𝛑 day is upon us. The 14th of March represented as 3.14 is called 𝛑 day. (I would have preferred the 22nd of July). It is a mostly forgotten day because E-commerce has not yet co-opted it. But, we at 2IIM are definitely fascinated by it.
𝛑 has enamoured us for 4000 years
The ratio of circumference to diameter has intrigued mathematicians for millennia. The Babylonians were among the first to think about it – they came up to 3.125; Archimedes went further with the idea of inscribing and circumscribing a circle with regular polygons. Newton had a go at it, and our own Ramanujan gave some efficient ways of finding approximations.
The latest approximation (it is still an approximation) goes up to 50000000000000 digits. That is 5 followed by 13 zeroes and beauty lies in the idea that we could be at this game for a while yet.
4 interesting geometry questions to keep you engaged
We have picked up 4 excellent questions from different topics all related to 𝛑 to keep you engrossed. These are tougher than what you can expect in the CAT but are fun to try nevertheless. Send us your solutions by 3:00 PM, 14th March 2020 to email@example.com and we will feature the best ones on our blog. Here are the interesting geometry questions:
- Five points are placed on the surface of the sphere. Prove that some four of them must be contained in some closed hemisphere.
- 100 people standing in a circle in an order 1 to 100. No. 1 has a sword. He kills the next person (i.e. No. 2) and gives the sword to the next (i.e. No. 3). All people do the same until only 1 survives. Which number survives at the last?
- The radii of the smaller semi circles are 2 and 1 cm respectively. Find the radius of the red circle.
- Data Sufficiency: Use the following answer choices for the question below.
A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
D. Each statement alone is sufficient to answer the question.
E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.
Is the area of a certain circle greater than the area of a certain equilateral triangle?
1) The perimeter of the equilateral triangle is less than the circumference of the circle.
2) The circumference of the circle is less than the perimeter of the equilateral triangle.
For more CAT questions from Geometry, head onto – 2IIM’s CAT Questionbank . Happy solving!
Detailed explanations with video solutions for the above tested questions are available here: https://online.2iim.com/cat-exam/blogs/cat-quantitative-aptitude/pi-day-solutions-to-interesting-geometry-questions/
No discussion on 𝛑 ends without a reference to the Circle of Life and a call-out to the utterly delightful phrase ‘Hakuna Matata’. Hakuna Matata means ‘No worries for the rest of your Days’. We at 2IIM wish that you jump into this CAT journey, have plenty of fun preparing for it and subscribe to the carefree philosophy Hakuna Matata.
Happy CAT preparation to you all!
Rajesh Balasubramanian takes the CAT every year and is a 4-time CAT 100 percentiler. He likes few things more than teaching Math and insists to this day that he is a better teacher than exam-taker.