Bibhorr formula

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Bibhorrmetric nomenclature in right triangle.

"Bibhorr formula" is a new mathematical correlation among the sides and angle of a right angled triangle.[1][2] The formula is an alternative tehnique to applied trigonometry. The formula is used for finding the angle of a right angle triangle if all the three sides are given. Practically, only two sides need to be known as the third could be found out through Pythagorean theorem. The symbolic notation of the equation employs Hindi syllabary. The formula is invented by Bibhorr, an Indian aerospace scholar and engineer.[3]

Consider a right triangle with longest side (hypotenuse) श्र, medium side लं and shortest side छ, the angle opposite the medium side (Bibhorr angle) बि is given as:[4]

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The above equation is the "Bibhorr formula".

The equation makes use of two constants - 90° or π / 2 radian and 1.5.

Units and Constants

The constant angle 90° known as Bibhorr sthiron is used as a reference for the evaluation of Bibhorr angle. The units of Bibhorr angle can either be degrees or radians depending on wheather the sthiron is in degree or radian form in the R.H.S of the equation.[5]

The rational invariable value 1.5 (fraction form: 3/2) employed in the equation is simply called Bibhorr constant. This mystical constant is independently represented as बँ.

Nomenclature

Unlike conventional trigonometry, the Bibhorrmetric concept introduces a new naming system for defining all the elements of a right triangle. The purpose of this nomenclature is to remove the flaws encountered in applied trigonometry. The following terminologies are used:[6] [7]

  • Shrav- The longest side or hypotenuse.
  • Lambu- The middle side in the triangle.
  • Chhutku- The shortest side of the right tiangle.
  • Bibhorr angle- The angle opposite lambu.
  • Ubhorr angle- The angle lying opposite to the chhutku.

Illustration

Illustration of Bibhorr formula.

Consider a right triangle ABC where AB, AC and BC are the shortest, medium and longest sides respectively. Now, let the measures of the sides AB, AC and BC be छ, लं and श्र respectively. Thus, the angle opposite AC i.e. Bibhorr angle is given as:[8]

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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

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=> Bibhorr angle, बि = 45.582°

Applications

Being a typical example of Applied mathematics, Bibhorr formula has following applications in real life:[9]

  • Astronomy
  • Navigation
  • Geography
  • Civil Engineering

References