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Related Concept Videos

Trigonometric Identities III01:27

Trigonometric Identities III

Cofunction identities are a key concept in trigonometry. They describe how trigonometric functions relate when their input angles are complementary — meaning the angles add up to 90°. On the unit circle, every angle θ— measured counterclockwise from the positive x-axis — corresponds to a point with coordinates (cos⁡ θ, sin ⁡θ). These values represent the horizontal and vertical components of the terminal side of the angle.If the same point on the unit circle is instead described using the...
Space Trusses: Problem Solving01:29

Space Trusses: Problem Solving

A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. Due to its adaptability and capacity to withstand complex loads, the space truss is widely used in various construction projects.
Consider a tripod consisting of a tetrahedral space truss with a ball-and-socket joint at C. Suppose the height and lengths of the horizontal and vertical...
Trigonometric Identities I01:27

Trigonometric Identities I

Trigonometric identities are equations that relate trigonometric functions and hold for all angles within their domains. A fundamental identity among these is the Pythagorean identity, which arises directly from the geometry of the unit circle. For any angle θ, a point on the unit circle has coordinates (cos⁡ θ, sin ⁡θ), and since the radius of the circle is one, the Pythagorean Theorem gives:This identity serves as the basis for deriving additional identities. Dividing the Pythagorean identity...
Aromatic Hydrocarbon Cations: Structural Overview01:18

Aromatic Hydrocarbon Cations: Structural Overview

Cycloheptatriene is a neutral monocyclic unsaturated hydrocarbon that consists of an odd number of carbon atoms and an intervening sp3 carbon in the ring. The three double bonds in the ring correspond to 6 π electrons, which is a Huckel number, and therefore satisfies the criteria of 4n + 2 π electrons. However, the intervening sp3 carbon disrupts the continuous overlap of p orbitals. As a result, cycloheptatriene is not aromatic.
Removing one hydrogen from the intervening CH2 group with both...
Trigonometric Identities II01:28

Trigonometric Identities II

Double-angle and half-angle trigonometric identities are derived from the fundamental sum and difference formulas and serve as essential tools for simplifying expressions, solving equations, and evaluating integrals. These identities reduce the complexity of trigonometric functions by relating functions of a multiple or fractional angle to functions of a single angle. Their applications extend across mathematics, physics, and engineering, particularly in Fourier analysis, wave mechanics, and...
Trigonometry of Right Triangles01:29

Trigonometry of Right Triangles

In a right triangle, trigonometric functions establish specific ratios that describe the relationship between the lengths of the triangle's sides and its acute angles. These relationships are foundational in understanding the structure of right-angled geometry. The sine function quantifies the proportion of the side opposite a given angle compared to the triangle's hypotenuse. In contrast, the cosine function expresses how the side adjacent to the angle relates to the hypotenuse in terms of...

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[Behçet and his triad].

Christel M P van Dongen1, Joost P Gijselhart, Jan van Gijn

  • 1Nederlands Tijdschrift voor Geneeskunde, Amsterdam, the Netherlands. c.van-dongen@hotmail.com

Nederlands Tijdschrift Voor Geneeskunde
|October 16, 2012
PubMed
Summary
This summary is machine-generated.

Hulusi Behçet described a rare oculo-urogenital syndrome characterized by eye, oral, and genital ulcers. This condition is now known as Behçet's disease.

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Area of Science:

  • Dermatology
  • Ophthalmology
  • Rheumatology

Background:

  • Hulusi Behçet, a Turkish dermatologist, was instrumental in establishing the Istanbul Faculty of Medicine.
  • Behçet published findings on a triad of symptoms: eye inflammation, oral ulcers, and genital ulcers.

Discussion:

  • The described symptom cluster, affecting the eyes, mouth, and genitals, was previously unexplained.
  • Behçet's meticulous case documentation led to the recognition of a distinct clinical entity.

Key Insights:

  • Identified and documented a unique triad of symptoms involving ocular, oral, and genital manifestations.
  • Established the foundation for the clinical recognition of Behçet's disease.

Outlook:

  • Further research into the pathogenesis and treatment of Behçet's disease.
  • Continued investigation into similar multi-system inflammatory conditions.