Quest – The First Ripples
“One need not possess earth shaking mental faculties. Love and common sense will do”

Till the time mathematicians take a call on junk mathematics, the subject should be made optional beyond class 4. Geometry should be made compulsory from class 1 to class 10.

1.

a) Is the National Highway -1 (NH-1) a static frame or a dynamic frame?

b) Is a car moving on NH-1 a static frame or a dynamic frame?

c) Are the celestial bodies’ auto dynamic or artificially dynamic frames?

d) Are the trigonometric ratios dynamic or pseudo-dynamic frames?

e) What differentiates a static frame from a dynamic frame?

Should we revisit the field of algebraic calculus in light of the above mentioned frames?

2. Do numbers exist between 0 and 1? If yes, what is the evidence?

f) We are acquainted with the theorem which states: between any two numbers there lies a rational number and hence an infinite number of rational numbers. Now by averaging 1 and 2, we obtain the number 1.5. The question however is: what is the origin of the number 1.7?

g) Talking about numbers, is √2 an irrational number or a rational length?

h) Kindly evaluate (2)0.70. Can the calculus help us in finding the solution of this problem?

i) Which of the following expressions does not belong to the same family and why?

p/q ( p , q ∈ I ,q ≠ 0) , Sin x/x, (x measured in radians), dy/dx ,( dy/dx are quantum positional Parameters of a point in two D plane)?

3.

j) We know that cosine graph leads the sine graph by 900. Kindly plot the following information in Cartesian plane;
d/dx sine x = cos x

k) The differential d/dx cos x=- sine x. It means that the graph is in the first quadrant and the derivative in the second. Correct! So this is a wrong derivation. Kindly find out where the mathematical goof up has been committed.

l) Discuss the utilitarian character of the derivative of the following function:
y = e cos 3x.

m) How can that character get terminated if we replace e by π

4.

n) The path followed by a colony of ants from a food source to their go down is drawn in Cartesian plane. Kindly convert the information into its equivalent algebraic function. The ant hill is at the top right corner of the plane.

5.

Kindly observe the hour and minute hand of a clock at 11: 58 and 12: 05. Observe how the vertex moves away from the Centre in the first case and then moves towards the Centre in the second case. Now let us recall when we prove:
Lt x →0 sinx/x =1.
I feel that the argument advanced in support of this limit is farfetched, because as the angle limits to Zero, the original triangles collapse and are no longer in existence?

o) Is logarithm(s) a mathematical tool or a problem? Am I correct in case I place the following questions in the category of junk mathematics? p) Differentiate:
I. Log (sec x +tan x)
II. Log [cos (log x)] III. Sine (log log 3x)
IV. Log [log (log x)]

6.

q) How is curvature of a curve defined mathematically? r) If curvature of a circle is equal to 1/r, how do we measure meter inverse in S I unit?

s) The 2- D geometry is sufficient to help us in finding the distance of moon from the earth approximately. Kindly teach me how can we do the same accurately with the help of 3-D geometry?

7.

t) Kindly solve the following simultaneous equation.
I. 2x+3y+3z=1
II. 3x+y+6z=13
III. -x+2y-3z=-12
IV. What is the nature of the alphabets x, y z. Are they constants or variables?

u) A boat goes 30 km up stream and 44 km downstream in 10 hrs. In 13 hours, It can go 40 kms upstream and 55kms downstream. Kindly determine the speed of boat and the speed of the stream with the help of one supposition only.

8.

v) A circle (radius7 units), an isosceles triangle (14, 15, 15), a rectangle (12×10) and square11units have equal perimeters. Why does the area of each of the figure differ from the other? (Reproduced from the first paper).