Roots and Mathematics

Who would believe that all the roots and absorbing hairs of grasses or cereals, be they rye, wheat or couch grass, put all together, could form a line surrounding the perimeter of an European country? In 1937, a German naturalist carried out this scrupulous work, measuring the surface and length of all roots of a rye during the earing period. It seems that plants use the same trick used by Elissa when she founded Carthage. Elissa had to buy a piece of land from the local Berbers, an area that had to be no larger than that comprised by an ox skin. The legend says she took the ox skin and cut it into such thin fringes that she could surround with them a surface of four square kilometers.

The rye roots counting found 143 roots of the first level, 30,000 roots of the second level, 2,300,000 of the third level and 11,500,000 of the fourth level, thus a number of 13,835,143 roots having a total length of about 600 km (375 mi).

Yet, the roots are covered by absorbing hairs. Their approximate number boosts the aforementioned total to 15 billion, summing a surface of 400 square meters and a length of 10,000 km (6,250 mi), one quarter of the Equator.

A rye plant daily forms 115 new roots and 119 million absorbing hairs. Thus, the total length of the roots grows daily by 5 km (3 mi) and that of the absorbing hairs by 80 km (50 mi), in the fight for conquering new soil areas.

Another biologist calculated the root length in the case of a 2-year old couch grass (Agropyrum cristatum). Its root system had a total length of 500 km (310 mi), occupying a soil volume 2 m (6.6 ft) deep and with a range of 1.2 m (4 ft) around the plant.

This remarkable development of the roots is an adaptation of the plants, meant to ensure them the necessary amounts of water; the extremely fine and complex weavings of the root system allows the contact with as large as possible a soil surface inside a small volume.

Grass and cereal roots make the most complex and dense network of roots in the plant world. But desert plant can come with examples of impressively long tap roots as well. These plants must drill deep to find table water.

For example, the camelthorn (Alhagi camelorum) is a humble Saharan shrub. One would hardly suspect its roots go down to even 30 m (100 ft) searching for water. It is the world's relatively longest root.

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