BILILEKE'S FORMULAE

MATHEMATICS

EXTRA-CURRICULUM ACTIVITY FOR STUDENTS

BILI LEKE’S FORMULAE

At = ¼ √[(2ab + L)(2ab – L)] L = a2 + b2 - c2 At = a2 tanα tanθ = a2 sinαsinθ 2(tanθ + tanα) 2sin(α+θ) a is adjacent to both θ and α BLF GRAPH At θ 900 1200

DEVELOPMENT OF CONCEPTUAL AND MANIPULATIVE SKILLS AND ITS APPLICATIONS

I have discovered two formulae in mathematics: BILI LEKE’S FORMULAE and the resulting graphs for mathematical applications, artistic design and visual delight. BILI LEKE’S FORMULAE; a development of conceptual and manipulative skills and its applications.

The book I wrote on my formulae is intended to serve as introduction of Bili Leke’s formulae for area of a triangle.

The central themes of the book involve

1. Knowing Bili Leke’s formulae,

2. Learning to prove Bili Leke’s formulae, and

3. Learning to find the area of a triangle by using Bili Leke’s formulae and solve related problems.

Biliaminu Adeleke Adediran-Adegoke, discovered and presented two formulae for area of a triangle in January 1994. These formulae were not in Mathematics Encyclopaedia by world authors, and Engineering Mathematics Encyclopaedia by Head, Godman, S. V. Brain, Rutherford Cruz, in any form, in 1994. The formulae were first presented in a workshop, in the workshop on the teaching of difficult topics in Further Mathematics for Lagos state secondary schools teachers organized by Lagos state ministry of education, on April 12^th 1994, by the author of these editions.

These formulae, the proofs, solutions to the questions in illustrations and worked examples and most of the questions are provided by the author. Usage and proof of these formulae would go far in helping students to develop conceptual and manipulative skills and its application.

First formula

If all sides of a triangle are known, the area of the triangle is given by:

A_t = ¼√(2ab + L)(2ab – L)

Where L = a² + b² – c²

A_t = ¼√(2ac + L)(2ac – L)

Where L = a² + c² – b²

A_t = ¼√(2bc + L)(2bc – L)

Where L = b² + c² – a²

a, b, c are the three sides of the triangle

Second formula

If two angles and a side of a triangle are known, the area of the triangle is given by:

A_t = (a²tanαtanθ)/[2(tanθ + tanα)

Where a is the side adjacent to both angles α and θ

It can be shown that;

A_t = (a²tanαtanθ)/[2(tanθ + tanα)

= (a²sinαsinθ)/[2sin(θ + α)]