## Category Archives: miscellaneous

### Express a given integral number in any scale (radix)

Several scales (radix) have been used by mathematicians. Binary (2), Ternary (3), Quaternary (4), Quinary (5), Senary (6), Septenary (7), Octenary(8), Nonary (9), Denary (10/Decimal), Undenary(11), Duodenary (12) and of course, hexadecimal (16). Note that in any scale the base radix is “10”. Thus, “10” stands for 2 in “binary”, “ten” in “decimal”, 8 for “octal” radix respectively, etc.

Let the digits used in a proposed scale(radix r) be $a_{0}, a_{1}, a_{2}, \ldots, a_{n}$. Let us express an integer in this scale. Let $a_{0}$ be unit’s digits. Analagous to the place value system (in decimal):

$N=a_{0} + a_{1} \times r^{1} + a_{2} \times r^{2} + \ldots + a_{n} \times r^{n}$

Now, let us say we want to express this number N in terms of these digits $a_{i}$s.

Dividing N by $r$, we get the unit’s digit $a_{0}$ as the remainder; and the quotient is:

$a_{1} + a_{2} \times r^{1} + a_{3} \times r^{2} + \ldots + a_{n} \times r^{n-1}$.

Dividing the above quotient by r, we get $a_{1}$ as the remainder and the quotient as:

$a_{2} \times r^{1} + a_{3} \times r^{2} + a_{4} \times r^{3} + \ldots + a_{n} \times r^{n-2}$, and so on.

Example: Express the denary number 5213 in the scale of seven.

Solution: $(5213)_{10} \div 7$ gives 5 as remainder and $(744)_{10}$ as quotient.

$(744)_{10} \div 7$ gives 2 as remainder and $(106)_{10}$ as remainder.

Continuing this way, we are able to express:

$(5213)_{10} = 2 \times 7^{4} + 1 \times 7^{3} + 1 \times 7^{2} + 2 \times 7 +5$. That is $(21125)_{7}$. You can check the equivalence by converting both to decimal values.

Cheers,

Nalin Pithwa.

### Wisdom of George Polya

A great discovery solves a great problem. But there is a grain of discovery in the solution of any problem.

— George Polya, How to Solve it

### To balance, to focus, for inner calm and concentration

Happiness Chemicals and how to hack them:

I) DOPAMINE: The reward chemical:

• Doing self-care activities
• Eating food
• Celebrating little wins

II) SEROTONIN: The mood stabilizer:

• Meditating
• Running
• Sun exposure
• Walk in nature
• Swimming
• Cycling

III) OXYTOCIN: The love hormone

• Playing with a dog
• Playing with a baby
• Holding hand
• Give compliment

IV) ENDORPHIN: The pain killer

• Laughter exercise
• Essential oils
• Watch a comedy
• Dark chocolate
• Exercising

### The City with a large heart : Bombay/Mumbai

Mumbai is rich,

Mumbai is poor,

Mumbai is fast,

Mumbai is slow.

Little bit sweet,

and little bit sour.

Sometimes its hot,

but not too cold.

Mornings r energetic

& evenings are electric.

Noons r lazy but

Nights are crazy.

he always says “M busy”

Dude, life in Mumbai

Is not so easy…!

There is lot of Masti with

Welcome to the city that

can’t live without our Bollywood Chaska!

Sev puri, Vada Pav and bhel puri

are all Mumbai chaat.

Relishing it with spicy chutney is no easy art

From popcorn to icecream, all sold

on cart

Mumbai o Mumbai you’re always

close to my heart!

Where local trains

usually run on time

And violently rushing

for a seat is not a crime.

Here 3 PM for lunch and

12AM to dine,

People face hardships,

but still say, “It’s fine”!

to Woodhouse Cathedral in Town,

And ISKCON in Juhu to Haji Ali in

Mumbai’s Crown,

Marathi, Malayalee, Christian to

Gujarati,

Everyone together celebrate

Christmas and Diwali,

Holi is colourful and Diwali is cheerful,

Spend some time here and your life

will be unforgetful!

Billionaires to beggars,

all found in this city,

Be careful dude,

this place is a bit witty…

Overall this dream world

is huge but pretty

Mumbai Mumbai,

you’re wonderful city

After all a mother is called

MUM in English

BA in Gujarati &

Ai in Marathi

That’s My Mumbai

Dedicated to all Mumbaikars !!

### Some thoughts on teaching

If you learn you teach, but if you teach you learn. (Bertrand Russell) Teaching is like gardening. To teach is to teach to learn to think deep. To teach is to uncover a subject or rediscover a subject rather than to finish the syllabus. To teach is to prepare for the uncertain future. To teach is to gradually emerge the potential and motivation of the student. To teach is to impart a love for lifelong learning of the subject. To teach is to impart intellectual clarity. Passion is the key. To teach is to assume that the students are bright, hard working and motivated. To teach is to Kindle curiosity. In my mother tongue it is said the following are the pillars of teaching : prayatna ( to try ), protsahan ( to encourage ), prashansha ( to praise), and pralobhan ( some fantastic tangible motivation). In education, there is a wise quote : we go from the known to the unknown. From darkness to the light of knowledge. Knowledge means understanding not rote memorization of the subject. …To teach is to teach the art of problem solving.

Regards

Nalin Pithwa

### Wisdom of Yajurveda

As are the crests on the crowns of peacocks,

As are the gems on the hoods of cobras,

So is mathematics at the helm of all Sciences.

— Yajurveda circa 400 BC