Maths Etymology

🧮 Numbers & Quantity

• Digit – from Latin digitus, meaning finger — because people counted on fingers
• Decimal – from Latin decem, meaning ten
• Zero – from Arabic ṣifr, which itself came from Sanskrit śūnya (meaning empty or void)
• Numeral – from Latin numerus, meaning number or count
• Even – from Old English efen, meaning level, equal, or smooth — originally used to mean “balanced” or “without bumps”
• Odd – from Old Norse oddi, meaning triangle or point — referred to a leftover item when things were paired off
• Prime – from Latin primus, meaning first — prime numbers were seen as the fundamental building blocks
• Composite – from Latin componere (to put together) — composite numbers are “assembled” from multiple factors
• Square (number) – from Latin quadrare, meaning to make square — these numbers form perfect squares when arranged spatially
• Cube (number) – from Greek kybos, meaning cube or die — cube numbers fill a cube shape when visualised as volume
• Factor – from Latin facere, meaning to make or do — factors are the numbers that “make” another when multiplied
• Multiple – from Latin multiplex, meaning many-fold — multiples are repeated additions or copies of a base number
• Divisible – from Latin dividere (to divide) + -ibilis (able to be) — meaning “able to be evenly separated into parts”
• Cardinal – from Latin cardo, meaning hinge — these are the numbers everything else “hinges” on
• Ordinal – from Latin ordo, meaning order or arrangement

🔢 Place Value & Base Systems

• Place value – from Old French place (position or location) and Latin valere (to be strong or worth)
• Marked value – “Marked” comes from Old English mearc, meaning sign or boundary
• Base – from Latin basis, from Greek basis, meaning “foundation” or “step”
• Base-ten/ Decimal system – from Latin decem, meaning ten
• Base-two/ Binary system – from Latin bini, meaning “two by two”
• Base-sixty / Sexagesimal system – from Latin sexaginta, meaning sixty
• Multi-base systems – from Latin multi (many) + basis (foundation)

➕ Operations

• Add – from Latin addere, meaning to give to
• Subtract – from Latin subtrahere, to draw from below
• Multiply – from Latin multiplicare, to fold many times
• Divide – from Latin dividere, from dis- (“apart”) + videre (“to separate”) — meaning “to force apart” or “distribute”
• Sum – from Latin summa, meaning “total” or “highest part”.
• Difference – from Latin differentia, from differre (“to carry apart”) — meaning “distinction” or “separation”.
• Product – from Latin productum, from producere (“to bring forth”) — meaning “that which is brought forth”.
• Quotient – from Latin quotientem, from quot (“how many”) — meaning “how many times”.

⚖️ Equality, Identity & Balance

• Equals – from Latin aequare, meaning to make level or even — literally “to equalise”
• Equivalent – from Latin aequivalens, from aequus (equal) + valere (to be strong or worth) — “equal in value or strength”
• Equality – from Latin aequalitas, from aequalis (equal or level) — sameness in measure or value
• Equation – from Latin aequatio, from aequare (to make equal) — a statement of balanced values
• Identity – from Latin identitas, from idem (the same) — in maths, a statement that is always true, e.g. sin²(x) + cos²(x) = 1
• Congruent – from Latin congruere, meaning to come together, agree, or coincide — in geometry, shapes that are exactly equal in form and size
• Symmetry – from Greek symmetria, from syn- (together) + metron (measure) — “measured together” or balanced
• Parity – from Latin paritas, from par (equal) — in mathematics, used for evenness or equivalence

📏 Geometry & Measurement

• Perimeter – from Greek peri (around) + metron (measure) — meaning “measure around”
• Area – from Latin area, meaning open space, threshing floor, or level ground
• Polygon – from Greek poly (many) + gōnia (angle) — meaning “many-angled”
• Angle – from Latin angulus, meaning corner or bend — related to angere, “to compress or tighten”; the sharp change in direction creates a “corner”
• Triangle – from Latin triangulus, from tri- (three) + angulus (angle)
• Scalene – from Greek skalenos, meaning uneven or unequal. A scalene triangle has no equal sides or angles.
• Isosceles – from Greek isos (equal) + skelos (leg) — literally “equal legs”. An isosceles triangle has two equal sides.
• Equilateral – from Latin aequus (equal) + latus (side) — all sides are equal in length. An equilateral triangle also has equal angles (60° each).
• Quadrilateral – from Latin quattuor (four) + latus (side) — a shape with four sides.
• Square – from Latin exquadrare, from quadrare (to make square) + quattuor (four). A square has four equal sides and four right angles.
• Rectangle – from Latin rectus (right, straight) + angulus (angle) — “right-angled”. A rectangle has four right angles, with opposite sides equal.
• Rhombus – from Greek rhombos, meaning something that spins or whirls — likely referring to its diamond shape. A rhombus has all sides equal but angles that aren’t 90°.
• Parallelogram – from Greek parallelos (beside each other) + gramma (line or letter). A four-sided shape with opposite sides parallel.
• Trapezium – from Greek trapezion, a small table, from trapeza (table). Refers to a four-sided shape with only one pair of parallel sides (UK definition).
• Circle – from Latin circulus, diminutive of circus, meaning ring or round course
• Radius – from Latin radius, meaning spoke of a wheel or ray
• Diameter – from Greek dia (across) + metron (measure) — “measure across”
• Circumference – from Latin circum (around) + ferre (to carry) — “to carry around”
• Arc – from Latin arcus, meaning bow or curve — an arc is a portion of the curved boundary of a circle.
• Sector – from Latin sectus, the past participle of secare, meaning to cut — a sector is a “cut-out” portion of a circle like a slice of pie.
• Segment – from Latin segmentum, from secare (to cut) — a segment is also a part of a circle, but unlike a sector, it’s bounded by a chord and an arc.
• Chord – from Latin chorda, from Greek khordÄ“, meaning gut or string — originally used in music and anatomy; in geometry, a chord is a straight line connecting two points on a curve.
• Tangent – from Latin tangere, meaning to touch — a tangent is a line that touches a curve at a single point without crossing it.
• Centre – from Latin centrum, from Greek kentron, meaning a sharp point or the pivot of a compass — the point from which all points on the circle are equidistant.
• Pi (π) – from the Greek letter π, the first letter of periphery (periphereia) — it represents the ratio of a circle’s circumference to its diameter.
• Annulus – from Latin annulus, meaning a little ring — a ring-shaped region between two concentric circles.
• Sphere – from Greek sphaira, meaning globe or ball
• Volume – from Latin volumen, meaning roll or scroll — originally from the idea of something that can be unrolled or filled
• Surface – from Latin super (above) + facies (face or form) — “upper face”
• Vertex – from Latin vertex, meaning whirl, top, or summit — used for a corner point
• Edge – from Old English ecg, meaning border or blade
• Face – from Latin facies, meaning form, shape, or surface
• Line – from Latin linea, meaning string or thread
• Point – from Latin punctum, meaning something pricked or a small mark

📐 Angle Relationships

• Angle – from Latin angulus, meaning corner, nook, or bend. It is a diminutive of angus or angere, meaning to bend, compress, or tighten. The same root gives us words like anguish (emotional tightness) and ankle (a bend in the leg).
• Angle (definition) – In geometry, an angle describes the amount of turn between two rays or lines that meet at a common point, called the vertex. It tells us how much one would rotate from one line to reach the other, and is measured in degrees or radians.
• Angle (Bonus fact) – In Old English, angle also referred to a fishhook due to its sharp bend. This gave rise to the word angler — someone who fishes.
• Perpendicular – from Latin perpendiculum, meaning plumb line (from per = thoroughly, + pendere = to hang) — something that hangs straight down forms a right angle
• Parallel – from Greek parallēlos, from para (beside) + allēlōn (each other) — lines “beside each other” that never meet.
• Protractor – from Latin protrahere (to draw forth or stretch out) — the name evolved from the instrument’s use in extending or measuring angles
• Bearings – from Old English beran (to carry) — in navigation, the direction one “carries” or points toward, usually expressed in degrees
• Vertically opposite angles –
  “Vertical” comes from Latin vertex (whirl or summit), from vertere (to turn).
• Adjacent angles –
  From Latin adjacere (to lie near), from ad- (to) + jacere (to lie or rest).
  Adjacent angles “lie next to” each other, sharing a common arm and vertex.
• Complementary angles –
  From Latin complementum, meaning that which completes — from com- (together) + plere (to fill).
  Complementary angles “complete” a right angle (90° together).
• Supplementary angles –
  From Latin supplementum, meaning that which fills up — from sub- (under) + plere (to fill).
  Supplementary angles “fill up” a straight line (180° together).
• Corresponding angles –
  From Latin correspondere, from com- (together) + respondere (to answer).
  They “answer” each other across parallel lines — matching in position relative to the transversal.
• Alternate angles –
  From Latin alternare, meaning to do by turns or take in rotation.
  Alternate angles appear “alternately” on opposite sides of the transversal but within the same angular structure.
• Interior angles –
  From Latin interior, meaning inner or inward — angles found inside a polygon or between two lines.
• Exterior angles –
  From Latin exterior, meaning outer — angles formed outside a polygon when a side is extended.

🔤 Algebra & Relationships

• Algebra – from Arabic al-jabr, meaning “the reunion of broken parts” — from the title of a 9th-century book by al-Khwārizmī.
• Variable – from Latin variabilis, meaning changeable or inconsistent
• Equation – from Latin aequare, meaning to make equal
• Expression – from Latin exprimere, meaning to press out or represent
• Solve – from Latin solvere, meaning to loosen or untie — solving a problem means “freeing” the unknown
• Function – from Latin functio, meaning performance or execution
• Coefficient – from Latin com- (together) + efficere (to accomplish) — meaning “working together with” a variable
• Formula – from Latin formula, a diminutive of forma (shape or form) — originally a small rule or method
• Term – from Latin terminus, meaning boundary or limit — in algebra, a term is a bounded part of an expression

➗ Fractions, Ratios & Proportion

• Fraction – from Latin fractio, meaning a breaking or fragment — literally a broken part of a whole
• Numerator – from Latin numerare, meaning to count — the part being counted
• Denominator – from Latin denominare, meaning to name — it names the size of each part
• Ratio – from Latin ratio, meaning reckoning, reason, or proportion
• Proportion – from Latin proportio, from pro- (for) + portio (part or share) — “for each part”
• Percent – from Latin per centum, meaning “per hundred”
• Reciprocal – from Latin reciprocus, meaning moving back and forth — the inverse or “flipped” fraction

📊 Data, Statistics & Probability

• Data – from Latin datum, meaning “that which is given” — plural of datum, referring to given facts
• Statistics – from Latin status, meaning state or condition — originally used in political state data
• Graph – from Greek graphō, meaning “to write” or “to draw”
• Mean – from Old French meien, from Latin medianus (middle) — average or central value
• Median – from Latin medianus, meaning in the middle
• Mode – from Latin modus, meaning manner, measure, or method — the most common “manner” a value appears
• Range – from Old French ranger, meaning to arrange in a line — in data, the spread from lowest to highest
• Probability – from Latin probabilitas, meaning credibility or likelihood
• Chance – from Latin cadere, meaning to fall — originally implying something that befalls you randomly
• Outlier – from out + lier (to lie) — something that lies outside the general pattern

⏱️ Measurement & Time

• Measure – from Latin mensura, meaning a measuring or standard
• Unit – from Latin unitas, from unus (one) — meaning oneness, a single standard
• Length – from Old English lengðu, meaning “extent” or “distance”
• Width – from Old English wīde, meaning “broad”
• Height – from Old English hēah, meaning “high”
• Depth – from Old English dēop, meaning “deep”
• Mass – from Latin massa, meaning lump or dough — later used for physical quantity
• Weight – from Old English wiht, meaning something carried or a burden
• Time – from Old English tīma, meaning period or season
• Second – from Latin secunda minuta (the second small part), following prima minuta (the first small part, or minute)
• Minute – from Latin minuta, meaning small — originally a “small part” of an hour
• Hour – from Latin hora, from Greek hōra, meaning “season” or “time of day”
• Speed – from Old English spēdan, meaning to succeed or prosper — later applied to rate of movement
• Rate – from Latin ratus, past participle of reri, meaning to reckon or calculate
• Temperature – from Latin temperatura, meaning a proper mixture — related to balancing qualities like hot and cold

⚙️ Mechanics & Motion

• Speed – from Old English spēdan, meaning to succeed or prosper — later applied to rate of movement
• Velocity – from Latin velocitas, from velox (swift) — velocity includes both speed and direction
• Distance – from Latin distantia, from dis- (apart) + stare (to stand) — “standing apart”
• Time – from Old English tīma, meaning a period or season — linked to division of the day
• Acceleration – from Latin accelerare, from ad- (toward) + celer (swift) — “to hasten”
• Deceleration – from Latin de- (down) + celer (swift) — “to slow down”
• Force – from Latin fortis, meaning strong — through Old French force, meaning strength or power
• Mass – from Latin massa, meaning lump or dough — later used for amount of matter
• Weight – from Old English wiht, meaning something carried or a burden
• Gravity – from Latin gravitas, meaning heaviness or seriousness
• Friction – from Latin frictio, from fricare, meaning to rub
• Moment – from Latin momentum, meaning movement or importance — in mechanics, a turning effect
• Work – from Old English weorc, meaning activity or labour — in physics, force × distance
• Energy – from Greek energeia, meaning activity or operation
• Power – from Latin potere, meaning to be able — rate of doing work
• Vector – from Latin vector, meaning one who carries — in physics, a quantity with both magnitude and direction
• Scalar – from Latin scala, meaning ladder — used for quantities with only magnitude (no direction)
• Displacement – from Latin dis- (apart) + placere (to place) — the overall change in position
• Momentum – from Latin momentum, meaning movement or impulse — mass × velocity

📘 Appendix: Greek & Latin Roots in Mathematics

Root	Meaning	Origin	Examples
numer-	number	Latin	numeral, numerator
digit-	finger	Latin	digit, digital
cent-	hundred	Latin	percent, century
dec-	ten	Latin	decimal, decagon
tri-	three	Latin	triangle, trigonometry
quadri-	four	Latin	quadrilateral, quadrangle
poly-	many	Greek	polygon, polynomial
gon / gonia	angle	Greek	polygon, trigonometry
meter	measure	Greek	perimeter, diameter, thermometer
circum-	around	Latin	circumference, circuit
dia-	across, through	Greek	diameter, diagonal
radius	ray, spoke	Latin	radius, radial
pend-	to hang	Latin	perpendicular, pendulum
para-	beside	Greek	parallel, parameter
graph-	write, draw	Greek	graph, graphic, paragraph
solve / solut-	to loosen, untie	Latin	solve, solution, absolute
stat-	to stand	Latin	statistics, status, stationary

This list and library has been designed with the help of ChatGPT by Open AI.