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| <title>Mathematics Batch 07 - Historical & Educational - Programming Framework Analysis</title> | |
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| <h1>Mathematics Batch 07 - Historical & Educational - Programming Framework Analysis</h1> | |
| <p>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.</p> | |
| <h2>1. Euclid's Geometry Process</h2> | |
| <div class="figure"> | |
| <div class="mermaid"> | |
| 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 | |
| </div> | |
| <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;"> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Euclidean Methods | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Geometric Operations | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products | |
| </div> | |
| </div> | |
| <div class="figure-caption"> | |
| <strong>Figure 1.</strong> 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. | |
| </div> | |
| </div> | |
| </div> | |
| <h2>2. Aristotle's Syllogism Process</h2> | |
| <div class="figure"> | |
| <div class="mermaid"> | |
| 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 | |
| </div> | |
| <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;"> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Syllogistic Methods | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Logical Operations | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products | |
| </div> | |
| </div> | |
| <div class="figure-caption"> | |
| <strong>Figure 2.</strong> 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. | |
| </div> | |
| </div> | |
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| <h3>Navigation</h3> | |
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| <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a> | |
| <a href="mathematics_batch_06.html" class="nav-link">← Previous: Discrete Mathematics</a> | |
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| <p><strong>Generated using the Programming Framework methodology</strong></p> | |
| <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p> | |
| <div class="contact-info"> | |
| <p><strong>Gary Welz</strong></p> | |
| <p>Retired Faculty Member</p> | |
| <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p> | |
| <p>Borough of Manhattan Community College, CUNY</p> | |
| <p>CUNY Graduate Center (New Media Lab)</p> | |
| <p>Email: gwelz@jjay.cuny.edu</p> | |
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