Are you are a junior, high or secondary school student in Nigeria and you are looking for some hidden facts in Maths in PDF format available for download? Perhaps you intend to sit for an exam which could be internal or extrernal exams like WAEC, GCE, JAMB, or NECO.

After reading this article you will learn hidden facts and new things about Maths, you will be glad you found answers here.

Here are some 10 hidden facts about Mathematics which you never knew about:

1. Zero is Even
   Many people don’t realize that zero is classified as an even number. By definition, an even number is divisible by 2 without a remainder. Since 0 ÷ 2 = 0 0÷2=0, it fits the definition perfectly.
   
2. There Are Different Sizes of Infinity
   Infinity isn’t a single concept. Georg Cantor showed that some infinities are larger than others. For example, the set of real numbers between 0 and 1 is uncountably infinite, while the set of natural numbers is countably infinite. Surprisingly, the former is a larger type of infinity.
   
3. Most Numbers Are Irrational
   If you pick a random real number, there’s an almost 100% chance it’s irrational—meaning it can’t be expressed as a simple fraction. Rational numbers are dense, but the irrationals vastly outnumber them.
   
4. 1 = 0.999…
   This one often surprises people: the repeating decimal 0.999… 0.999… is exactly equal to 1. This can be shown algebraically: Let 𝑥 = 0.999… x=0.999…. Then, 10 𝑥 = 9.999… 10x=9.999…. Subtracting, 10 𝑥 − 𝑥 = 9 10x−x=9, so 9 𝑥 = 9 9x=9, which gives 𝑥 = 1 x=1.
   
5. The Fibonacci Sequence Appears in Nature
   The Fibonacci sequence (1, 1, 2, 3, 5, 8…) shows up in places like pinecones, sunflowers, and nautilus shells. These patterns optimize packing and growth in natural systems.
   
6. The Number ‘e’ is Everywhere
   The constant 𝑒 ≈ 2.718 e≈2.718 arises naturally in compound interest, probability, and calculus. It’s also the base rate of growth shared by many systems in nature and finance.
   
7. You Can’t “Square the Circle”
   For centuries, mathematicians tried to construct a square with the same area as a given circle using only a compass and straightedge. In 1882, it was proven impossible because 𝜋 π is transcendental, not constructible.
8. All Triangles Are the Same in Taxicab Geometry
   In taxicab geometry, which measures distance along a grid (like city blocks), every triangle has the same shape: the sum of the angles doesn’t necessarily equal 180°, and some familiar geometric rules break down.
   
9. Some Problems Can’t Be Solved
   Gödel’s Incompleteness Theorems showed that in any sufficiently powerful mathematical system, there are true statements that can’t be proven. This shattered the dream of finding a complete, consistent set of mathematical rules.
   
10. There Are Equations with No Solution in Integers
    Fermat’s Last Theorem states that there are no three positive integers 𝑎, 𝑏, 𝑐
    a,b,c such that 𝑎 𝑛 + 𝑏 𝑛 = 𝑐 𝑛 a n +b n =c n
    for any integer 𝑛 > 2 n>2
    This deceptively simple statement remained unproven for over 350 years, until Andrew Wiles proved it in 1994.
    

Conclusion
Mathematics is full of hidden gems and surprising truths. From the strange behavior of infinity to the limits of human reasoning, these facts show that math is not just about numbers—it’s a deep, rich language for understanding the world and beyond.

We hope you learnt something new today. Stay tuned for more fresh knowledge which we will share with you later.