• Corpus ID: 252568056

A new proof of the Pythagorean Theorem inspired by novel characterizations of unital algebras

@inproceedings{Greensite2022ANP,
  title={A new proof of the Pythagorean Theorem inspired by novel characterizations of unital algebras},
  author={Fred Greensite},
  year={2022}
}
. A new proof of the Pythagorean Theorem is presented, utilizing George Birkhoff’s version of the postulates of Euclidean geometry as incorpo- rating R . Generalization of the mechanism of proof forwards novel characterizations of real finite-dimensional unital associative algebras which, along with the accompanying functor, are also presented and applied. 

Tables from this paper

Novel characterizations of real finite-dimensional unital algebras

. Alternative characterizations of real finite-dimensional unital algebras are introduced based on a functor arising from the ways the inverse operation on the units can be uncurled.

Origin of the Proto-norm functor from an Inverse Problems regularization method

. Characterization of real finite-dimensional unital associative algebras with the Proto-norm functor is shown to have its origin in the interpre- tation of a particular Inverse Problems

Cosmology from a non-physical standpoint: an algebraic analysis

. We present a non-physical interpretation of the Cosmological Constant based on a particular algebraic analysis. This also introduces some novel algebraic structures, such as “Unital Norms” and

References

SHOWING 1-6 OF 6 REFERENCES

Novel characterizations of real finite-dimensional unital algebras

. Alternative characterizations of real finite-dimensional unital algebras are introduced based on a functor arising from the ways the inverse operation on the units can be uncurled.

Origin of the Proto-norm functor from an Inverse Problems regularization method

. Characterization of real finite-dimensional unital associative algebras with the Proto-norm functor is shown to have its origin in the interpre- tation of a particular Inverse Problems

Cosmology from a non-physical standpoint: an algebraic analysis

. We present a non-physical interpretation of the Cosmological Constant based on a particular algebraic analysis. This also introduces some novel algebraic structures, such as “Unital Norms” and

A Set of Postulates for Plane Geometry, Based on Scale and Protractor

The Pythagorean Theorem, a 4000 year history

  • 2007