Bryant's Triangle

Bryant's triangle (th. Bryant) is a geometric figure that is formed by the intersection of two planes, one of which passes through the vertex of the triangle, and the other through the center of the circumscribed circle. As a result of the intersection of these planes, a triangle is formed, which is called the Bryant triangle or Bryant's triangle.

The Bryant triangle has three vertices, which are the intersection points of three lines: one line passing through the vertex of the original triangle and one line parallel to the opposite side of the original triangle. Also, a triangle has three sides that are equal to the sides of the original triangle, and three angles that are equal to the angles of the original triangle.

Properties of the Bryant triangle:

– All sides of the Bryant triangle are equal to the sides of the original triangle;
– All angles of the Bryant triangle are equal to the angles of the original triangle;
– Bryant’s triangle is regular, that is, all its angles and sides are equal;
– The circumcenter of the Bryant triangle coincides with the circumcenter of the original triangle;
– The length of the median dropped onto the side of the Bryant triangle is equal to the length of the median dropped onto the corresponding side of the original triangle.

Bryant's triangle is a term used in the medical field to describe the process of antibody formation in the body after vaccination. This is the process by which the human immune system begins to produce antibodies in response to the introduction of an antigen (pathogen) into the body. Antibody formation occurs in a triangular geometric shape

Bryant's triangle *Unilateral avulsive hyperteloric scar of oval or irregular shape. It grows from a deep skin groove and occupies one third of the eyebrow. In the lower part there is sometimes an intermittent transverse scar.*

Rationale for diagnosis When collecting anamnesis by a dermatologist, it is necessary to pay attention to

Bryant triangle is a concept in mathematics that describes the relationship between two lines and one point lying on these lines. This is one of the most famous geometric figures, which has many applications in various fields of science and technology. The figure's name comes from its inventor, Bryant Wilson, who first described it in his book A Study of the Bell Curve in 1947.

The triangle formula is as follows: sin2(A)=r^2/2⋅cos(B)sin(B), where A is the magnitude of the angle A between the legs tg A=r⋅tg B (or tg B = r⋅tg A ).

The description of a triangle was first given by Brian Wilson himself, as well as other mathematicians. Later it changed several times, but the essence remained the same. In general form, the formula looks like this: a triple of numbers (a, b, c) forms a Bryant triangle if and only if the equality a ^ 2 + (-b ) ^ 4 + c ^ 3 = a ^ (-1/2) holds )*b^7^/2*c^-1. (Note: a, b and c are complex numbers). The triangle is also named after the author of this formula, Danish scientist Jan Bjornson, but sometimes the abbreviated term “Bryant” triangle is used. For a Brian-deformed triangle to appear, the following conditions must be met: when calculating with complex numbers, the inverse complex number must be used, the modulus of this number cannot be equal to one, and the angles must have different signs. In general, a triangle is described by the equalities sin2α=r * tan β, where α is the value of one of the angles, tan α = r*(-tga)*btg β. For example s * tgsin α/cos β=r²ctgsin β tg a; or sin 2*α/sin²A=r cos²β⁻¹tg²A. It was these formulas that gave the right to call this geometric figure a “triangle”.