The golden ratio appears in geometry naturally: it defines the ratio of a regular pentagon’s diagonal to its side. NEW
A perfect number equals the sum of its proper divisors: like 6 = 1+2+3.
Doctors use calculus-based equations to model drug effects and disease spread.
Modern AI uses logic-based reasoning, from propositional logic to predicate calculus, for decision-making.
In a 52-card deck, the chance of an ace is 1/13, while a face card is 3/13.
A coin spun on a table isn’t perfectly fair: its heavier side is slightly more likely to land facing down!
Euler’s Identity combines five fundamental constants: e, i, π, 1, and 0, in a single elegant equation.
A circle has the largest area of any shape with the same perimeter.
Zero is the only number that cannot be represented by Roman numerals.
A circle has infinite lines of symmetry, while a square has only four.
Solving for x began over 4,000 years ago in ancient Babylonian math.
The concept of infinity is central to calculus: especially when finding limits.
Rolling two dice creates 36 combinations, but only 11 possible totals.
1729 is the smallest number expressible as the sum of two cubes in two different ways: 1729 = 1³ + 12³ = 9³ + 10³.
In logic, an AND statement is only true if both parts are true.
Triangles are the only shapes guaranteed to be rigid: that’s why bridges use them.
Negative numbers were once considered nonsense by ancient mathematicians.
Derivatives measure how fast things change: like speed in physics.
Pi (π) never repeats or ends: it’s an irrational number that starts 3.14159...
Hexagons are the most efficient shape for tiling: bees use them for honeycombs.
Mathematical logic helped develop the modern computer.
The word algebra comes from an Arabic book titled “Al-Jabr.”
The angles of any triangle always add up to 180°: unless you’re on a curved surface.
A truth table helps visualize every possible outcome in a logic problem.
Equations like y = mx + b form the basis of every linear graph.
The chance of flipping 10 heads in a row is less than 0.1%.
Integration finds the area under curves: it’s like adding infinite slices.
A mobius strip has only one side and one edge: twisty math made real.
You’re more likely to share a birthday with someone than you think: only 23 people are needed for a >50% chance.
Isaac Newton and Leibniz invented calculus at the same time: and had a feud about it.
The number e (≈2.718) appears in growth formulas and compound interest.
A bell curve shows how most people fall near the average.
The slope of a curve at a point is its derivative at that point.
A palindromic number reads the same forward and backward: like 12321.
“Or” in logic is inclusive unless stated otherwise: it includes both options.
In probability, the word or means either, or both: not just one of them.
Limits describe what a function is approaching: even if it never actually gets there.
Infinity is not a number: it’s a concept representing something that has no end.
In Euclidean geometry, parallel lines never meet: even if extended to infinity.
A prime number has exactly two factors: 1 and itself.
Contrapositive logic flips and negates a statement: if A → B, then not B → not A.
A quadratic equation has the form ax² + bx + c = 0 and forms a parabola when graphed.
Standard deviation tells you how spread out the numbers in a dataset are.
A factorial multiplies all whole numbers from 1 to that number: 4! = 4×3×2×1.
In Euclidean geometry, pi (π) is the ratio of a circle’s circumference to its diameter: always about 3.14.
Perfect squares are numbers like 1, 4, 9, 16: each the square of a whole number.
In math, proof is absolute: once something is proven, it’s always true.
The area under a curve between two points is calculated using a definite integral.
Logical fallacies are common reasoning errors: like assuming “if A then B” means “if B then A.”
Systems of equations can be solved by substitution or elimination.
In statistics, correlation does not mean causation.
Logic gates like AND, OR, and NOT are the building blocks of computers.
A tessellation is a repeating pattern of shapes that covers a surface with no gaps.
Some equations have no solution: like x + 3 = x + 5.
Your odds of getting a royal flush in poker are 1 in 649,740.
The order of operations is BODMAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction.
Riemann sums approximate area under a curve by stacking rectangles.