Orange Peels and Fresnel Integrals

• Published in 2012
• Added on 2012-02-15

There are two standard ways of peeling an orange: either cut the skin along meridians, or cut it along a spiral. We consider here the second method, and study the shape of the spiral strip, when unfolded on a table. We derive a formula that describes the corresponding flattened-out spiral. Cutting the peel with progressively thinner strip widths, we obtain a sequence of increasingly long spirals. We show that, after rescaling, these spirals tends to a definite shape, known as the Euler spiral. The Euler spiral has applications in many fields of science. In optics, the illumination intensity at a point behind a slit is computed from the distance between two points on the Euler spiral. The Euler spiral also provides optimal curvature for train tracks between a straight run and an upcoming bend. It is striking that it can be also obtained with an orange and a kitchen knife.

Links

• http://arxiv.org/abs/1202.3033
• http://arxiv.org/pdf/1202.3033v1

Other information

BibTeX entry

@article{Bartholdi2012,
	key = {Bartholdi2012},
	type = {article},
	title = {Orange Peels and Fresnel Integrals},
	author = {Bartholdi, Laurent and Henriques, Andr{\'{e}} G.},
	abstract = {There are two standard ways of peeling an orange: either cut the skin along meridians, or cut it along a spiral. We consider here the second method, and study the shape of the spiral strip, when unfolded on a table. We derive a formula that describes the corresponding flattened-out spiral. Cutting the peel with progressively thinner strip widths, we obtain a sequence of increasingly long spirals. We show that, after rescaling, these spirals tends to a definite shape, known as the Euler spiral. The Euler spiral has applications in many fields of science. In optics, the illumination intensity at a point behind a slit is computed from the distance between two points on the Euler spiral. The Euler spiral also provides optimal curvature for train tracks between a straight run and an upcoming bend. It is striking that it can be also obtained with an orange and a kitchen knife.},
	comment = {},
	date_added = {2012-02-15},
	date_published = {2012-02-01},
	urls = {http://arxiv.org/abs/1202.3033,http://arxiv.org/pdf/1202.3033v1},
	collections = {Attention-grabbing titles,Easily explained,Things to make and do,Food,Geometry,Fun maths facts},
	archivePrefix = {arXiv},
	arxivId = {1202.3033},
	eprint = {1202.3033},
	journal = {Time},
	month = {feb},
	pages = {1--3},
	url = {http://arxiv.org/abs/1202.3033 http://arxiv.org/pdf/1202.3033v1},
	year = 2012,
	primaryClass = {math.HO},
	urldate = {2012-02-15}
}