uses of set square

Play with Set Square

Set square is a triangular piece of transparent plastic with the centre removed and can be seen in every geometry box you purchase. But in most of the cases we are not aware of its uses and in my 15 years of teaching I have never seen any students using it and in some cases I have noticed that students don’t bring these two set in their geometry box.  These set squares come in two usual forms, both right triangles: one with 90-45-45 degree angles, the other with 30-60-90 degree angles. Combining the two forms by placing the hypotenuses together will also yield 15° and 75° angles. 

Set squares are used to draw –

·       Parallel and Perpendicular lines

·       Draw squares, equilateral triangle

·       Rectangles, parallelograms

·       Rhombus

·       Set, square in combination with a T- square is used to draw more accurate angles.

Drawing Parallel Lines

Parallel lines can be drawn using set squares and a ruler. Follow the steps and check

·       Position one edge of Set Square against the ruler and draw a line along the other edge.

·       Move the position of set square while keeping the ruler fixed, draw a line along the same edge done earlier.

 

 

 

 

Drawing Perpendicular Lines

·       Take a ruler and a set square

·       Draw a line AB and take a point P on that where you will draw perpendicular lines

·       Place a set square on point P

·       Draw a line as shown

Drawing Quadrilaterals

Rhombus: - If you take 4 sets of 90- 60 -30 Set square you will get Rhombus

Square: - If you set 2 pieces of 90-45-45 set square you get a Square.

Rectangle: - If you set two 90-30-60 set square and place it accordingly you will get a rectangle.

Parallelogram:- If you place 4 sets of set square in different position as shown below you get a parallelogram.

(Photo credit: - Courtesy – http://www.ekshiksha.org.in/eContent-Show.do?documentId=225)

 

 

 Drawing Rhombus 

Making square 

Making Trapezium 

PI APPROXIMATION DAY (22/07) QUIZ

 Dear All

On the occasion of Pi Approximation Day being celebrated on 22nd July (22/7) every year, Here is one very interesting quiz dedicated to Pi. There are 40 questions related to Pi. Let's know the mysterious number pi. Don't forget to share with your known/students/teachers/

Just give a TRY

 The story of pi is more than 4000 years old but the race to find its value is still continued.

Interesting Facts:-

1.  

                                             (Courtesy:- From the Tweet of @Cliff Pickover)

2. 22nd July is the birthday of -- GAUSTAV HERTZ      ---- WILHELM BESSEL  and great Indian mathematician - SHREERAM SHANKAR ABHYANKAR 

3. 22nd July 2025 is the 203rd day of the year.  203 is the 6th Bell number, i.e. it is the number of partitions of a set of size 6.

203 is a palindrome in base 3  (21112),   base 6 (535), and base 8(313),

203^2 + 203^3 + 1 is prime. 203 is the number of nondegenerate triangles that can be made from rods of lengths 1,2,3, 4,...,12

                                                      A brief Introduction of Pi

Value of Pi = 22/7 is probably taken because Archimedes (born in 287 BC) calculated the ratio of circumference to diameter coming out to be lying between 223/71 and 22/7.

Aryabhata (born in 476AD) was the first Indian mathematician who calculated the value of pi correct up to 4 decimal places. His value of pi was 3.1416. 

The Mahabharta decodes the value of pi as 3.

योजनानां सहस्राणि विष्कम्भो द्वादशास्य वै ॥ 6-12-40
परिणाहेन षट्त्रिंशद्विपुलत्वेन चानघ ।
षष्टिमाहुः शतान्यस्य बुधाः पौराणिकास्तथा ॥ 6-12-41
चन्द्रमास्तु सहस्राणि राजन्नेकादश स्मृतः ।
विष्कम्भेण कुरुश्रेष्ठ त्रयस्त्रिंशत्तु मण्डलम् ॥ 6-12-42
एकोनषष्टिविष्कम्भं शीतरश्मेर्महात्मनः ॥ 6-12-43
सूर्यस्त्वष्टौ सहस्राणि द्वे चान्ये कुरुनन्दन।
विष्कम्भेण ततो राजन्मण्डलं त्रिंशता समम् ॥ 6-12-44
अष्टपञ्चाशतं राजन्विपुलत्वेन चानघ।
श्रूयते परमोदारः पतगोऽसौ विभावसुः ॥ 6-12-45
एतत्प्रमाणमर्कस्य निर्दिष्टमिह भारत ।

The Moon is handed down by memory to be eleven thousand yojanas in diameter. Its peripheral circle happens to be thirty three thousand yojanas when calculated.

The Sun is eight thousand yojanas and another two thousand yojanas in diameter. From that its peripheral circle comes to be equal to thirty thousand yojanas.

The Bible says -

Also he made a molten sea of ten cubits from brim to brim round in compass and five cubits the height thereof; and a line of thirty cubits and compass it round about.  --- Old Testament

William L Schoff says -

Probably no symbol in mathematics has evolved much mystery, romanticism, misconception and human interest as the number of pi.

      

          Buffon

Buffon calculated the value of pi using needle. Ancient Hebrews who built Solomon's temple used pi = 3 while Shatapatha Brahmin calculated the value of pi equals to 3.085.

In 1901, Italian mathematician Mario Lazzarini Performed the Buffon Needle experiment tossing a needle 3408 times, he obtained the approximation of pi which was a very accurate value. 

Archimedes in 3rd century inscribed and circumscribed regular polygons up to 96 sides and showed the upper limit is 22/7 and lower limit is 223/71.

           Pi  Day = March 14 (3/14)

Aryabhata calculated the value of pi correct  up to 4 decimal places and can be termed as the first mathematician to do so.

Add 4 to 100, multiply it by 8 and then add 62000. The result is approximately the circumference of a circle of diameter 20000.

Madhava, the founder of Kerala School of Mathematics also calculated the value of pi before James Gregory using the infinite series.

व्यासे वारिधिनिहते रूपहृते व्याससागराभिहते।

त्रिशरादिविषमसंख्यामत्तमृणं स्वं पृथक् क्रमात् कुर्यात् ॥

यत्संख्ययात्र हरणे कृते निवृत्ता हृतिस्तु जामितया।

                         तस्या उर्धगताया समसंख्या तद्दालं गुणोऽन्ते स्यात् \\

Ramanujan made several attempt and calculated the value of pi through numerous formula.

You can also calculate the value of pi using his formula.

Yale Bablonian Tablet known as YBC 7302 also approximates pi as 3.125 . . .

Interesting Facts About Pi:- 

At position 763 which is also known as Feynman Point, there are six nines in a row. 

Johann Lambert proved Pi is irrational in 1768.

I hope you have read the information shared here. It is the time to play quiz to explore your knowledge about pi. 

CLICK HERE FOR QUIZ

A certificate is attached with the quiz provided you score 75% marks so try your luck and win certificate.

Rajesh K Thakur

google.com, pub-5194588720185623, DIRECT, f08c47fec0942fa0 google.com, pub-5194588720185623, DIRECT, f08c47fec0942fa0