Math Is Fun Forum

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#8770. What does the term is Biology 'Microevolution' mean?

#8771. What does the term in Biology 'Mitochondrion' mean?

Important Notes on Angles

0^o < \ Acute \ angle < \ {90}^o

gives

{90}^o < \ Obtuse \ angle < {180}^o

gives

{180}^o < \ Reflex \ angle < {360}^o

gives

A \ right \ angle \ is \ equal \ to \ {90}^o

gives

A \ straight \ angle \ is \ equal \ to {180}^o.

gives

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#2059. What does the medical term 'Cranial nerves' mean?

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#5523.

35) Fermi–Dirac statistics

Fermi–Dirac statistics (F–D statistics) is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac, each of whom derived the distribution independently in 1926 (although Fermi derived it before Dirac). Fermi–Dirac statistics is a part of the field of statistical mechanics and uses the principles of quantum mechanics.

F–D statistics applies to identical and indistinguishable particles with half-integer spin (1/2, 3/2, etc.), called fermions, in thermodynamic equilibrium. For the case of negligible interaction between particles, the system can be described in terms of single-particle energy states. A result is the F–D distribution of particles over these states where no two particles can occupy the same state, which has a considerable effect on the properties of the system. F–D statistics is most commonly applied to electrons, a type of fermion with spin 1/2.

A counterpart to F–D statistics is Bose–Einstein statistics (B–E statistics), which applies to identical and indistinguishable particles with integer spin (0, 1, 2, etc.) called bosons. In classical physics, Maxwell–Boltzmann statistics (M–B statistics) is used to describe particles that are identical and treated as distinguishable. For both B–E and M–B statistics, more than one particle can occupy the same state, unlike F–D statistics.

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#8546.

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#8768. What does the term 'Grammatology' mean?

#8769. What does the term 'Graphology' mean?

Circle

A circle is a curved plane figure. Every point on the circle is equidistant from a fixed point known as the center of the circle. It is a 2D shape and is measured in terms of radius. The word ‘Circle’ is derived from the Latin word 'circulus' meaning small ring.

What is Circle?

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Parts of a Circle

There are many parts or components of a circle that we should know to understand its properties. A circle has mainly the following parts:

* Circumference: It is also referred to as the perimeter of a circle and can be defined as the distance around the boundary of the circle.

* Radius of Circle: Radius is the distance from the center of a circle to any point on its boundary. A circle has many radii as it is the distance from the center and touches the boundary of the circle at various points.

* Diameter: A diameter is a straight line passing through the center that connects two points on the boundary of the circle. We should note that there can be multiple diameters in the circle, but they should:

** pass through the center.
** be straight lines.
** touch the boundary of the circle at two distinct points which lie opposite to each other.

* Chord of a Circle: A chord is any line segment touching the circle at two different points on its boundary. The longest chord in a circle is its diameter which passes through the center and divides it into two equal parts.

* Tangent: A tangent is a line that touches the circle at a unique point and lies outside the circle.

* Secant: A line that intersects two points on an arc/circumference of a circle is called the secant.

* Arc of a Circle: An arc of a circle is referred to as a curve, that is a part or portion of its circumference.

* Segment in a Circle: The area enclosed by the chord and the corresponding arc in a circle is called a segment. There are two types of segments - minor segment, and major segment.

* Sector of a Cirlce: The sector of a circle is defined as the area enclosed by two radii and the corresponding arc in a circle. There are two types of sectors - minor sector, and major sector.

Properties of Circle

Here is a list of properties of a circle:

* A circle is a closed 2D shape that is not a polygon. It has one curved face.
* Two circles can be called congruent if they have the same radius.
* Equal chords are always equidistant from the center of the circle.
* The perpendicular bisector of a chord passes through the center of the circle.
* When two circles intersect, the line connecting the intersecting points will be perpendicular to the line connecting their center points.
* Tangents drawn at the endpoints of the diameter are parallel to each other.

Let's see the list of important formulae pertaining to any circle.

Area of a Circle Formula: The area of a circle refers to the amount of space covered by the circle. It totally depends on the length of its radius :

Area = \pi{r^2} square units

gives .

Circumference of a Circle Formula: The circumference is the total length of the boundary of a circle.

Circumference = 2\pi{r} units

gives

Arc Length Formula: An arc is a section (part) of the circumference.

Length \ of \ an \ arc = \theta \times r. \ Here, \theta \ is \ in \radians.

gives

Area of a Sector Formula: If a sector makes an angle θ (measured in radians) at the center, then the area of the sector of a circle =

(\theta \times r^2) \div 2. \ Here, \theta \ is \ in \ radians.

gives

Length of Chord Formula: It can be calculated if the angle made by the chord at the center and the value of radius is known.

Length \ of \ chord = 2 r sin\dfrac{\theta}{2}. \ Here, \ \theta \ is \ in \ radians.

gives

Area of Segment Formula: The segment of a circle is the region formed by the chord and the corresponding arc covered by the segment.

The \ area \ of \ a \ segment = r^2(\theta − sin\theta) \div 2. Here, \theta \ is \ in \ radians.

gives

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#2058. What does the medical term 'Stress fracture' mean?

Hi,

#5522.

1557) Bone

Summary

A bone is a rigid organ that constitutes part of the skeleton in most vertebrate animals. Bones protect the various other organs of the body, produce red and white blood cells, store minerals, provide structure and support for the body, and enable mobility. Bones come in a variety of shapes and sizes and have complex internal and external structures.[2] They are lightweight yet strong and hard and serve multiple functions.

Bone tissue (osseous tissue), which is also called bone in the uncountable sense of that word, is hard tissue, a type of specialized connective tissue. It has a honeycomb-like matrix internally, which helps to give the bone rigidity. Bone tissue is made up of different types of bone cells. Osteoblasts and osteocytes are involved in the formation and mineralization of bone; osteoclasts are involved in the resorption of bone tissue. Modified (flattened) osteoblasts become the lining cells that form a protective layer on the bone surface. The mineralized matrix of bone tissue has an organic component of mainly collagen called ossein and an inorganic component of bone mineral made up of various salts. Bone tissue is mineralized tissue of two types, cortical bone and cancellous bone. Other types of tissue found in bones include bone marrow, endosteum, periosteum, nerves, blood vessels and cartilage.

In the human body at birth, there are approximately 300 bones present; many of these fuse together during development, leaving a total of 206 separate bones in the adult, not counting numerous small sesamoid bones. The largest bone in the body is the femur or thigh-bone, and the smallest is the stapes in the middle ear.

The Greek word for bone is "osteon", hence the many terms that use it as a prefix—such as osteopathy. In anatomical terminology, including the Terminologia Anatomica international standard, the word for a bone is os (for example, os breve, os longum, os sesamoideum).

Details

Bone is a rigid body tissue consisting of cells embedded in an abundant hard intercellular material. The two principal components of this material, collagen and calcium phosphate, distinguish bone from such other hard tissues as chitin, enamel, and shell. Bone tissue makes up the individual bones of the human skeletal system and the skeletons of other vertebrates.

The functions of bone include (1) structural support for the mechanical action of soft tissues, such as the contraction of muscles and the expansion of lungs, (2) protection of soft organs and tissues, as by the skull, (3) provision of a protective site for specialized tissues such as the blood-forming system (bone marrow), and (4) a mineral reservoir, whereby the endocrine system regulates the level of calcium and phosphate in the circulating body fluids.

Evolutionary origin and significance

Bone is found only in vertebrates, and, among modern vertebrates, it is found only in bony fish and higher classes. Although ancestors of the cyclostomes and elasmobranchs had armoured headcases, which served largely a protective function and appear to have been true bone, modern cyclostomes have only an endoskeleton, or inner skeleton, of noncalcified cartilage and elasmobranchs a skeleton of calcified cartilage. Although a rigid endoskeleton performs obvious body supportive functions for land-living vertebrates, it is doubtful that bone offered any such mechanical advantage to the teleost (bony fish) in which it first appeared, for in a supporting aquatic environment great structural rigidity is not essential for maintaining body configuration. The sharks and rays are superb examples of mechanical engineering efficiency, and their perseverance from the Devonian Period attests to the suitability of their nonbony endoskeleton.

In modern vertebrates, true bone is found only in animals capable of controlling the osmotic and ionic composition of their internal fluid environment. Marine invertebrates exhibit interstitial fluid compositions essentially the same as that of the surrounding seawater. Early signs of regulability are seen in cyclostomes and elasmobranchs, but only at or above the level of true bone fishes does the composition of the internal body fluids become constant. The mechanisms involved in this regulation are numerous and complex and include both the kidney and the gills. Fresh and marine waters provide abundant calcium but only traces of phosphate; because relatively high levels of phosphate are characteristic of the body fluids of higher vertebrates, it seems likely that a large, readily available internal phosphate reservoir would confer significant independence of external environment on bony vertebrates. With the emergence of terrestrial forms, the availability of calcium regulation became equally significant. Along with the kidney and the various component glands of the endocrine system, bone has contributed to development of internal fluid homeostasis—the maintenance of a constant chemical composition. This was a necessary step for the emergence of terrestrial vertebrates. Furthermore, out of the buoyancy of water, structural rigidity of bone afforded mechanical advantages that are the most obvious features of the modern vertebrate skeleton.

Chemical composition and physical properties

Depending upon species, age, and type of bone, bone cells represent up to 15 percent of the volume of bone; in mature bone in most higher animals, they usually represent only up to 5 percent. The nonliving intercellular material of bone consists of an organic component called collagen (a fibrous protein arranged in long strands or bundles similar in structure and organization to the collagen of ligaments, tendons, and skin), with small amounts of proteinpolysaccharides, glycoaminoglycans (formerly known as mucopolysaccharides) chemically bound to protein and dispersed within and around the collagen fibre bundles, and an inorganic mineral component in the form of rod-shaped crystals. These crystals are arranged parallel with the long axes of collagen bundles and many actually lie in voids within the bundles themselves. Organic material constitutes 50 percent of the volume and 30 percent of the dry weight of the intercellular composite, with minerals making up the remainder. The major minerals of the intercellular composite are calcium and phosphate. When first deposited, mineral is crystallographically amorphous, but with maturation it becomes typical of the apatite minerals, the major component being hydroxyapatite. Carbonate is also present—in amounts varying from 4 percent of bone ash in fish and 8 percent in most mammals to more than 13 percent in the turtle—and occurs in two distinct phases, calcium carbonate and a carbonate apatite. Except for that associated with its cellular elements, there is little free water in adult mammalian bone (approximately 8 percent of total volume). As a result, diffusion from surfaces into the interior of the intercellular substance occurs at the slow rates more typical of diffusion from surfaces of solids than within liquids.

The mineral crystals are responsible for hardness, rigidity, and the great compressive strength of bone, but they share with other crystalline materials a great weakness in tension, arising from the tendency for stress to concentrate about defects and for these defects to propagate. On the other hand, the collagen fibrils of bone possess high elasticity, little compressive strength, and considerable intrinsic tensile strength. The tensile strength of bone depends, however, not on collagen alone but on the intimate association of mineral with collagen, which confers on bone many of the general properties exhibited by two-phase materials such as fibre glass and bamboo. In such materials the dispersion of a rigid but brittle material in a matrix of quite different elasticity prevents the propagation of stress failure through the brittle material and therefore allows a closer approach to the theoretical limiting strength of single crystals.

The fine structure of bone has thus far frustrated attempts to determine the true strength of the mineral-matrix composite at the “unit” structural level. Compact (cortical) bone specimens have been found to have tensile strength in the range of 700–1,400 kg per square cm (10,000–20,000 pounds per square inch) and compressive strengths in the range of 1,400–2,100 kg per square cm (20,000–30,000 pounds per square inch). These values are of the same general order as for aluminum or mild steel, but bone has an advantage over such materials in that it is considerably lighter. The great strength of bone exists principally along its long axis and is roughly parallel both to the collagen fibre axis and to the long axis of the mineral crystals.

Although apparently stiff, bones exhibit a considerable degree of elasticity, which is important to the skeleton’s ability to withstand impact. Estimates of modulus of elasticity of bone samples are of the order of 420 to 700 kg per square cm (6,000 to 10,000 pounds per square inch), a value much less than steel, for example, indicating the much greater elasticity of bone. Perfect elasticity exists with loads up to 30 to 40 percent of breaking strength; above this, “creep,” or gradual deformation, occurs, presumably along natural defects within the bony structure. The modulus of elasticity in bone is strikingly dependent upon the rate at which loads are applied, bones being stiffer during rapid deformation than during slow; this behaviour suggests an element of viscous flow during deformation.

As might be anticipated from consideration of the two-phase composition of bone, variation in the mineral-collagen ratio leads to changes in physical properties: less mineral tends ultimately to greater flexibility and more mineral to increased brittleness. Optimal ratios, as reflected in maximal tensile strength, are observed at an ash content of approximately 66 percent, a value that is characteristic of the weight-bearing bones of mammals.

Bone morphology

Grossly, bone tissue is organized into a variety of shapes and configurations adapted to the function of each bone: broad, flat plates, such as the scapula, serve as anchors for large muscle masses, while hollow, thick-walled tubes, such as the femur, the radius, and the ulna, support weight or serve as a lever arm. These different types of bone are distinguished more by their external shape than by their basic structure.

All bones have an exterior layer called cortex that is smooth, compact, continuous, and of varying thickness. In its interior, bony tissue is arranged in a network of intersecting plates and spicules called trabeculae, which vary in amount in different bones and enclose spaces filled with blood vessels and marrow. This honeycombed bone is termed cancellous or trabecular. In mature bone, trabeculae are arranged in an orderly pattern that provides continuous units of bony tissue aligned parallel with the lines of major compressive or tensile force. Trabeculae thus provide a complex series of cross-braced interior struts arranged so as to provide maximal rigidity with minimal material.

Bones such as vertebrae, subject to primarily compressive or tensile forces, usually have thin cortices and provide necessary structural rigidity through trabeculae, whereas bones such as the femur, subject to prominent bending, shear, or torsional forces, usually have thick cortices, a tubular configuration, and a continuous cavity running through their centres (medullary cavity).

Long bones, distinctive of the body’s extremities, exhibit a number of common gross structural features. The central region of the bone (diaphysis) is the most clearly tubular. At one or commonly both ends, the diaphysis flares outward and assumes a predominantly cancellous internal structure. This region (metaphysis) functions to transfer loads from weight-bearing joint surfaces to the diaphysis. Finally, at the end of a long bone is a region known as an epiphysis, which exhibits a cancellous internal structure and comprises the bony substructure of the joint surface. Prior to full skeletal maturity the epiphysis is separated from the metaphysis by a cartilaginous plate called the growth plate or physis; in bones with complex articulations (such as the humerus at its lower end) or bones with multiple protuberances (such as the femur at its upper end) there may be several separate epiphyses, each with its growth plate.

Additional Information:

Bones: All you need to know

Bones are more than just the scaffolding that holds the body together. Bones come in all shapes and sizes and have many roles. In this article, we explain their function, what they consist of, and the types of cells they involve.

Bones are living, active tissues that the body is constantly remodeling.

Their functions include supporting body structure, protecting vital organs, and allowing the body to move. Also, they provide an environment for bone marrow, where the body creates blood cells, and they act as a storage area for minerals, particularly calcium.

The skeleton accounts for around 15%Trusted Source of body weight. At birth, humans have around 270Trusted Source soft bones. As they grow, some fuse.

By adulthood, people have between 206 and 213 bones. The reason for the difference is that some people have more or fewer bones in their ribs, vertebrae, fingers, and toes.

The largest bone in the human body is the thighbone, or femur, and the smallest is the stapes in the middle ear, at around 3 millimetersTrusted Source long.

Bones consist mostly of the protein collagen, which forms a soft framework. The mineral calcium phosphate hardens this framework, giving it strength. The bones contain 99% of the body’s calcium.

Bones have an internal structure similar to a honeycomb, which makes them rigid yet relatively light.

The structure of bones

Bones are composed of two types.

Compact (cortical) bone is a hard outer layer that is dense, strong, and durable. It makes up around 80% of adult bone mass and forms the outer layer of bone.

Cancellous (trabecular or spongy) bone makes up the remaining 20% of bone and consists of a network of trabeculae, or rod-like, structures. It is lighter, less dense, and more flexible than compact bone.

Bones also contain:

* osteoblasts and osteocytes, responsible for creating bone
*vosteoclasts, or bone-resorbing cells
* osteoid, a mix of collagen and other proteins
* inorganic mineral salts within the matrix
*bnerves and blood vessels
* bone marrow
* cartilage
* membranes, including the endosteum and periosteum

Bone cells

Bones are not static tissue but need constant maintenance and remodeling. There are threeTrusted Source main cell types involved in this process.

Osteoblasts are responsible for generating and repairing bone. They produce a protein mixture that doctors call osteoid, which is mineralized and becomes bone.

Osteocytes are inactive osteoblasts that are mineralized and remain within the bone they have created. They communicate with other bone cells and help support metabolic functions within the bone.

Osteoclasts are large cells with more than one nucleus. They useTrusted Source acids resulting from certain reactions to break down used bone. This process is called resorption. Osteoclasts help remodel injured bones and create pathways for nerves and blood vessels to travel through.

Bone marrow

Bone marrow is present in almost all bones where cancellous, or spongy, bone is present.

Bone marrow produces blood cells, including:

* red blood cells, which deliver oxygen to cells
* white blood cells, essential for the body’s immune system
* platelets, which the body uses for clotting

The marrow produces around 2 million red blood cells every second. It also produces lymphocytes, or the white blood cells involved in the immune response.

Extracellular matrix

Bones are essentially living cells embedded in a mineral-based organic matrix. This extracellular matrix consists of organic components (mostly type 1 collagen) and inorganic components, including hydroxyapatite and other salts, such as calcium and phosphate.

Collagen gives bone its tensile strength, namely resistance to pulling apart. Hydroxyapatite gives the bones compressive strength, or resistance to compression.

What do bones do?

Bones serve various functions that affect the whole body. StudiesTrusted Source show that, in addition to structure and movement, bones support energy metabolism, the production of blood cells, the immune system, and brain function.

Mechanics

Bones provide a frame to support the body. Muscles, tendons, and ligaments attach to bones. Without anchoring to bones, muscles could not move the body.

Protection

Some bones protect the body’s internal organs. For instance, the skull protects the brain, and the ribs protect the heart and lungs.

Synthesis

Cancellous bone is a vital reservoir for developing red blood cells, platelets, and white blood cells. Also, the body destroys defective and old red blood cells in bone marrow.

Metabolism

The metabolic functions of bone include:

* Storage: Bones act as a reserve for minerals, particularly calcium and phosphorous. Bone marrow adipose tissue can also store fatty acids.
* Endocrine function: Bones produce the precursors to various hormones, including those involved in growth, insulin production, and brain development. They release hormones that act on the kidneys and influence blood sugar regulation and fat deposition.
* Calcium balance: Bones can raise or reduce calcium in the blood by forming bone, or breaking it down in a process called resorption.
* pH balance: Some research has suggested bones can release or absorb alkaline salts, helping blood to stay at the right pH level, but scientists need more studies to confirm this.
* Detoxification: Bones can absorbTrusted Source heavy metals such as lead, mercury, and math from the blood.

Types of bone

There are five types of bones in the human body:

* Long bones: These are mostly compacted bones with little marrow and include most of the bones in the limbs. They tend to support weight and help movement.
* Short bones: These have a squat, cubed shape and include bones of the wrist and ankle.
* Flat bones: These have a flat, broad surface. They consist of two outer layers of compact bone and an inner layer of spongy bone. The bones of the skull, breastbone, ribs, and shoulder blades are flat bones. They tend to have a protective role.
* Sesamoid bones: These are embeddedTrusted Source in muscles and tendons near the surfaces of joints. They include the patella or kneecap. They protect tendons from wear and stress.
* Irregular bones: These bones do not fit into the first four categories and have an unusual shape. They include the bones of the spine and pelvis. They often protect organs or tissues.

The bones of the skeleton belong to two groups: The appendicular and axial skeletons.

The appendicular skeleton comprises 126 bones, including those of the limbs, shoulders, and pelvic girdle. It provides structure and support to other parts of the body.

The axial skeleton has less range of motion than the appendicular skeleton. It comprises the bones of the skull, vertebral column, and thoracic cage.

Bone remodeling

The body is always remodeling bone. This allows the body to fix damaged bone, reshape the skeleton during growth, and regulate calcium levels.

Remodeling is a two-part process. During formation, the body lays down new bone tissue. In resorption, osteoclasts break down and remove bone.

If one part of the skeleton comes under increased stress over time — for instance, during exercise — the sections of bone under most pressure will become thicker in response.

Osteocytes, osteoclasts, and osteoblasts play key roles, but other elements also contribute. These include parathyroid hormone, vitamin D, estrogen, and testosterone.

What is osteoporosis?

Osteoporosis is a bone disease that involves a reductionTrusted Source in bone mineral density. This increases the risk of fractures.

It most commonly occurs in females after menopause. However, it can affect males too, and it can start before menopause.

Osteoporosis occurs either when removal or resorption of bone happens too quickly, new bone forms too slowly, or for both reasons.

Risk factors include:

* low calcium levels
* vitamin D deficiency
* smoking tobacco
* using corticosteroids
* a high alcohol intake

Screening can help prevent or slow the progression of osteoporosis. Tests can show that osteopenia, the early stage of osteoporosis, is present. At this point, a doctor may recommend dietary measures or supplements.

As bone deterioration worsens, medications are available to slow its progression.

What other bone diseases are there?

Recent research : Currently, researchers are looking into ways to regenerate bone. This could help people with osteoarthritis, osteoporosis, and other conditions. It could also help mend broken bones.

Bone regeneration is a complex process. Scientists are currently looking at various aspects, including ways to:

* speed up mineral production for the generation of new bone
* use natural or synthetic grafts to enhance bone healing
* scaffold new bone and allow growth to occur
* use artificial biomaterials to achieve bone regeneration
* stimulate nerve pathways to encourage authentic bone production
* regenerate bones with surfaces that allow for nutrient absorption
* use stem cells to encourageTrusted Source bone to regenerate

Frequently asked questions

Here are some answers to questions people often ask about bones:

Why are bones important for overall health?

Bones support the body’s structure and protect vital organs, but they also play a key role in blood cell production, the immune system, the storage of calcium, the release of essential hormones, and many other functions.

What things are important for bone health?

Following a varied diet with plenty of calcium, getting enough vitamin D, and exercising are important for bone health. Avoiding smoking and limiting alcohol intake can also help prevent osteoporosis.

How do you know if your bones are unhealthy?

Various health problems can affect the bones. Signs of osteoporosis include a loss of height, an increasingly stooped posture, and fractures that happen often or easily. A screening test can show if a person has reduced bone density.

Bone pain can be a sign of bone damage, infection, or bone cancer. Bones can become soft if there is a vitamin D deficiency. This can lead to bent shins in children, known as rickets. In adults, doctors call this osteomalacia.

A nontraumatic bone fracture in adults over 50 years old may also be an early sign of undiagnosed cancer, such as metastatic breast or lung cancer or multiple myeloma.

In short

Bones play an essential role in the structure and function of the human body.

As well as enabling movement, they maintain appropriate levels of many compounds. They regulate hormonal pathways, contribute to metabolism, support the immune system, and more.