# Orange Peels and Fresnel Integrals

- Published in 2012
- Added on

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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

## Other information

- arxivId
- 1202.3033
- journal
- Time
- pages
- 1--3

### BibTeX entry

@article{Bartholdi2012, 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.}, archivePrefix = {arXiv}, arxivId = {1202.3033}, author = {Bartholdi, Laurent and Henriques, Andr{\'{e}} G.}, eprint = {1202.3033}, journal = {Time}, month = {feb}, pages = {1--3}, title = {Orange Peels and Fresnel Integrals}, url = {http://arxiv.org/abs/1202.3033 http://arxiv.org/pdf/1202.3033v1}, year = 2012, primaryClass = {math.HO}, urldate = {2012-02-15}, collections = {Attention-grabbing titles,Easily explained,Things to make and do,Food,Geometry,Fun maths facts} }