http://www.ams.org/news?news_id=4009

Heartiest congratulations and best wishes to Samuel Goodman! ๐

—*Nalin Pithwa.*

Mathematics demystified

January 17, 2018 – 2:53 am

http://www.ams.org/news?news_id=4009

Heartiest congratulations and best wishes to Samuel Goodman! ๐

—*Nalin Pithwa.*

January 2, 2018 – 7:05 am

A math blog, I would request my students/readers to read and solve/contribute regularly:

https://mathforlove.com/2018/01/mathematician-at-play-puzzle-1/

Thanks Dan for allowing me to share your blog(s)/website(s)!

*Nalin Pithwa.*

December 31, 2017 – 2:39 pm

AMS (American Mathematical Society) link:

http://bookstore.ams.org/mbk-106/?_ga=2.200133421.246483269.1514729371-1691390747.1513651870

Amazon India link:

** comment: sheer joy…**๐ ๐ ๐

— I am just waiting for the book to be available in Amazon India. ! —- Nalin Pithwa.

December 28, 2017 – 5:11 am

December 28, 2017 – 2:02 am

Thanks and regards to Melvyn Bragg from Nalin Pithwa.

December 24, 2017 – 9:48 pm

December 23, 2017 – 10:28 pm

**Say mathematician, how many are the combinations in one composition with ingredients of six different tastes — sweet, pungent, astringent, sour, salt and bitter — taking them by ones, twos, or threes, etc.?**

—- Fromย **Lilavathiย **ofย **Bhaskara (the great twelfth century mathematician of India).**

*— Nalin Pithwa.*

PS: *Almost all countries/nations have some culture of math just as they do of music and poetry and singing and dancing ๐ ๐ ๐ย *

December 18, 2017 – 8:43 pm

**Part I: Multiple Choice Questions:**

*Example 1:*

Locus of the mid-points of the chords of the circle which subtend a right angle at the centre is (a) (b) (c) (d)

*Answer 1: C.*

Solution 1:

Let O be the centre of the circle , and let AB be any chord of this circle, so that . Let be the mid-point of AB. Then, OM is perpendicular to AB. Hence, . Therefore, the locus of is .

*Example 2:*

If the equation of one tangent to the circle with centre at from the origin is , then the equation of the other tangent through the origin is (a) (b) (c) (d) .

*Answer 2: C.*

Solution 2:

Since touches the given circle, its radius equals the length of the perpendicular from the centre to the line . That is,

.

Let be the equation of the other tangent to the circle from the origin. Then,

, which gives two values of m and hence, the slopes of two tangents from the origin, with the product of the slopes being -1. Since the slope of the given tangent is -3, that of the required tangent is 1/3, and hence, its equation is .

*Example 3.*

A variable chord is drawn through the origin to the circle . The locus of the centre of the circle drawn on this chord as diameter is (a) (b) (c) (d) .

*Answer c.*

Solution 3:

Let be the centre of the required circle. Then, being the mid-point of the chord of the given circle, its equation is .

Since it passes through the origin, we have .

Hence, locus of is .

**Quiz problem:**

A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is (a) (b) (c) (d) .

*To be continued,*

*Nalin Pithwa.*

December 17, 2017 – 2:15 am

http://www.crraoaimscs.org/downloads/10_Statistics_Olympiad.pdf

Here’s to Statistics with love !

Nalin Pithwa.

December 14, 2017 – 9:33 pm

https://www.amtionline.com/book_list

(I found this v nice organization and the list of its v cheap, high quality publications in Math for kids in a blog of Mr. Gaurish Korpal.)

Quite frankly, these mathematics teachers are doing/have done profound service to India’s budding, aspiring generations of child mathematicians!! ๐ And, also to many parents in India, who mostly (in my personal opinion) think of only law, engineering, and medicine as the only respectable professions…:-( like Professor “Virus” of the famous movie, Three Idiots ! ๐

Hats off to AMTI !!!

*Nalin Pithwa.*