The surface areas of volumetric figures known from the school course of stereometry, such as a cube, parallelepiped, pyramid, prism, cylinder and others, are not difficult to calculate. Their sides and bases are the simplest. They can be squares, rectangles, triangles, circles, and so on. If the figure is more complex, it is divided into small ones and the areas of their surface faces are added. Thus, they achieve the desired result. But if a certain object of volumetric space is endowed with the most intricate form, for example, the human body. The area formula in this case is far from simple. Moreover, each of the people is endowed by nature with their own characteristics.
Practical use
But why do such calculations at all? Besides scientific interest, the practical importance of this is beyond doubt. And a vivid example of this is medicine and physiology. The air exchange with the surrounding space depends on the skin surface. From the body area - metabolism, that is, the internal metabolic processes of the body. These include the processing of food elements, turning it into tiny particles and removing unnecessary substances. The mechanics of the most important human organs depend on proper metabolism, which means health and life.
Body weight is largely built from adipose tissue, which can be observed in the body as an excess or deficiency. Therefore, the weight of a person is not always able to be an indicator of the exchange process due to individual characteristics. With this in mind, in medicine it is believed that the important factor is precisely the surface area of the human body. Therefore, its formula is considered necessary.
Chemotherapy
Chemotherapy often plays an important role in getting rid of infectious and parasitic diseases. Usually it has a greater effect than treatment with currently known drugs, and at the same time gives sometimes less negative consequences for the body. Its purpose is the destruction of infectious agents or parasites, and not a simple correction of violations, as occurs in the case of pharmacological methods. The consequence is the restoration of organ functions. The same method is used, wanting to rid the patient of cancer cells, which in many cases has a tangible result.
The exact formula of a person’s body area for chemotherapy is very important. Based on this indicator, the dose of the necessary drugs is calculated. Without knowledge of this, it is difficult to expect a positive outcome.
Other applications
Knowing the area of body cover opens up additional opportunities for physiological research. Its characteristics for different ages can be calculated and systematized. Here, the chance is significantly increased not only in time to identify a tendency to obesity and other diseases, but also to conduct valuable scientific research based on the data obtained.
Such calculations are necessary to calculate the dosage of drugs with great accuracy, funds with an extremely compressed therapeutic index, that is, a small border between the dose that causes a positive effect and harms the body. This turns out to be vital not only with chemotherapy, but also with the appointment of hormonal drugs. Ultrasound examinations of cardiac functions also require knowledge of the human body area formula. In addition, it is used to study the intensity of glomerular filtration in nephrology. This is an important indicator of studying kidney activity.
How to measure?
To calculate the area of volumetric geometric shapes, there are special formulas. They are mostly derived in ancient times, and modern people recognize them from reference books and school books.
It is also easy to calculate the volume of the human body, even despite its complex parameters. The great Archimedes also coped with a similar task. He found that it is enough to immerse a certain object in a tank filled to the brim with water and collect the liquid displaced by it into a vessel, then the volume of water, which is easy to measure, will turn out to be equal to the volume of the body. According to a legend that came to us from ancient times, a similar idea, like all ingenious, the idea came to the great ancient Greek scientist when he took a bath.
What would Archimedes say?
But what about the formula for calculating a person’s body area? Here, even Archimedes would have found it difficult to answer, this seemingly elementary task is so complicated. Let us immediately explain that by area we mean not the outlines of the human body that can be obtained by leaning it against a wall and drawing a chalk around the silhouette. This refers to the surface of the skin. But how to measure it? After all, the skin cannot be removed like clothes, and laid out on the floor, to make the necessary measurements.
Of course, you can paste someone upside down with a band-aid, then remove it and measure the surface area. There is also a chance to try to cover the entire human body with napkins, but neatly, evenly and without overlaps. And then remove all the elements, count and multiply by the surface area of one napkin. However, this is too cumbersome and complex process, in reality almost impossible to implement. Moreover, the probability of error is so great! But still, people, in the end, found a solution to this problem.
Calculation principles
The first formula for such calculations was developed by the American Dubois. All the calculation methods proposed later are not fundamentally fundamentally different from the specified method. They use indicators of body weight and human growth, that is, its length, raised to a certain extent. Then their product is multiplied by a coefficient preliminarily calculated in a practical way, less than 1. This is the most convenient option, since without such a formula, measuring a person’s body area is an extremely complicated process from the point of view of spatial geometry.
Most of the methods require data on the weight and height of a person to calculate. However, when calculating by the method of Livingston and Scott, only mass is used. This is also characteristic of the formulas of Kosteff and Mattara.
Example
The Yu method can be given as an example of calculating a person’s body area. This formula is the simplest, and therefore in our time has become widespread. It is similar to the Mosteller method. Here, the numerical values of height and weight are raised to the power of 0.5 (i.e., the square root is extracted). And then the result is multiplied by 0.015925. In this case, the mass should be converted into kilograms. The length is taken in centimeters. For all that, the value of the area is obtained in square meters, and this circumstance should also be taken into account.
Now it is easy to calculate the surface area with a height of 169 cm and a weight of 64 kg. After calculating the square roots of the proposed values, it will be 0.015925 x 13 x 8. The final result will be after rounding 1.66 m 2 .
Having figured out how to calculate the surface area of the human body and the formula, one can now make similar calculations for various ages with certain parameters and, if desired, make tables and diagrams from them. They help to reveal the general picture of changes in body surface area during a person’s life from infancy to adulthood.
Below are data for boys from 8 to 12 years old, calculated by Dubois.
Dubois nomogram
But is it possible to find out all the data without inconvenient calculations? Visually, without difficulties and formulas, the body area of a person can be found using the nomogram. It was also proposed and compiled by Dubois. It is presented below. How to use it?
Numbers horizontally indicate body weight, vertically - the height of a person. To determine the surface area using this nomogram, it is necessary to mentally draw perpendicular lines horizontally and vertically from the required indicators until they intersect. The resulting point on the curves presented and will show the desired result, according to the calculations of Dubois. For example, using a nomogram, it is easy to find that with a height of 160 cm and a weight of 75 kg, the surface area of the body will be 1.8 m 2 .
Medicine and Math
Having examined the issue, we realized that the knowledge about the human body area and the formula by which it is possible to determine it, which is so necessary for a healthy life, is provided to medicine by mathematics.
And this is far from the only information that doctors are able to get from the Queen of Sciences. Indeed, in the language of numbers in this world, almost everything can be expressed. The geometry of the human body is a huge world full of amazing discoveries. And many organs: joints, bones and muscles, it is no coincidence that they received their name by the name of geometric shapes. Mathematics is also important in genetics, ophthalmology, medical statistics and in many other areas of medicine.
Indicators of growth and weight are necessary with the correct calculation of the diet. In the end, accurate measurements of human organs, both internal and external, are extremely important for the manufacture of modern electronic prostheses, and not only damaged limbs. Nowadays, artificial valves for hearts are even produced and successfully applied in practice. And this is just another bright example.