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Because microorganisms include most unicellular organisms from all three domains of life they can be extremely diverse. Two of the three domains, Archaea and Bacteria, only contain microorganisms. The third domain Eukaryota includes all multicellular organisms as well as many unicellular protists and protozoans that are microbes. Some protists are related to animals and some to green plants. There are also many multicellular organisms that are microscopic, namely micro-animals, some fungi, and some algae, but these are generally not considered microorganisms.

Microbes are important in human culture and health in many ways, serving to ferment foods, and to produce fuel, enzymes, and other bioactive compounds. Microbes are essential tools in biology as model organisms and have been put to use in biological warfare and bioterrorism. Microbes are a vital component of fertile soil. In the human body, microorganisms make up the human microbiota, including the essential gut flora. The pathogens responsible for many infectious diseases are microbes and, as such, are the target of hygiene measures.

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Microorganisms are found virtually everywhere, except for environments that have been made artificially sterile by humans. Even these must be constantly sterilized and carefully protected, lest microorganisms be tracked in from the outside world.

Microorganisms live in water, in soil, and on the skin and in the digestive tracts of animals. This is why all living things must have immune systems – while many microorganisms can be helpful to them, some can be harmful and cause disease.

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Main concepts

The following are some of the most important concepts in geometry.

• Axioms

Euclid introduced certain axioms, or postulates, expressing primary or self-evident properties of points, lines, and planes. He proceeded to rigorously deduce other properties by mathematical reasoning. The characteristic feature of Euclid’s approach to geometry was its rigor, and it has come to be known as axiomatic or synthetic geometry.

• Points

Points are generally considered fundamental objects for building geometry. They may be defined by the properties that thay must have, as in Euclid’s definition as “that which has no part”, or in synthetic geometry. In modern mathematics, they are generally defined as elements of a set called space, which is itself axiomatically defined.

• Lines

Euclid described a line as “breadthless length” which “lies equally with respect to the points on itself”. In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic geometry, a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation, but in a more abstract setting, such as incidence geometry, a line may be an independent object, distinct from the set of points which lie on it. In differential geometry, a geodesic is a generalization of the notion of a line to curved spaces.

• Planes

In Euclidean geometry a plane is a flat, two-dimensional surface that extends infinitely; the definitions for other types of geometries are generalizations of that. Planes are used in many areas of geometry. For instance, planes can be studied as a topological surface without reference to distances or angles; it can be studied as an affine space, where collinearity and ratios can be studied but not distances; it can be studied as the complex plane using techniques of complex analysis; and so on.

• Angles

Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. In modern terms, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

• Curves

A curve is a 1-dimensional object that may be straight (like a line) or not; curves in 2-dimensional space are called plane curves and those in 3-dimensional space are called space curves.

• Surfaces

A surface is a two-dimensional object, such as a sphere or paraboloid. In differential geometry and topology, surfaces are described by two-dimensional ‘patches’ (or neighborhoods) that are assembled by diffeomorphisms or homeomorphisms, respectively. In algebraic geometry, surfaces are described by polynomial equations.

• Length, area, and volume

Area and volume can be defined as fundamental quantities separate from length, or they can be described and calculated in terms of lengths in a plane or 3-dimensional space.Mathematicians have found many explicit formulas for area and formulas for volume of various geometric objects. In calculus, area and volume can be defined in terms of integrals, such as the Riemann integral or the Lebesgue integral.

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0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …
The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths.

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Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750-420 terahertz, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths).

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Cells can acquire specified function and carry out various tasks within the cell such as replication, DNA repair, protein synthesis, and motility. Cells are capable of specialization and mobility within the cell. Most cells are measured in micrometers due to their small size.

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Current

• Current is the flow of particles in a particular direction. E.g air currents that cause winds or water currents.
• When particles flow in an electric circuit to produce electricity, it is called an electric current.

Electric current

The flow of electric charges in a circuit is called an electric current. The direction is taken from the positive terminal to the negative terminal of the battery in an external circuit.

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