The three kings: Harry Benjamin, John Money, Robert Stoller

A rigid body subjected to three forces acting at three points is known as a three-force member. These forces must have concurrent lines of action, except for parallel forces, where the lines of action are parallel.
For example, consider a dumpster connected to a pin support at point A and a pin attached to a hydraulic cylinder at point B.

A function of three variables assigns a single real number to each point in three-dimensional space. Every point is identified by its Cartesian coordinates, x, y, and z, and the function maps this ordered triple to a scalar value. Such functions are commonly used to describe physical quantities that vary throughout space.A representative example is the electric potential generated by a point charge. In this case, the potential at a given location depends only on the distance from the charge. If...

On the basis of mirror symmetry, stereoisomers of an organic molecule can be further classified into diastereomers and enantiomers. Diastereomers are stereoisomers that are not mirror images of each other. Substituted alkenes, such as the cis and trans isomers of 2-butene, are diastereomers, as these molecules exhibit different spatial orientations of their constituent atoms, are not mirror images of each other, and do not interconvert. Here, the interconversion is suppressed due to restricted...

We typically love the people with whom we form relationships, but the type of love we have for our family, friends, and lovers differs. Robert Sternberg (1986) proposed that there are three components of love: intimacy, passion, and commitment. These three components form a triangle that defines multiple types of love: this is known as Sternberg’s triangular theory of love. Intimacy is the sharing of details and intimate thoughts and emotions. Passion is the physical attraction—the flame in the...

Isomerism in Complexes
Isomers are different chemical species that have the same chemical formula.
Transition metal complexes often exist as geometric isomers, in which the same atoms are connected through the same types of bonds but with differences in their orientation in space. Coordination complexes with two different ligands in the cis and trans positions from a ligand of interest form isomers. For example, the octahedral [Co(NH3)4Cl2]+ ion has two isomers (Figure 1) In the cis...

When disubstituted benzenes undergo electrophilic substitution, the product distribution depends on the directing effect of both substituents. When the directing effects of both substituents reinforce each other, a single product is obtained. For example, bromination of p-nitrotoluene occurs ortho to the methyl group and meta to the nitro group, which is the same position, resulting in a single product. However, if the directing effects of the two groups oppose each other, the more strongly...