Mathematics Batch 07 - Historical & Educational - Programming Framework Analysis
This document presents historical and educational mathematics processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.
1. Euclid's Geometry Process
graph TD
A1[Geometric Problem] --> B1[Euclidean Axioms]
C1[Postulates] --> D1[Common Notions]
E1[Geometric Construction] --> F1[Proof Method]
B1 --> G1[Point Line Plane]
D1 --> H1[Equality Axioms]
F1 --> I1[Logical Deduction]
G1 --> J1[Postulate One]
H1 --> K1[Transitive Property]
I1 --> L1[Theorem Statement]
J1 --> M1[Postulate Two]
K1 --> N1[Reflexive Property]
L1 --> O1[Hypothesis Analysis]
M1 --> P1[Postulate Three]
N1 --> O1
O1 --> Q1[Conclusion Deduction]
P1 --> R1[Postulate Four]
Q1 --> S1[Proof Construction]
R1 --> T1[Postulate Five]
S1 --> U1[Geometric Proof]
T1 --> V1[Parallel Postulate]
U1 --> W1[Euclidean Result]
V1 --> X1[Euclidean Geometry]
W1 --> Y1[Geometric Analysis]
X1 --> Z1[Euclidean Geometry Output]
Y1 --> AA1[Euclidean Geometry Analysis]
Z1 --> BB1[Euclidean Geometry Final Result]
AA1 --> CC1[Euclidean Geometry Analysis Complete]
style A1 fill:#ff6b6b,color:#fff
style C1 fill:#ff6b6b,color:#fff
style E1 fill:#ff6b6b,color:#fff
style B1 fill:#ffd43b,color:#000
style D1 fill:#ffd43b,color:#000
style F1 fill:#ffd43b,color:#000
style G1 fill:#ffd43b,color:#000
style H1 fill:#ffd43b,color:#000
style I1 fill:#ffd43b,color:#000
style J1 fill:#ffd43b,color:#000
style K1 fill:#ffd43b,color:#000
style L1 fill:#ffd43b,color:#000
style M1 fill:#ffd43b,color:#000
style N1 fill:#ffd43b,color:#000
style O1 fill:#ffd43b,color:#000
style P1 fill:#ffd43b,color:#000
style Q1 fill:#ffd43b,color:#000
style R1 fill:#ffd43b,color:#000
style S1 fill:#ffd43b,color:#000
style T1 fill:#ffd43b,color:#000
style U1 fill:#ffd43b,color:#000
style V1 fill:#ffd43b,color:#000
style W1 fill:#ffd43b,color:#000
style X1 fill:#ffd43b,color:#000
style Y1 fill:#ffd43b,color:#000
style Z1 fill:#ffd43b,color:#000
style AA1 fill:#ffd43b,color:#000
style BB1 fill:#ffd43b,color:#000
style CC1 fill:#ffd43b,color:#000
style M1 fill:#51cf66,color:#fff
style N1 fill:#51cf66,color:#fff
style O1 fill:#51cf66,color:#fff
style P1 fill:#51cf66,color:#fff
style Q1 fill:#51cf66,color:#fff
style R1 fill:#51cf66,color:#fff
style S1 fill:#51cf66,color:#fff
style T1 fill:#51cf66,color:#fff
style U1 fill:#51cf66,color:#fff
style V1 fill:#51cf66,color:#fff
style W1 fill:#51cf66,color:#fff
style X1 fill:#51cf66,color:#fff
style Y1 fill:#51cf66,color:#fff
style Z1 fill:#51cf66,color:#fff
style AA1 fill:#51cf66,color:#fff
style BB1 fill:#51cf66,color:#fff
style CC1 fill:#51cf66,color:#fff
style CC1 fill:#b197fc,color:#fff
Triggers & Inputs
Euclidean Methods
Geometric Operations
Intermediates
Products
Figure 1. Euclid's Geometry Process. This historical mathematics process visualization demonstrates the axiomatic method of Euclidean geometry. The flowchart shows geometric problem inputs and postulates, Euclidean methods and axioms, geometric operations and proofs, intermediate results, and final Euclidean geometry outputs.
graph TD
A2[Logical Premises] --> B2[Syllogistic Form]
C2[Major Premise] --> D2[Minor Premise]
E2[Conclusion] --> F2[Logical Validity]
B2 --> G2[Major Term]
D2 --> H2[Middle Term]
F2 --> I2[Minor Term]
G2 --> J2[Universal Affirmative]
H2 --> K2[Universal Negative]
I2 --> L2[Particular Affirmative]
J2 --> M2[Particular Negative]
K2 --> N2[Barbara Syllogism]
L2 --> O2[Celarent Syllogism]
M2 --> P2[Darii Syllogism]
N2 --> O2
O2 --> Q2[Ferio Syllogism]
P2 --> R2[Syllogistic Figure]
Q2 --> S2[Logical Form Analysis]
R2 --> T2[Validity Check]
S2 --> U2[Syllogistic Result]
T2 --> V2[Logical Conclusion]
U2 --> W2[Aristotelian Logic]
V2 --> X2[Syllogistic Analysis]
W2 --> Y2[Logical Analysis]
X2 --> Z2[Aristotelian Logic Output]
Y2 --> AA2[Aristotelian Logic Analysis]
Z2 --> BB2[Aristotelian Logic Final Result]
AA2 --> CC2[Aristotelian Logic Analysis Complete]
style A2 fill:#ff6b6b,color:#fff
style C2 fill:#ff6b6b,color:#fff
style E2 fill:#ff6b6b,color:#fff
style B2 fill:#ffd43b,color:#000
style D2 fill:#ffd43b,color:#000
style F2 fill:#ffd43b,color:#000
style G2 fill:#ffd43b,color:#000
style H2 fill:#ffd43b,color:#000
style I2 fill:#ffd43b,color:#000
style J2 fill:#ffd43b,color:#000
style K2 fill:#ffd43b,color:#000
style L2 fill:#ffd43b,color:#000
style M2 fill:#ffd43b,color:#000
style N2 fill:#ffd43b,color:#000
style O2 fill:#ffd43b,color:#000
style P2 fill:#ffd43b,color:#000
style Q2 fill:#ffd43b,color:#000
style R2 fill:#ffd43b,color:#000
style S2 fill:#ffd43b,color:#000
style T2 fill:#ffd43b,color:#000
style U2 fill:#ffd43b,color:#000
style V2 fill:#ffd43b,color:#000
style W2 fill:#ffd43b,color:#000
style X2 fill:#ffd43b,color:#000
style Y2 fill:#ffd43b,color:#000
style Z2 fill:#ffd43b,color:#000
style AA2 fill:#ffd43b,color:#000
style BB2 fill:#ffd43b,color:#000
style CC2 fill:#ffd43b,color:#000
style M2 fill:#51cf66,color:#fff
style N2 fill:#51cf66,color:#fff
style O2 fill:#51cf66,color:#fff
style P2 fill:#51cf66,color:#fff
style Q2 fill:#51cf66,color:#fff
style R2 fill:#51cf66,color:#fff
style S2 fill:#51cf66,color:#fff
style T2 fill:#51cf66,color:#fff
style U2 fill:#51cf66,color:#fff
style V2 fill:#51cf66,color:#fff
style W2 fill:#51cf66,color:#fff
style X2 fill:#51cf66,color:#fff
style Y2 fill:#51cf66,color:#fff
style Z2 fill:#51cf66,color:#fff
style AA2 fill:#51cf66,color:#fff
style BB2 fill:#51cf66,color:#fff
style CC2 fill:#51cf66,color:#fff
style CC2 fill:#b197fc,color:#fff
Triggers & Inputs
Syllogistic Methods
Logical Operations
Intermediates
Products
Figure 2. Aristotle's Syllogism Process. This historical logic process visualization demonstrates syllogistic reasoning and logical deduction. The flowchart shows logical premise inputs and syllogistic forms, syllogistic methods and figures, logical operations and validity checks, intermediate results, and final Aristotelian logic outputs.