**Bibhorr formula** (also called **King of Equations ^{[7]}^{[5]}**) is a mathematical equation for establishing a relation between the sides and angle of a right triangle. The formula is a simplistic substitution to trigonometry as it is devoid of trigonometric functions. The equation demonstrates the relation of angle with the sides without implementing trigonometric functions. The formula proves useful in applied mathematics and mathematical physics.

Invented by an Indian aerospace engineer and scholar Bibhorr, the equation is notated in Hindi letters. For a right triangle with longest side (Shrav) श्र, medium side (Lambu) लं and shortest side (Chhutku) छ, the angle opposite the lambu (Bibhorr angle) बि is given as:

^{[2]}

This equation is called **Bibhorr formula.**

The equation makes use of two constants - 90° or π/2 radian and 1.5. The 90° is a constant angle, denoted by सि and called Bibhorr sthiron. 1.5 is a bare number which has no units and is called Bibhorr constant (denoted by बँ).

## Units

The units of Bibhorr angle depend on wheather the sthiron is 90° or (π/2). If Bibhorr sthiron is 90° then Bibhorr angle is in degrees, but if sthiron is (π/2) then obviously the angle would be in radians.

## Nomenclature

In order to combat flaws in trigonometry, Bibhorr formula employs a new naming system for recognizing each element of a right triangle.

The Bibhorrmetric nomenclature used to define the elements of a right triangle absorbs the following terminologies:

*Shrav*- The longest side or hypotenuse; denoted by श्र.*Lambu*- The middle side in the triangle; represented as लं.*Chhutku*- The shortest side of the right triangle; notated as छ.*Bibhorr angle*- The angle opposite*lambu*; represented as बि.*Ubhorr angle*- The angle lying opposite to the*chhutku;*denoted by ऊ.

## Explanation

Consider a right triangle ABC where AB, BC and AC are chhutku, lambu and shrav respectively. Now, let the measures of the sides AB, BC and AC be छ, लं and श्र respectively. Thus, the angle opposite BC i.e. Bibhorr angle is given as:

## Classification

Being the only of its kind, Bibhorr formula is capable of being a complete replacement to trigonometry and is the world’s only recorded Samāhikaran (स् class) to date. The term Samāhikaran signifies an equation from which many other concepts can be summarized.

LogicalHindu.com has classified the equation under Vedic Science.

## Example

For a right triangle with longest side (Hypotenuse) 7 cm and medium side 5 cm, all the angles of the triangle are to be found.

Bibhorrmetric Solution:

- Shrav (श्र) = 7 cm
- Lambu (ल) = 5 cm

From Pythagorean theorem, we get the third side –

Chhutku (छ) = 4.898979 cm

Applying Bibhorr formula, we get

*Bibhorr angle, बि = 45.582°*

## Applications

Bibhorr formula finds its applications in real life situations. Following are some of its applications:

**Astrophysics**: For finding distances between the astronomical bodies and objects.**Aerodynamics**: In finding the glide angle, angle of climb and various angles of attack.**Aerospace Engineering**: In finding the area of a vertical fin, main wing, etc.**Navigation:**In finding real time locations.**Geography:**In calculating distances between geographical locations.**Robotics**: In operating arms and for studying robotic movements.**Civil Engineering:**In analysing building structures and other architectures.