Circle and Circulation: The Language and Imagery of William Harvey's Discovery

The human circulatory system consists of blood, blood vessels that carry blood away from the heart, around the body, and back to the heart, and the heart itself, which acts as a central pump. The systemic circuit supplies blood to the whole body, the coronary circuit supplies blood to the heart, and the pulmonary circuit supplies blood flow between the heart and lungs.

The cardiovascular system is a vital transportation system in the body. It comprises the heart and blood vessels and facilitates the exchange of gases, nutrients, and waste products.
Heart
The heart is the central pump of the cardiovascular system that circulates blood throughout the body. It comprises two atria receiving the blood and two ventricles pumping blood out of the heart. Their rhythmic contractions, called heartbeats, ensure that blood flow remains continuous.
Blood Vessels
Blood...

The human body is a complex, well-organized machine, and at the heart of its operations lies the circulatory system. This network of blood vessels, which includes systemic arteries, plays a vital role in maintaining life by transporting nutrients, oxygen, and waste products to and from cells throughout the body.
Systemic circulation is the part of the cardiovascular system that carries oxygenated blood away from the heart to the body's tissues and returns deoxygenated blood back to the heart.

Green’s Theorem establishes a relationship between a line integral around a closed plane curve and a double integral over the region enclosed by that curve. It applies to a vector field F(x, y) = 〈P(x, y), Q(x, y)〉, where P and Q have continuous first partial derivatives on an open set containing the region.Let C be a positively oriented, simple, closed, piecewise smooth curve, and let R be the plane region bounded by C. Green’s Theorem states that\begin{equation*}\oint_C P\,dx+Q\,dy =\iint_R...

The study of fluid motion often involves understanding how local rotational behavior relates to global circulation. In the context of a pond with pollutants, direct measurement of water movement along an irregular shoreline can be impractical. Green’s Theorem in vector form provides an alternative by relating the circulation around a closed boundary to properties of the flow within the enclosed region.Measurements of water velocity at different points define a continuous vector field that...

Stokes’ Theorem provides a fundamental connection between the circulation of a vector field along a closed boundary and the cumulative rotational behavior across the surface it encloses. For a smooth three-dimensional surface with an oriented boundary curve, this theorem offers a unified way to relate motion along the edge to local rotational effects distributed over the surface.Mathematical FormulationThe theorem states that the circulation of a vector field along a closed curve is equal to...