Pia materPia mater (ˈpaɪ.ə_ˈmeɪtər or ˈpiːə_ˈmɑːtər), often referred to as simply the pia, is the delicate innermost layer of the meninges, the membranes surrounding the brain and spinal cord. Pia mater is medieval Latin meaning "tender mother". The other two meningeal membranes are the dura mater and the arachnoid mater. Both the pia and arachnoid mater are derivatives of the neural crest while the dura is derived from embryonic mesoderm. The pia mater is a thin fibrous tissue that is permeable to water and small solutes.
Absolute geometryAbsolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally, this has meant using only the first four of Euclid's postulates. The term was introduced by János Bolyai in 1832. It is sometimes referred to as neutral geometry, as it is neutral with respect to the parallel postulate. The first four of Euclid's postulates are now considered insufficient as a basis of Euclidean geometry, so other systems (such as Hilbert's axioms without the parallel axiom) are used instead.
Master's degreeA master's degree (from Latin magister) is a postgraduate academic degree awarded by universities or colleges upon completion of a course of study demonstrating mastery or a high-order overview of a specific field of study or area of professional practice. A master's degree normally requires previous study at the bachelor's level, either as a separate degree or as part of an integrated course.
Euclidean geometryEuclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
Bachelor's degreeA bachelor's degree (from Middle Latin baccalaureus) or baccalaureate (from Modern Latin baccalaureatus) is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six years (depending on institution and academic discipline). The two most common bachelor's degrees are the Bachelor of Arts (BA) and the Bachelor of Science (BS or BSc).
Spinal fusionSpinal fusion, also called spondylodesis or spondylosyndesis, is a neurosurgical or orthopedic surgical technique that joins two or more vertebrae. This procedure can be performed at any level in the spine (cervical, thoracic, lumbar, or sacral) and prevents any movement between the fused vertebrae. There are many types of spinal fusion and each technique involves using bone grafting—either from the patient (autograft), donor (allograft), or artificial bone substitutes—to help the bones heal together.
Spinal stenosisSpinal stenosis is an abnormal narrowing of the spinal canal or neural foramen that results in pressure on the spinal cord or nerve roots. Symptoms may include pain, numbness, or weakness in the arms or legs. Symptoms are typically gradual in onset and improve with leaning forward. Severe symptoms may include loss of bladder control, loss of bowel control, or sexual dysfunction. Causes may include osteoarthritis, rheumatoid arthritis, spinal tumors, trauma, Paget's disease of the bone, scoliosis, spondylolisthesis, and the genetic condition achondroplasia.
Nerve rootA nerve root (radix nervi) is the initial segment of a nerve leaving the central nervous system. Nerve roots can be classified as: Cranial nerve roots: the initial or proximal segment of one of the twelve pairs of cranial nerves leaving the central nervous system from the brain stem or the highest levels of the spinal cord. Spinal nerve roots: the initial or proximal segment of one of the 31 pairs of spinal nerves leaving the central nervous system from the spinal cord.
Ventricular systemThe ventricular system is a set of four interconnected cavities known as cerebral ventricles in the brain. Within each ventricle is a region of choroid plexus which produces the circulating cerebrospinal fluid (CSF). The ventricular system is continuous with the central canal of the spinal cord from the fourth ventricle, allowing for the flow of CSF to circulate. All of the ventricular system and the central canal of the spinal cord are lined with ependyma, a specialised form of epithelium connected by tight junctions that make up the blood–cerebrospinal fluid barrier.
Foundations of geometryFoundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint. The term axiomatic geometry can be applied to any geometry that is developed from an axiom system, but is often used to mean Euclidean geometry studied from this point of view.
3D modelingIn 3D computer graphics, 3D modeling is the process of developing a mathematical coordinate-based representation of any surface of an object (inanimate or living) in three dimensions via specialized software by manipulating edges, vertices, and polygons in a simulated 3D space. Three-dimensional (3D) models represent a physical body using a collection of points in 3D space, connected by various geometric entities such as triangles, lines, curved surfaces, etc.
Licentiate (degree)A licentiate (abbreviated Lic.) is an academic degree present in many countries, representing different educational levels. It may be similar to a master's degree when issued by pontifical universities and other universities in Europe, Latin America, and Syria. The term is also used for a person who holds this degree. The term derives from Latin licentia, "freedom" (from Latin licēre, "to be allowed"), which is applied in the phrases licentia docendi (also licentia doctorandi), meaning "permission to teach", and licentia ad practicandum (also licentia practicandi), meaning "permission to practice", signifying someone who holds a certificate of competence to practise a profession.
