Consider Dimension and Replace Pi

After reading this book, the reader will be able to:

• Define dimension and ‘Dimension as numerical value’ - P.

• Comprehend the importance of ‘Dimension as numerical value’ – P in different mathematical fo rmulas.

• Explain and avail rules to formulate different formulas for the determination of length, area and volume of different lines and shapes.

• Recognize and define ‘Standard Geometrical lines and shapes’ as well as determine their areas and volumes.

• Comprehend that the area and volume of different ‘Standard Geometrical Shapes’ are equal with equal the relevant dimensions and are determined directly by multiplying its relevant dimensions.

• Determine perimeter, area and volume of other geometrical ‘Shapes made from straight lines and flat surfaces’ by the formulation of new formulas using simple rules introduced in the chapter – ‘Dimension’. These formulas use ‘dimension as numerical value’ - P as a factor.

• Comprehend a uniform relationship between ‘Standard Geometrical Shapes’ with ‘Shapes made from straight lines/flat surfaces’.

• Define mathematical constant – M with its importance. It also explains its characteristics.

• Define ratio ‘M/P’ with its importance.

• Determine circumference of any circular line by using ratio ‘M/P’ following simple rules introduced in the chapter – ‘Dimension’.

• Determine area and volume of ‘Shapes made from curved line/surface’ by the formulation of new formulas using simple rules introduced in the chapter ‘Dimension’. These formulas use ratio ‘M/P’ as a factor.

• Comprehend a uniform relationship between ‘Standard Geometrical lines and shapes’ with ‘Circular lines’ as well as ‘Shapes made from a curved line/surface’.

• Determine surface area and volume of ‘Shapes made from both flat and curved surfaces’ by the formulation of new formulas using simple rules introduced in the chapter ‘Dimension’. These formulas also use ratio ‘M/P’ as a factor.

• Correlate quantity-wise different lines and shapes with each other with equal relevant dimensions and recognize its uniformity.

• Formulate formulas for different lines and Shapes just by looking/visualizing it.

• Understand and apply the mathematical constant, M and/or ‘dimension as numerical value’ - P in the different application of mathematics as well as other subjects.

• Comprehend prevalent formulas with/without Pi (π) as empirical and not pure mathematical formulas.