Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.

How would you rewrite Euclid’s fifth postulate so that it would be easier to understand ?

List five axioms (postulates) used in this book.

Using Euclid’s axioms/postulates bisect a given finite straight line.

Answer the following questions: Ray optics is based on the assumption that light travels in a straight line. Diffraction effects (observed when light propagates through small apertures/slits or around small obstacles) disprove this assumption. Yet the ray optics assumption is so commonly used in understanding location and several other properties of images in optical instruments. What is the justification?

Using Euclid’s axiom or postulate, prove the proposition that if in a triangle two angles are equal to one another, then the opposite sides are equal.

Consider ‘postulate’ given below. There exist at least three points that are not on the same line. Do this postulate contains any undefined term ? Is this postulate consistent ? Do they follow from Euclid’s postulate ? Explain.

State Bohr’s postulates for atomic model and using them derive an expression forthe total energy of an electron revolving in a stationary nth orbit of hydrogen atom.

State Bohr’s postulates for atomic modeland using them derive an expression for the radius of nth orbit in hydrogen atom and show that radii are in the ratio 1 : 4 : 9 :16 :..........

Consider ‘postulate’ given below. Given any two distinct points A and B, there exists a third point C which is between A and B. Do this postulate contains any undefined term ? Is this postulate consistent ? Do they follow from Euclid’s postulate ? Explain.

Consider the following statement : There exists a pair of straight lines that are everywhere equidistant from one another. Do you think that this statement is (or is not) a direct consequence of Euclid’s fifth postulate ? Explain.