Generating finitely many circles from one circle using Banach-Tarski decomposition paradox

[microreview]

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We prove the Banach-Tarski decomposition paradox applied to a circle.

https://doi.org/10.31219/osf.io/mh5gx

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 142, 2020 [FN]

Differential Forms (Open Mathematics Knowledge Base)

[knowledge base]

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We present a list of mathematical results about differential forms for future implementation in a digital Open Mathematics Knowledge Base.

https://doi.org/10.31219/osf.io/g7uqb

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 122, 2020 [ES]

Dark matter and bubbles of void

[original insight]

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This is a thought experiment with the following conjecture: bubbles of spacetime void alter the gravitational field of the galaxy and might explain the dark matter phenomenon.

https://doi.org/10.31219/osf.io/w7m3q

Open Physics Collaboration

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Op. J. Math. Phys.
Volume 1, Article 33, 2019 [BG]

Axioms of space?

[original idea]

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Here, we propose the discussion of which axioms nature really follow in the very quantum realm of spacetime.

https://doi.org/10.31219/osf.io/kx35m

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 1, Article 9, 2019 [AI]

Tangent Vectors on Tangent Euclidean Spaces

[microreview]

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This is an article on differential geometry that connects tangent vectors and tangent Euclidean spaces.

https://doi.org/10.31219/osf.io/vpz9x

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 1, Article 3, 2019 [AC]

The metric tensor pullback

[microreview]

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This article connects metric tensor with its pullback.

https://doi.org/10.31219/osf.io/puhzw

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 1, Article 2, 2019 [AB]