AXIOM FINAL ROUND ANSWERS

Pentagram

BM

SC

E

*Q1.

• “To a topologist, a sphere, a cigar and a rabbit’s head are all the same because they can be deformed into one another, therefore, anything without holes has to be a sphere.”

The above quote is fundamental to a famous problem, X, in mathematics. X was successfully solved by Y in 2002, who denied the prize money of $1 million associated with X.

ID X and Y.

• X = The Poincare ConjectureY = Grigori Perelman

¡ Nnt 51 H+eW he5 hp08hɹ3^3

Q2 Decode.

By rotating the given code 180 degrees in clockwise direction,

we get,

EvEryBOdY Say MaTH IS fUN !

¡ Nnt 51 H+eW he5 hp08hɹ3^3

Sherlocked.

The upcoming 5 questions are linked to each other.

A correct answer carries +2 each and giving the right connect at the end carries +5.

No negative marking.

Q3 A

IT WAS AROUND 1AM, FEB 01, JIM MORIARTY WAS FOUND DEAD INSIDE ROOM 1409. THE POLICE HAD JUST ARRIVED IN THE BUILDING, WHICH WAS NAMED AFTER A CERTAIN PERSON WHO HAD WRITTEN PRINCIPIA MATHEMATICA.

• Issac Newton, author of Principia Mathematica.

Q3 B

Bewildered Sherlock rushes to his next destination, the Louvre Pyramid where each base is 38m long. He finds the height of the pyramid by looking at the apex from the center. Take sqrt(2) as 1.41

• Height of a square pyramid of side a,

a/sqrt(2) ~ 27m

153370371407

Q3 CSherlock inspects the area around and finds a book called, “That's one small step for a man, one giant leap for mankind.”And finds that the following pages of the book were marked.

• 153, 370, 371 and 407 are called Armstrong numbers as they satisfy

JCMO:HELP::NSOD:_____

Q3 DHe finds moriarty’s phone and tries to crack the password:

•LUNE

*Q3 E

These were the paintings found near the dead body. But what do they have in common?

• The two paintings, The Vitruvian Man and Monalisa, by Leonardo Da Vinci have successfully embodied the significance of Golden Ratio over centuries.

*Q3F Connect.

Finally, after cracking all the codes and hints, he realizes that it was Moriarty’s trick to fool him once again. Is Moriarty actually dead?Amused Sherlock looks at the night sky, but what do all these clues(A-E) point out to?

• The connect is MOON.

***• Newton discovered gravitation laws and the motion of moon and

other planets.• 27 days is the period of revolution of moon around the earth. • Neil Armstrong was the first man to step on moon. • LUNE is French for Lunar(or moon).• 1.62 is the acceleration due to gravity, g, on moon.

Q4.

• As X himself wrote: “I have discovered a truly marvellous proof of this(Y), which this margin is too narrow to contain.”

That’s really too bad, because while X posed this problem in 1637, it went unproven for quite a while. And by a while, it was proven in 1995 (358 years later) by a man named Andrew Wiles.

ID X and Y.

• X = Pierre De FermatY= Fermat’s Last Theorem,

*Q5.

• “How(3) I(1) need(4) a(1) drink(5), alcoholic(9) in(2) nature(6), after(5) the(3) heavy(5) lectures(8) involving(9) quantum(7) mechanics(9).”

The above line is a piem (pi+poem). It was designed to memorize the first fourteen digits of pi, 3.14159265358979. There have been many such mnemonics created in various languages to remember a span of digits of pi and the study of such mnemonics is termed as X.

ID X.

• Piphilology

*Q6.

• If a given circle is rotated around a given line on the same plane in 3-dimensions, what are the 4 possible types of figures obtained?

-Part marks for figure and name of the object formed.

• The four possible figures are Sphere, Ring Torus, Spindle Torus and Horn Torus.

Q7.

• X is an international prize presented by the King of Norway to one or more outstanding mathematicians every year. Named after Norwegian mathematician Niels Henrik Abel (1802–1829), the award was established in 2001 by the Government of Norway.

X has often been described as the “Mathematician's Nobel Prize". It comes with a monetary award of US$1 million.

ID X.

• Abel Prize.

Q8.

• X is a type of number that is not the root of any integer polynomial i.e. it cannot be expressed as a solution of an equation. All X are irrational. Joseph Liouville first proved the existence of X in 1844.

e, π are the prominent examples of X.

ID X.

• X = Transcendental Number

POUNCE.

• This is a rapid fire round consisting of 7 questions.

• If you know the answer, shout “Pounce”. Don’t answer until you are asked to.

• Correct answer = +3, Incorrect answer = -1

• A team can pounce a particular question ∞ times.

Q9.

• Find the number of solutions of :

• No solution.

Q10. • ID the figure.

• Cardiode

Q11.

• He’s known for his immense contributions in math and electrostatics, fondly called as the Prince of Mathematics, ID him.

• Carl Friedrich Gauss

Q12.

• Find the number of real solution(s) of the system:y = x² - 1 y = x³

• 1 real solution.

Q13.

• A square of area 60 unit² inscribes a circle. The circle in turn inscribes a square within. Find the area of the smaller square.

Q14.

• What did Arab mathematician Al-Khwarizmi give to the world around 800 BC?

• Algebra

Q15. • Find the area enclosed by the following ellipse.

• 12π square units.