Ex pede Herculem, "from his foot, [we can measure] Hercules", is a maxim of proportionality inspired by an experiment attributed to Pythagoras.
Ex pede Herculem, "from his foot, [we can measure] Hercules", is a maxim of proportionality inspired by an experiment attributed to Pythagoras.
According to Aulus Gellius' Noctes Atticae:
"The philosopher Pythagoras reasoned sagaciously and acutely in determining and measuring the hero's superiority in size and stature. For since it was generally agreed that Hercules paced off the racecourse of the stadium at Pisae, near the temple of Olympian Zeus, and made it six hundred feet long, and since other courses in the land of Greece, constructed later by other men, were indeed six hundred feet in length, but yet were somewhat shorter than that at Olympia, he readily concluded by a process of comparison that the measured length of Hercules' foot was greater than that of other men in the same proportion as the course at Olympia was longer than the other stadia. Then, having ascertained the size of Hercules' foot, he made a calculation of the bodily height suited to that measure, based upon the natural proportion of all parts of the body, and thus arrived at the logical conclusion that Hercules was as much taller than other men as the race course at Olympia exceeded the others that had been constructed with the same number of feet." (translated by John C. Rolfe of the University of Pennsylvania for the Loeb Classical Library, 1927)
In other words, one can extrapolate the whole from the part. Ex ungue leonem, "from its claw [we can know] the lion," is a similar phrase, noted in Benet's Reader's Encyclopedia 1948.
The principle was raised to an axiom of biology by D'Arcy Wentworth Thompson, in On Growth and Form, 1917; it has found dependable use in paleontology, where the measurements of a fossil jawbone or a single vertebra offer a close approximation of the size of a long-extinct animal, in cases where comparable animals are already known. The studies of proportionality in biology are pursued in the fields of morphogenesis, biophysics and biostatistics.
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In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling, possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other.
Jumping or leaping is a form of locomotion or movement in which an organism or non-living mechanical system propels itself through the air along a ballistic trajectory. Jumping can be distinguished from running, galloping and other gaits where the entire body is temporarily airborne, by the relatively long duration of the aerial phase and high angle of initial launch.
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Brobdingnag is a fictional land, which is occupied by giants, in Jonathan Swift's 1726 satirical novel Gulliver's Travels. The story's main character, Lemuel Gulliver, visits the land after the ship on which he is travelling is blown off course. As a result, he becomes separated from a party exploring the unknown land. In the second preface to the book, in 1727, Gulliver laments that the publisher misspelled the land's name, which Gulliver asserts is actually called Brobdingrag.
The Discourses and Mathematical Demonstrations Relating to Two New Sciences published in 1638 was Galileo Galilei's final book and a scientific testament covering much of his work in physics over the preceding thirty years. It was written partly in Italian and partly in Latin.
The twenty-foot equivalent unit is a general unit of cargo capacity, often used for container ships and container ports. It is based on the volume of a 20-foot-long (6.1 m) intermodal container, a standard-sized metal box which can be easily transferred between different modes of transportation, such as ships, trains, and trucks.
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A shoe size is an indication of the fitting size of a shoe for a person.
Allometry is the study of the relationship of body size to shape, anatomy, physiology and behaviour, first outlined by Otto Snell in 1892, by D'Arcy Thompson in 1917 in On Growth and Form and by Julian Huxley in 1932.
The Pythagoras tree is a plane fractal constructed from squares. Invented by the Dutch mathematics teacher Albert E. Bosman in 1942, it is named after the ancient Greek mathematician Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to depict the Pythagorean theorem. If the largest square has a size of L × L, the entire Pythagoras tree fits snugly inside a box of size 6L × 4L. The finer details of the tree resemble the Lévy C curve.
The sector, also known as a proportional compass or military compass, was a major calculating instrument in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It was used for solving problems in proportion, multiplication and division, geometry, and trigonometry, and for computing various mathematical functions, such as square roots and cube roots. Its several scales permitted easy and direct solutions of problems in gunnery, surveying and navigation. The sector derives its name from the fourth proposition of the sixth book of Euclid, where it is demonstrated that similar triangles have their like sides proportional. Some sectors also incorporated a quadrant, and sometimes a clamp at the end of one leg which allowed the device to be used as a gunner's quadrant.
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The largest body part is either the largest given body part across all living and extinct organisms or the largest example of a body part within an existing species. The largest animals on the planet are not the only ones to have large body parts, with some smaller animals actually having one particularly enlarged area of the body.
The long-footed potoroo is a small marsupial found in southeastern Australia, restricted to an area around the coastal border between New South Wales and Victoria. It was first recorded in 1967 when an adult male was caught in a dog trap in the forest southwest of Bonang, Victoria. It is classified as vulnerable.
A scale ruler is a tool for measuring lengths and transferring measurements at a fixed ratio of length; two common examples are an architect's scale and engineer's scale. In scientific and engineering terminology, a device to measure linear distance and create proportional linear measurements is called a scale. A device for drawing straight lines is a straight edge or ruler. In common usage, both are referred to as a ruler.
Diaulos was a double-stadion race, c. 400 metres , introduced in the 14th Olympiad of the ancient Olympic Games . The length of each foot race varied depending on the length of the stadium. This was because the Greek foot varied widely from one locality to another, for example the stadium at Olympia was 192.27 metres but at Delphi it was 177.50 metres (582.35 ft) long. Scholars debate whether or not the runners had individual "turning" posts for the return leg of the race, or whether all the runners approached a common post, turned, and then raced back to the starting line. Although at Delphi an inscription referenced "turning-posts" as opposed to "turning-post", which suggests each runner had their own turning post, to prevent an outside runner from losing 3–4 metres (9.8–13.1 ft). These were called kampteres. Archaeological evidence at Nemea also shows that there were individual turning posts.
An artistic canon of body proportions, in the sphere of visual arts, is a formally codified set of criteria deemed mandatory for a particular artistic style of figurative art. The word canon was first used for this type of rule in Classical Greece, where it set a reference standard for body proportions, to produce a harmoniously formed figure appropriate to depict gods or kings. Other art styles have similar rules that apply particularly to the representation of royal or divine personalities.
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.