may overlap a bit with previous lecture(s)…

Mathematics demystified

January 9, 2019 – 4:24 am

may overlap a bit with previous lecture(s)…

October 23, 2018 – 9:43 pm

*Slightly difficult questions, I hope, but will certainly re-inforce core concepts:*

- Prove that the segment of the tangent to the curve which is contained between the co-ordinate axes, is bisected at the point of tangency.
- Find all tangents to the curve for that are parallel to the line .
- Prove that the curves , where and , where is a differentiable function, have common tangents at common points.
- Find the condition that the lines may touch the curve .
- If and are lengths of the perpendiculars from origin on the tangent and normal to the curve respectively, prove that .
- Show that the curve , is symmetrical about x-axis and has no real points for . If the tangent at the point t is inclined at an angle to OX, prove that . If the tangent at meets the curve again at Q, prove that the tangents at P and Q are at right angles.
- A tangent at a point other than on the curve meets the curve again at . The tangent at meets the curve at and so on. Show that the abscissae of form a GP. Also, find the ratio of area .
- Show that the square roots of two successive natural numbers greater than differ by less than .
- Show that the derivative of the function , when , and when vanishes on an infinite set of points of the interval .
- Prove that for .

More later, cheers,

Nalin Pithwa.

April 25, 2018 – 12:51 pm

Dr. Neale simply beautifully nudges, gently encourages mathematics olympiad students to learn to think further on their own…

March 14, 2018 – 12:05 pm

February 2, 2018 – 5:42 am

It is true …universally, including India…

Hats off to the “Intellect of the Wise Mathematicians”, late, adorable professor of mathematics, Paul Erdos.

— humble tribute …from Nalin Pithwa.

January 25, 2018 – 2:45 pm

July 20, 2017 – 8:35 pm

I have a bright kid working towards his IITJEE Foundation math. Some days back I had suggested to him to solve some hard word problems based on simultaneous equations from a very old classic text. He started on his own, almost with some guidance from me. Until he attacked very well — those “age” kind of problems. Father’s age vs. son’s age, etc. But, in this case, he suddenly sprang to his feet: He almost yelled, “Sir! Please check my solution! I am getting the answer as husband’s age is 48 and wife’s age is 23!” Actually, I too was a bit shocked; but, I checked his calculations in detail; they were mathematically correct. It suddenly flashed in my head:

“Do you know Vedant? Mathematics is not human! It has no emotions, no feelings, whatsoever! I told him the following quote of Bertrand Russell: ” Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty, cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.””

And, of course, equations//numbers don’t lie! ðŸ™‚ ðŸ™‚ ðŸ™‚

*Nalin Pithwa.*

June 23, 2017 – 2:02 pm