Tech UPTechnologyThe universal formula for eggs: how to draw an...

The universal formula for eggs: how to draw an egg

The ovoid is a flat geometric figure widely represented in schools. It is a closed symmetrical curve that is built with four arcs of circumference. It is easy to represent and should not be confused with the oval, even if the eye can deceive us. A curious example of the use of the ovoid is the section of the sewer pipes, to avoid the sedimentation of waste. If the sewer doesn’t stink any more than it should, it’s thanks to math. Regarding the oval, an example that you have surely seen on television is that of the oval circuit of motor racing or motorcycling. Despite the resemblance of the ovoid to eggs, it does not represent the profile of all the eggs that we see in nature. Neither do ovals. There are eggs of all sizes, shapes, colors, and textures. Come on, for tastes, eggs. And it seems that they can all be studied in a mathematical expression that Valeriy Narushin, Michael Romanov and Darren Griffin have developed. A study published in August 2021.

Due to their nutritional interest, eggs have attracted the attention of mathematicians, biologists and engineers from an analytical point of view. According to the article, bird eggs had so far escaped a general formula. Egg analysis has always been based on four shapes: ovoid, sphere, ellipsoid, and pyriform curves (pear shapes). In this case, adjustments have been made to the expression of the ovoid, to be able to apply it to any egg. Everything is based on introducing indexes of shapes, depending on the different characteristics observed in the ovoid world. The first of these indexes is already a classic of Romanoff and Romanoff ( The Avian Egg , New York, 1949). The R&R index established the relationship between the maximum width of the egg (B) and the length of the egg (L). This index has been used in the chicken egg industry to evaluate the shape and to be able to classify them. Because we like eggs and that they are all neatly arranged in a carton and, if possible, the same size and shape.


Let’s keep touching the eggs

Taking a look at the bibliography of the study, we see that for several years all kinds of eggs have been touched. Not just chicken eggs, which are the ones we are used to seeing and eating. We are going to touch the eggs with the eyes of mathematics, we do not want misunderstandings. Scientists have been putting their hand in the formulas to end up including a greater number of shape indexes and of better quality. In the new study, a review of previous work is made to arrive at a formula that works for all types of eggs. It is explained that eggs with circular or elliptical shapes do not present problems, since we have clear and delimited definitions for this. Therefore, the focus is on oval and pyriform eggs.


The false architectural eggs

The authors allude to the fact that the formulas used so far are valid for the artistic context, that is, to represent them in works of architecture. For example, the profile seen in a semicircular arch may somewhat resemble an egg, if only because of the distribution of stresses. But it is not shaped like an egg, even though the example is used to talk about such a static study. They are, therefore, not accurate enough to accurately represent reality, at least for practical and scientific research purposes, especially in the field of biology. A problem that this team already addressed in a previous work (Digital imaging assisted geometry of chicken eggs using Hügelschäffer’s model).


Testing eggs

Four examples are presented in the paper: the uralense tawny owl (Strix uralensis ), a species of owl that presents circular eggs; common emu ( Dromaius novaehollandiae ), as a representative of elliptical eggs; Song thrush ( Turdus philomelos ) and osprey ( Pandion haliaetus ) in the oval team and, finally, the Brünnich’s or broad-billed guillemot ( Uria lomvia ) with the elusive pyriform eggs. Once the formula was established from these species, they applied it to others: king snipe ( Gallinago media ) and king penguin ( Aptenodytes patagonicus ). And the result was surprisingly optimal. In the conclusions they are enthusiastic and open ways for their formula to be used in industry and as a tool for researchers in various areas of knowledge.

In the conclusions of the article they collect the four parameters necessary to characterize any egg: length of the egg (L), maximum width (B), displacement of the vertical axis (w) and diameter at a distance of a quarter of the length of the egg, measured from the narrow end DL / 4). The formula can throw anyone back, but it is not difficult to implement in a function graphing program. We have done it with GeoGebra, which is an educational graphing tool. It’s intuitive and maybe even fun. You can also represent piriform eggs with GeoGebra.



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