# Geometry Constructions: Why?

**URL:** https://boards.straightdope.com/t/geometry-constructions-why/267201
**Category:** Factual Questions
**Created:** [October 2, 2004, 3:39pm UTC](https://boards.straightdope.com/t/geometry-constructions-why/267201 "2004-10-02T15:39:03Z")
**Posts on this page:** 1
**Page:** 2

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### Author: ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)
#### Post date: [October 4, 2004, 8:57pm UTC](https://boards.straightdope.com/t/geometry-constructions-why/267201/21 "2004-10-04T20:57:43Z")

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> [@ultrafilter](#):
>
> It’s a minor point, but I can’t agree. An algorithm is not a proof–they’re two different types of objects. The proof that the algorithm is correct is the proof that the construction is possible.

Okay, I may have been slightly inexplicit. A construction is an essential part of a (constructive) proof. Note that nonconstructive proofs really didn’t go over well with ancient geometers, nor with many modern mathematicians.

To pop up the stack, I’m not really confounding construction and proof, as **Jinx** suggested. In fact, a standard “geometry construction” (the kind of thing the OP was talking about) is a problem asking for a construction _with a proof_ that it is correct.

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