Before the Calculator

26-hikoya, jami 40 ta

Hikoyani tinglang

Highlighted words are key vocabulary — tap one to see its translation. Colors show the part of speech:

Verb Adjective Adverb Expression

Open a mathematics textbook printed in 1950 and you will not find a single answer with a square root underneath a line. There is a reason, and it has nothing to do with beauty.

Before calculators, every division was done by hand. Suppose you needed one divided by the square root of two. You would look up the square root of two in a table — 1.41421 — and then face the job of dividing 1 by 1.41421, which is a long division with a five-figure divisor and plenty of room for a mistake.

Now move the root upstairs. The same quantity can be written as the square root of two divided by two, and that is 1.41421 halved: 0.70711. A schoolchild can do it in five seconds and get it right.

The two expressions are the same number, written differently — but one of them took a minute of careful work and the other took a breath. Multiplied across a page of calculations, that difference decided how long a engineer worked and how often he was wrong.

So the habit spread, and it stayed after the reason for it disappeared. Today it is a convention, not a rule of arithmetic: examiners still write answers with the radical on top, so a pupil who leaves it underneath may have the right value and still fail to find it among the choices.

Which is a small lesson about mathematics in general. Some of what looks like law is only habit — but habits are worth knowing, because the answer sheet was written by somebody who has them.

Matndagi atamalar

Kartani bosing — taʼrifi chiqadi.

textbook
darslik
square root
kvadrat ildiz
calculators
kalkulyator
table
jadval
divisor
boʻluvchi
halved
ikkiga boʻlingan
right
toʻgʻri
expressions
ifodalar
calculations
hisob-kitob
engineer
muhandis
examiners
imtihon tuzuvchilar
habit
odat
answer sheet
imtihon varaqasi

Qoida va formulalar

Matnda ishlatilgan matematik qoida.

by hand

Qoʻlda, asbobsiz. Kalkulyatorgacha boʻlgan davrni tasvirlashda doimiy ibora.

  • Dividing by 1.414 by hand took a minute; halving took seconds.

the same number, written differently

Bir xil son, boshqacha yozilgan. Ratsionallash qiymatni emas, shaklni oʻzgartiradi.

  • Those two expressions are the same number, written differently.

a convention, not a rule of arithmetic

Qoida emas, kelishuv. Matematikada baʼzi narsalar toʻgʻri-notoʻgʻri emas, odat masalasi.

  • Rationalising is a convention, not a rule of arithmetic.

Tekshirib koʻring

Matnni oʻqing, keyin hisoblang. Javobni bosib tekshiring.

1. Why was 1 divided by the square root of 2 difficult before calculators?

2. What makes the rewritten form easier to compute?

3. According to the text, why does the habit still matter today?