🧮 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 – a teaching term often used in contrast with place value. It refers to the actual written value of a digit, without considering its position. For example, in 345, the marked value of the 3 is “3”, but its place value is 300. “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, to separate

⚖️ 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. sin²θ + cos²θ = 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)
• Quadrilateral – from Latin quattuor (four) + latus (side)
• 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”
• 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 – Etymologies

• 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 rise to words like anguish (emotional tightening) and ankle (a bend in the leg). In geometry, an angle describes the space formed by two lines diverging from a common point — the vertex.
• Bonus angle etymology fact : In Old English, angle also referred to a fishhook due to its sharp bend. This gave rise to the term angler — a person 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).
  When two lines cross, the angles “opposite” each other across the vertex are equal — they mirror each other in this turning.
• 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 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.