Analogy: Constructions and Proofs
Constructions are very similar to proofs. It's plausible that the very concept of "proof" had its roots in the idea of geometric construction in ancient Greece. In Euclid's "Elements," the ideas of construction and proof are intertwined.
Here's a chart emphasizing the similarities
between constructions and proofs. CONSTRUCTION PROOF Input: Starting point ("Givens" in
GSP) Hypothesis Basic construction rules (the
Construct menu in GSP). Basic proof rules: axioms and rules of
logic. Output: Result of the
construction Conclusion
Each step of the construction uses something already
constructed, and the basic rules.
Each step of the proof uses something already proved, and
the basic rules.