In 1653, the French philosopher and scientist Blaise Pascal published "Treatise on the Equilibrium of Liquids," which discussed the principles of static fluids. A static fluid is a fluid that is not in motion. When a fluid is not flowing, we say that the fluid is in static equilibrium. If the fluid is water, we say it is in hydrostatic equilibrium. For a fluid in static equilibrium, the net force on any part of the fluid must be zero; otherwise, the fluid will start to flow. Pascal observed...

The halo effect is a cognitive bias in which an individual's overall impression influences judgments about their specific traits. This psychological phenomenon leads people to associate positive characteristics with those they perceive as generally good and negative characteristics with those they view as bad. This effect is particularly influential in social perception, professional evaluations, and decision-making processes.The Psychological Basis of the Halo EffectThe halo effect is rooted...

An ellipse is formed when a right circular cone is intersected by an inclined plane that does not cut through its base. This intersection yields a closed, symmetric curve characterized by distinctive geometric properties. Most notably, an ellipse is defined as the collection of all points in a plane for which the combined distances to two fixed points—called the foci—remain constant.The ellipse features two principal axes: the major and the minor axes. The major axis is the longest diameter,...

Social proof is a form of persuasion based on comparison and conformity. People compare their behavior and actions to what others are doing and will change to conform to do what their peers do.

The quotient rule is a fundamental differentiation technique in calculus used to differentiate functions expressed as a ratio of two differentiable functions. Given a function of the form:Where g(x) and h(x) are both differentiable and h(x) ≠ 0, the derivative of f(x) is given by:Example:The quotient rule is beneficial when differentiating rational functions, trigonometric ratios, and exponential functions. For example, given:applying the quotient rule,This rule is essential in solving problems...

In social interactions, individuals frequently seek to understand the motivations and causes behind others' behaviors. This fundamental aspect of social perception, known as attribution, plays a crucial role in shaping interpersonal relationships and guiding future actions. Attribution refers to the cognitive process through which people infer the reasons behind others' behaviors, allowing them to assess character traits, intentions, and situational influences.Attribution Theory and Its...