Henrik Enghoff and the volumen inefficax

The vestibular system is a set of inner ear structures that provide a sense of balance and spatial orientation. This system is comprised of structures within the labyrinth of the inner ear, including the cochlea and two otolith organs—the utricle and saccule. The labyrinth also contains three semicircular canals—superior, posterior, and horizontal—that are oriented on different planes.

The function of the kidneys is to filter, reabsorb, secrete, and excrete. Every day the kidneys filter nearly 180 liters of blood, initially removing water and solutes but ultimately returning nearly all filtrates into circulation with the help of osmoregulatory hormones. This process removes wastes and toxins but is also crucial to maintain water and electrolyte levels. Most of these functions are performed by the tiny but numerous nephrons contained within the kidneys.

Trophic level transfer efficiency (TLTE) is a measure of the total energy transfer from one trophic level to the next. Due to extensive energy loss as metabolic heat, an average of only 10% of the original energy obtained is passed on to the next level. This pattern of energy loss severely limits the possible number of trophic levels in a food chain.

Small population sizes put a species at extreme risk of extinction due to a lack of variation, and a consequent decrease in adaptability. This weakens the chances of survival under pressures such as climate change, competition from other species, or new diseases. Large populations are more likely to survive pressures such as these, as such populations are more likely to harbor individuals that have genetic variants that are adaptive under new stresses. Small populations are much less likely to...

For solids whose cross-sectional areas vary in a predictable way, volume can be determined by integrating these areas along an axis perpendicular to the slices. This approach is particularly useful for polyhedral solids, where classical geometric formulas may not be immediately applicable. A tetrahedron provides a clear example of how cross-sectional integration can be applied to a three-dimensional object with continuously changing geometry.Consider a tetrahedron with height h and a base that...