The Diagonal of a Regular Pentagon

• Published in 2026
• Added on 2026-10-18

We demonstrate the well-known fact that the diagonal of a unit regular pentagon has length the golden ratio. While similar to other proofs, we provide a novel figure that we believe is particularly well-suited to achieve full understanding at a glance.

Links

• https://arxiv.org/abs/2610.18903v1
• https://arxiv.org/pdf/2610.18903v1

Other information

BibTeX entry

@article{TheDiagonalofaRegularPentagon,
	key = {TheDiagonalofaRegularPentagon},
	type = {article},
	title = {The Diagonal of a Regular Pentagon},
	author = {Dan McQuillan},
	abstract = {We demonstrate the well-known fact that the diagonal of a unit regular pentagon has length the golden ratio. While similar to other proofs, we provide a novel figure that we believe is particularly well-suited to achieve full understanding at a glance.},
	comment = {},
	date_added = {2026-10-18},
	date_published = {2026-10-18},
	urls = {https://arxiv.org/abs/2610.18903v1,https://arxiv.org/pdf/2610.18903v1},
	collections = {easily-explained,fun-maths-facts,geometry},
	url = {https://arxiv.org/abs/2610.18903v1 https://arxiv.org/pdf/2610.18903v1},
	year = 2026,
	urldate = {2026-10-18},
	archivePrefix = {arXiv},
	eprint = {2610.18903},
	primaryClass = {math.HO}
}