Euler’s Identity: 'The Most Beautiful Equation' By Robert Coolman Euler's Identity is a remarkable equation that comprises the five most important mathematical constants.

What Is Topology? By Robert Coolman Topology is a branch of mathematics that describes mathematical spaces, in particular the properties that stem from a space’s shape.

Properties of Pascal’s Triangle By Robert Coolman Pascal's triangle, a simple yet complex mathematical construct, hides some surprising properties related to number theory and probability.

What Is Symmetry? By Robert Coolman In geometry, an object exhibits symmetry if it looks the same after a transformation, such as reflection or rotation. Symmetry is important in art, math, biology and chemistry.

What Is Trigonometry? By Robert Coolman Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

What Are Logarithms? By Robert Coolman A logarithm determines how many times a certain number must be multiplied by itself to reach another number.

What Is Calculus? By Robert Coolman Calculus is a branch of mathematics that explores variables and how they change by looking at them in infinitely small pieces.

What Are Quadratic Equations? By Robert Coolman Quadratic equations are basic to algebra and are the math behind parabolas, projectiles, satellite dishes and the golden ratio.

What Is Algebra? By Robert Coolman Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Tessellation: The Geometry of Tiles, Honeycombs and M.C. Escher By Robert Coolman Tessellation is a repeating pattern of the same shapes without any gaps or overlaps. These patterns are found in nature, used by artists and architects and studied for their mathematical properties.

What Is Quantum Mechanics? By Robert Coolman Quantum mechanics is the body of scientific laws that describe the wacky behavior of photons, electrons and the other particles that make up the universe.

What Is Classical Mechanics? By Robert Coolman Classical mechanics is the mathematical study of the motion of everyday objects and the forces that affect them.

What Is a Proof? By Robert Coolman A proof is a rigorous argument that shows a mathematical claim to be true. Arguments that are proven become theorems, such as the Pythagorean Theorem.

What is a Transistor? By Robert Coolman Transistors are tiny switches that can be triggered by electric signals. They are the basic building blocks of microchips.

Keeping Time: Leap Years and the Gregorian Calendar By Robert Coolman The Gregorian calendar — used by most of the world — was introduced to fix errors in the Julian calendar mostly having to do with leap years.

Keeping Time: Months and the Modern Calendar By Robert Coolman Our modern Western calendar is almost entirely a Roman invention, but it has changed significantly throughout history.

Keeping Time: The Origin of B.C. & A.D. By Robert Coolman The use of "anno domini" and "before Christ" to mark time began in the early days of Christianity, when clerics needed to know when Easter would fall.

Keeping Time: Origins of the Days of the Week By Robert Coolman The Romans named the days of the week after their gods. The Germanic people adapted the Roman system and gave us the English names of the days.

Keeping Time: Time Zones, Trains and the 24-Hour Day By Robert Coolman The Egyptians started dividing the day into 24 units, a practice that continues to influence how we tell time.

Zeno’s Paradox: Understanding Convergent & Divergent Series By Robert Coolman A convergent series is a mathematical series in which the sequence of partial sums converges to a finite number. A divergent series is just the opposite — the sums do not meet a finite limit.

Keeping Time: Why 60 Minutes? By Robert Coolman Dividing the day into hours, minutes and seconds is a recent practice with thousands of years of science and tradition behind it.

Building Green-Gas Technology Without a Manual By Robert Coolman Robert Coolman explores pyrolysis and biofuels.

Building Green Gas Technology Without a Manual By Robert Coolman Robert Coolman is on the cutting edge of biofuel research

Green Gasoline Comes Closer to Fueling Your Car By Robert Coolman Researchers have discovered how to make gasoline from sawdust and other plant materials and are currently moving from the lab to the power plant.