The most expensive painting in the world

A curved roof has a surface area that is generally larger than its flat projection. To estimate the cost of painting it, the curved surface area must first be calculated. If the roof is represented parametrically by a vector-valued function r(u,v), then each point in a parameter domain D corresponds to a point on the surface S. This connection allows the curved surface to be studied through a two-dimensional parameter region.The parameter domain D is divided into many small rectangles. A...

The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms.

Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.

The coronary arteries, originating from the ascending aorta, bifurcate from two sinuses located within the ascending aorta. Positioned just above the aortic semilunar valve, these sinuses house essential aortic baroreceptors and chemoreceptors, crucial for maintaining cardiac function. The left coronary artery and the right coronary artery branch off from the left posterior and anterior aortic sinuses, respectively.
Encircling the heart, the coronary arteries form a ring-like structure before...

The retina is a layer of nervous tissue at the back of the eye that transduces light into neural signals. This process, called phototransduction, is carried out by rod and cone photoreceptor cells in the back of the retina.

In 1882, Flemming observed lampbrush chromosomes (LBC) in salamander eggs. Later in 1892, Rückert observed LBCs in shark egg cells and coined the term "lampbrush chromosomes" because they looked like brushes used to clean kerosene lamps.
LBCs are made up of two pairs of conjugating homologous chromatids. Each chromatid consists of alternatively positioned regions of condensed-inactive chromatin and loosely placed-active side loops, which can be contracted and extended. The loops resemble the...