Sentence examples for diagrammatic proof from inspiring English sources

The theory is exemplified with a diagrammatic proof of the Theorem of Pythagoras.

His analysis of Euclid's diagrammatic proof method reveals that Euclid employs diagrams in a controlled, systematic way.

Our diagrammatic proof of the dominance theorem follows the proof of Arrow's possibility theorem in [ 29].

For further details of a diagrammatic proof, including a demonstration that the result holds for any number of lineages, we refer to [ 29].

Accordingly, philosophers concerned with the nature of mathematics found themselves obliged to comment on the diagrammatic proofs of the text.

A central task of formalizing Euclid's diagrammatic proofs is accounting for this i.e., providing with its rules a method for distinguishing general co-exact features from non-general ones in diagrammatic representations of constructions.

It is clear that in a process that counts as thinking through this proof, the diagrammatic thinking is neither superfluous nor replaceable by non-diagrammatic thinking.

That is enough to refute claim (a), the claim that all diagrammatic thinking in thinking through a proof is superfluous.

Most importantly, the reader will witness logicians tackle the issue of whether there is any intrinsic reason that sentential systems, but not diagrammatic systems, could provide us with rigorous proofs, and their success in answering this question in the negative.

That entire process would constitute thinking through a proof of the conclusion; and the diagrammatic thinking involved would not be superfluous.

With claim (a) disposed of, consider again claim (b) that, while not all diagrammatic thinking in a process of thinking through a proof is superfluous, all non-superfluous diagrammatic thinking will be replaceable by non-diagrammatic thinking in a process of thinking through that same proof.