of Kite
• 1. Area of Regular Polygon
• 1. Area of Circle
• 1. Circumference
• 1. Pi
• 1. Perimeter
• 1. Prism
• 1. Pyramid
• 1. Cylinder
• ...and 19 more

TRI (TRI)

Count: 28 concepts (14.0%)

Concepts:

• 1. Triangle Congruence
• 1. SSS Congruence
• 1. SAS Congruence
• 1. ASA Congruence
• 1. AAS Congruence
• 1. HL Congruence
• 1. CPCTC
• 1. Triangle
• 1. Scalene Triangle
• 1. Isosceles Triangle
• 1. Equilateral Triangle
• 1. Acute Triangle
• 1. Right Triangle
• 1. Obtuse Triangle
• 1. Triangle Sum Theorem
• ...and 13 more

SIM (SIM)

Count: 20 concepts (10.0%)

Concepts:

• 1. Similar Figures
• 1. Scale Factor
• 1. Similarity Ratio
• 1. AA Similarity
• 1. SAS Similarity
• 1. SSS Similarity
• 1. Proportional Segments
• 1. Geometric Mean
• 1. Altitude to Hypotenuse
• 1. Pythagorean Theorem
• 1. Pythagorean Triple
• 1. Converse Pythagorean Theorem
• 1. Distance in Coordinate Plane
• 1. Sine Ratio
• 1. Cosine Ratio
• ...and 5 more

CIRC (CIRC)

Count: 20 concepts (10.0%)

Concepts:

• 1. Circle
• 1. Center of Circle
• 1. Radius
• 1. Diameter
• 1. Chord
• 1. Secant
• 1. Tangent to Circle
• 1. Point of Tangency
• 1. Central Angle
• 1. Inscribed Angle
• 1. Intercepted Arc
• 1. Major Arc
• 1. Minor Arc
• 1. Semicircle
• 1. Arc Length
• ...and 5 more

LOGIC (LOGIC)

Count: 19 concepts (9.5%)

Concepts:

• 1. Inductive Reasoning
• 1. Deductive Reasoning
• 1. Conjecture
• 1. Counterexample
• 1. Conditional Statement
• 1. Hypothesis
• 1. Conclusion
• 1. Converse
• 1. Inverse
• 1. Contrapositive
• 1. Biconditional Statement
• 1. Postulate
• 1. Theorem
• 1. Proof
• 1. Two-Column Proof
• ...and 4 more

POLY (POLY)

Count: 16 concepts (8.0%)

Concepts:

• 1. Polygon
• 1. Regular Polygon
• 1. Interior Angles of Polygon
• 1. Exterior Angles of Polygon
• 1. Quadrilateral
• 1. Parallelogram
• 1. Rectangle
• 1. Rhombus
• 1. Square
• 1. Trapezoid
• 1. Isosceles Trapezoid
• 1. Kite
• 1. Pentagon
• 1. Hexagon
• 1. Octagon
• ...and 1 more

ANGLE (ANGLE)

Count: 14 concepts (7.0%)

Concepts:

• 1. Acute Angle
• 1. Right Angle
• 1. Obtuse Angle
• 1. Straight Angle
• 1. Complementary Angles
• 1. Supplementary Angles
• 1. Adjacent Angles
• 1. Vertical Angles
• 1. Linear Pair
• 1. Angle Bisector
• 1. Corresponding Angles
• 1. Alternate Interior Angles
• 1. Alternate Exterior Angles
• 1. Same-Side Interior Angles

LINES (LINES)

Count: 13 concepts (6.5%)

Concepts:

• 1. Parallel Lines
• 1. Perpendicular Lines
• 1. Skew Lines
• 1. Perpendicular Bisector
• 1. Distance Formula
• 1. Midpoint Formula
• 1. Transversal
• 1. Parallel Postulate
• 1. Slope
• 1. Slope-Intercept Form
• 1. Point-Slope Form
• 1. Equations of Parallel Lines
• 1. Equations of Perpendicular Lines

Foundation Concepts - Prerequisites (FOUND)

Count: 12 concepts (6.0%)

Concepts:

• 1. Point
• 1. Line
• 1. Plane
• 1. Ray
• 1. Line Segment
• 1. Angle
• 1. Vertex
• 1. Collinear Points
• 1. Coplanar Points
• 1. Intersection
• 1. Midpoint
• 1. Segment Bisector

TRANS (TRANS)

Count: 10 concepts (5.0%)

Concepts:

• 1. Translation
• 1. Rotation
• 1. Reflection
• 1. Dilation
• 1. Rigid Motion
• 1. Image
• 1. Pre-Image
• 1. Composition of Transformations
• 1. Congruent Figures
• 1. Corresponding Parts

CONST (CONST)

Count: 8 concepts (4.0%)

Concepts:

• 1. Compass Construction
• 1. Straightedge Construction
• 1. Copying a Segment
• 1. Copying an Angle
• 1. Bisecting a Segment
• 1. Bisecting an Angle
• 1. Constructing Perpendiculars
• 1. Constructing Parallels

APP (APP)

Count: 6 concepts (3.0%)

Concepts:

• 1. Scale Drawing
• 1. Scale Model
• 1. Optimization Problem
• 1. Modeling with Geometry
• 1. Design Challenge
• 1. Geometric Proof Portfolio

Recommendations

• ✅ Excellent balance: Categories are evenly distributed (spread: 14.0%)
• ✅ MISC category minimal: Good categorization specificity

Educational Use Recommendations

• Use taxonomy categories for color-coding in graph visualizations
• Design curriculum modules based on taxonomy groupings
• Create filtered views for focused learning paths
• Use categories for assessment organization
• Enable navigation by topic area in interactive tools

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Report generated by learning-graph-reports/taxonomy_distribution.py