Quiz of the Day
Pi Approximation Day: Mathematics & Famous Mathematicians
Wednesday, 22 July 2026
22/7 ≈ π — celebrating the infinite, irrational number that holds the universe together
1. Why is July 22 celebrated as Pi Approximation Day?
- Pi was discovered on this date in 1706
- A calculator first displayed pi on July 22, 1983
- It's the birthday of the mathematician who calculated pi to 100 digits
- The fraction 22/7 is a common approximation of pi
22 divided by 7 equals approximately 3.142857... which matches pi (3.14159...) to two decimal places. This approximation was used by Archimedes around 250 BC and is still used by engineers when extreme precision isn't needed. The better approximation 355/113 is accurate to 6 decimal places — remarkable for a simple fraction.
2. Pi (π) is described as an irrational number. What does 'irrational' mean in this mathematical context?
- It behaves unpredictably in calculations
- It cannot be expressed as a fraction of two integers
- It has no pattern in its digits
- It was discovered accidentally
Johann Lambert proved pi is irrational in 1768. Pi is also 'transcendental' — meaning it cannot be the root of any polynomial equation with rational coefficients. This makes it fundamentally more unusual than irrational numbers like √2. The transcendence of pi also proved a centuries-old problem (squaring the circle) was impossible.
3. To how many decimal places is pi currently known?
- Exactly 1 trillion
- About 50 trillion
- Around 100 trillion
- A few billion
As of 2022, Google engineer Emma Haruka Iwao calculated pi to 100 trillion digits — a record at the time. The calculation took 157 days using Google Cloud. For most practical purposes, 40 decimal places of pi is more than enough — it would allow calculation of a circle the size of the observable universe accurate to within a hydrogen atom's width.
4. The symbol π for pi was first used by which mathematician in 1706?
- Carl Friedrich Gauss
- Leonhard Euler
- Isaac Newton
- William Jones
Welsh mathematician William Jones introduced the symbol π in his 1706 work, choosing it as the first letter of the Greek word 'perimetros' (perimeter). Euler adopted it in 1737, and his mathematical authority made it universal. Before Jones, pi had no standard symbol — mathematicians wrote out phrases like 'the ratio of circumference to diameter.'
5. Who is considered the greatest mathematician of ancient times, credited with calculating pi to remarkable precision without modern tools?
- Thales
- Archimedes
- Euclid
- Pythagoras
Archimedes estimated pi using 96-sided polygons inscribed inside and outside a circle, arriving at a value between 3 10/71 and 3 1/7 — accurate to 99.9%. He lived in Syracuse from around 287-212 BC and is considered among history's greatest mathematicians. Legend says a Roman soldier killed him while he was drawing mathematical diagrams.
6. The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13...) is intimately connected to which irrational number?
- Euler's number (e)
- The square root of 2
- Pi
- The golden ratio (phi)
As the Fibonacci sequence progresses, the ratio between consecutive terms approaches φ (phi = 1.618...). The golden ratio appears in plant spirals, shell growth, and has been claimed (somewhat exaggeratedly) to underlie art and architecture. Pi and phi are both irrational but unrelated — despite similar mystical reputations.
7. In mathematics, what is a 'prime' number?
- The first number in any sequence
- A number that can't be squared
- Any number greater than 1 divisible only by 1 and itself
- Any odd number greater than 2
There are infinitely many prime numbers — proved by Euclid around 300 BC in one of mathematics' most elegant proofs. The largest known prime (as of 2024) has over 41 million digits. Primes are the foundation of modern cryptography — the RSA encryption protecting internet transactions relies on the difficulty of factoring large primes.
8. The 'Riemann Hypothesis,' considered mathematics' greatest unsolved problem, is about the distribution of what?
- Prime numbers
- Irrational constants
- Perfect squares
- Infinite series
The Riemann Hypothesis, proposed in 1859, predicts a pattern in the zeros of the Riemann zeta function that would reveal precise information about how prime numbers are distributed. The Clay Mathematics Institute offers $1 million for a proof. Billions of zeros have been computed and all confirm the hypothesis — but no general proof exists.
9. Which mathematician developed calculus independently at the same time as Newton, sparking a bitter priority dispute?
- René Descartes
- Blaise Pascal
- Gottfried Wilhelm Leibniz
- Pierre de Fermat
Newton developed calculus in the 1660s but didn't publish it until later. Leibniz published his version in 1684. The priority dispute was viciously personal, with accusations of plagiarism that divided European mathematics for generations. Today's standard calculus notation (dy/dx, ∫) comes from Leibniz, not Newton.
10. What is Euler's Identity, often called the most beautiful equation in mathematics?
- e^(iπ) + 1 = 0
- π² + φ² = 3
- e = mc²
- i² = -1
Euler's Identity connects five of mathematics' most fundamental constants: e (Euler's number), i (imaginary unit), π, 1, and 0 — in one elegant equation. Physicists and mathematicians regularly name it the most beautiful formula ever written. Its depth is staggering: it links exponential growth, circular geometry, and imaginary numbers in a single line.
11. The 'Monty Hall problem' is a famous probability puzzle involving what game show scenario?
- Picking the right door to win a car
- Flipping a coin to predict the future
- Rolling dice to win a prize
- Drawing cards to avoid elimination
The problem: you pick one of three doors; a car is behind one, goats behind the others. The host opens a goat door. Should you switch? Yes — switching wins 2/3 of the time. This seems counterintuitive, and when Marilyn vos Savant published the correct answer in 1990, thousands of mathematicians wrote in to tell her she was wrong. She wasn't.
12. Mathematician Alan Turing, famous for breaking WWII codes, proposed a test for machine intelligence. What did his test involve?
- A machine solving complex mathematical proofs
- A machine passing a visual pattern recognition test
- Distinguishing a machine from a human through text conversation
- A computer beating a chess grandmaster
The Turing Test (1950) proposed that if a machine could hold a conversation indistinguishable from a human's, it should be considered intelligent. Turing predicted machines would pass by 2000. Modern large language models arguably pass it — but critics say the test measures conversational mimicry rather than genuine understanding or consciousness.
13. The mathematician Srinivasa Ramanujan, who made extraordinary contributions to number theory, was largely self-taught and came from which country?
- China
- India
- Japan
- Egypt
Ramanujan had almost no formal training yet independently rediscovered or advanced results that took European mathematicians decades to prove. Working from Madras, he wrote to Cambridge mathematician G.H. Hardy, who immediately recognised his genius and brought him to England. Ramanujan died at 32 of illness, likely leaving enormous mathematical discoveries undiscovered.
14. 'Fermat's Last Theorem,' famously solved after 358 years, states that there are no positive integer solutions to which equation?
- aⁿ + bⁿ = cⁿ for n > 2
- a² + b² ≠ c² for any integers
- aⁿ × bⁿ = n for n > 3
- a + b + c = n² for n > 4
Pierre de Fermat scribbled the theorem in a book margin in 1637, claiming he had a proof 'too large to fit in the margin.' No proof was found until Andrew Wiles spent seven years secretly working on it and announced a solution in 1993 — at which point a flaw was found. Wiles fixed it in 1995, after what he called the most emotionally intense experience of his mathematical life.
15. The concept of 'zero' as a number was developed by mathematicians in which ancient civilisation?
- Ancient Babylon
- Ancient Egypt
- Ancient Greece
- Ancient India
Indian mathematicians, including Brahmagupta (7th century CE), were the first to treat zero as a number with its own mathematical properties — not just a placeholder. The concept spread via Arab mathematicians to Europe, where it replaced Roman numerals and made the modern mathematics revolution possible. Without zero, calculus, computing, and most of modern science would be impossible.