History of the Math

The potter's wheel — inertia smooths intermittent power.

Law of the lever proven from first principles.

Law of the lever — moment as force times arm.

Areas and volumes of curved figures — the segment's ancestry (circa).

Volume of the cylinder — the formula, permanently (circa).

Chord tables lock in the 360° Babylonian circle.

Antikythera mechanism — geared ratios compute the heavens.

Friction laws found experimentally — and left in notebooks.

Observes the area–velocity trade in channels (circa).

'Nova Scientia' — 45° named the range-maximizing elevation.

Chip log described — speed counted in literal knots.

Isochronism of small swings observed.

Publishes the first logarithm tables — the mathematical machinery under every dB.

Logarithms — the machinery.

Logarithms — arithmetic for multiplicative quantities.

Nova stereometria — wine-barrel gauging done with proto-calculus.

Third law: T² ∝ r³.

States Q = A·V — continuity as a law.

Poses the cantilever strength problem in Two New Sciences — brilliantly, and wrongly.

Projectile path proven parabolic.

The cantilever problem posed — beam strength becomes science.

Air resistance identified as why falling bodies differ.

Mercury barometer — pressure measured as a column height.

The barometer — pressure measured as fluid height.

Efflux law — the √ in the formula.

Puy de Dôme experiment proves pressure falls with altitude.

Puy de Dôme experiment: pressure falls with altitude.

Pressure transmits equally in a confined fluid.

Pendulum clock — timekeeping improves a hundredfold.

P·V constant at fixed temperature.

PV = constant at fixed temperature.

Compound pendulum solved — rotational inertia in practice.

First demonstration that light has a finite speed, from Jupiter's moons.

'Ut tensio, sic vis' — the linear spring law published.

Linear elasticity — 'ut tensio, sic vis'.

The linear spring — the oscillator's restoring force.

Vis viva — motion's measure proportional to v².

Theorem of moments — lever law becomes general statics.

Principia adds drag — and takes the parabola away.

First theoretical sound speed (air) in the Principia.

Principia — resistance proportional to V².

V² drag regime quantified.

Orbits derived from gravitation; the cannonball argument.

The cannonball argument defines escape.

Principia embeds moments in the laws of motion.

Links beam curvature to bending moment.

Friction laws published: load-proportional, area-independent.

231 in³ wine gallon — ancestor of the US gallon.

231 in³ wine gallon — still the US gallon.

Neutral axis located correctly.

Identifies the natural (radian) measure of angle.

Reproducible mercury thermometers and the °F scale.

Gridiron pendulum cancels expansion with brass against steel.

Early quantified ventilation — air per occupant (circa).

The pitot tube measures flow by its dynamic pressure.

Hydrodynamica — ½ρV² enters the pressure budget.

Hydrodynamica — the pressure-velocity-height budget.

Pressure-to-velocity budget underpinning the meter.

Hydrodynamica — head, velocity, and pressure unified.

'Institutions de Physique' unites theory with the clay-ball experiments.

Centigrade scale proposed (inverted; flipped by 1745).

Critical buckling load derived via calculus of variations.

The Leyden jar — first capacitor, discovered twice.

The Leyden jar — capacitive energy storage.

Circular-function machinery — ω = 2πf.

e and the exponential function formalized.

The Euler–Bernoulli beam equation — the math under this card.

Charge conservation analysis of the jar.

Involute tooth profile analyzed — the modern gear tooth.

Euler's turbomachine equation.

Turbomachine equation — pumps deliver head, not pressure (circa).

Hydraulic lime identified for the Eddystone Lighthouse — modern concrete's starting gun.

Equations of compressible fluid motion.

Continuity embedded in the general flow equations.

The equation in its modern form.

Specific and latent heat distinguished (circa).

'Moment of inertia' defined; rigid-body dynamics founded.

Vena contracta explains C_d ≈ 0.61.

First slope–radius channel formula (circa).

Wedge theory of earth pressure — soil mechanics begins.

Crank-and-flywheel patent turns steam strokes into rotation.

Measures V–I proportionality using shocks to his own body; never publishes.

Systematic dilatometer measurements of expansion coefficients.

Horsepower defined — pumping becomes a priced commodity.

Defines the horsepower to price steam engines against horses.

Defines the horsepower to sell steam engines against horses.

Torsion of wires quantified — the torsion balance.

Static vs kinetic friction; the engineering model completed.

Sound velocities in solids from resonating rods and plates.

'Mécanique analytique' — virtual work subsumes the lever.

Conservation of mass — the bookkeeping behind dilution.

Metre defined from the Earth's meridian.

Gradian — the right angle decimalized to 100.

Hydraulic press patented — force multiplication by area.

The metre — the metric flow units' ancestor.

Litre defined as the cubic decimeter.

'Dark stars' — escape velocity meets light speed (circa).

The converging-diverging meter principle.

First parachute descent from a balloon.

Constricted-tube effect behind flow metering.

Cannon-boring: friction makes heat without limit.

Platinum Mètre des Archives deposited.

Kilogramme des Archives — the kilogram realized.

The voltaic pile — the first battery.

The pile — cells in series, the first battery.

Flat-belt line shafting becomes the standard factory transmission.

Volume–temperature law.

Volume–temperature law published (crediting Charles).

Partial pressures and the saturation curve of water vapor.

Early experiments on conduction in bars (circa).

The barometric formula — pressure vs. height, mathematically.

Elastic modulus defined as a material property.

Times sound racing through an iron water main vs air.

Equal volumes, equal molecules — n enters the equation.

Molar volume concept — density becomes PM/RT.

Early derivation of rocket motion — forgotten for a century.

Reversible pendulum measures g with precision.

Zone construction in the prize memoir on diffraction.

'Principles of Carpentry' — section design for practitioners.

Macadam road construction — engineered aggregate layers (circa).

Prony brake — the first practical shaft-power dynamometer.

The stress tensor — stress made rigorous.

Théorie analytique de la chaleur — heat flow proportional to ΔT.

Théorie analytique de la chaleur — the law and the series.

Imperial gallon defined — the US/imperial fork is permanent.

Patents Portland cement.

Volumetric analysis; the burette and pipette named (circa).

Turns beam theory into usable engineering design formulas.

Linear bending theory: σ = M·c/I.

Publishes Die galvanische Kette — V = IR, to initial ridicule.

V = IR — the law the divider applies twice.

Resistance defined — the quantity being combined.

Die galvanische Kette — V = IR.

Work defined; the ½mv² form fixed.

Electromagnetic induction — the transformer's physics.

Self-induction discovered (the henry remembers him).

Invents the four-arm bridge circuit.

Exact thick-cylinder stress solution published.

Negative temperature coefficient observed in Ag₂S — the first semiconductor effect.

Geometric picture of free rotation — the inertia ellipsoid.

Combined ideal gas equation PV = nRT.

Combines the laws into PV = nRT.

Dielectrics and the measure of capacitance.

Maximum power transfer theorem — why matching matters.

Quantifies electrical heating — the P = VI power relation.

Awards Ohm the Copley Medal; the law finally sticks.

I²R heating — the physical meaning of RMS.

'Principles of Mechanism' systematizes gear-train kinematics.

Proposes the frequency shift of moving sources.

States the mechanical equivalent of heat.

Bakerian Lecture popularizes the bridge (crediting Christie).

Falling-weight experiments price mechanical energy in heat.

Paddle-wheel experiments price heat in work, refined through 1850.

Mechanical equivalent of heat — energy accounting unified.

The Magnus saturation-vapor-pressure formula.

Circuit laws, published at age 21, formalize series-parallel analysis.

Current law — why parallel conductances add.

Confirms it with musicians on a moving train.

Modern head-loss equation with f.

Precision gas-density measurements (circa).

Hydraulic crane launches industrial fluid power.

Conservation of energy stated in full generality.

Absolute thermodynamic temperature scale.

Bourdon-tube gauge puts a pressure dial on every boiler.

The term 'kinetic energy' coined.

Induction coil — stored magnetic energy as a product.

Pendulum demonstrates the Earth's rotation.

Viscous-flow theory — the µ in the denominator.

Curved-vane impeller shows efficiency is design, not luck.

Predicts LC oscillation mathematically.

The term 'potential energy' coined.

LC oscillation predicted — the reactive tug-of-war.

RC law of the telegraph cable — the time constant's debut.

RC transient law from telegraph cable theory.

General torsion theory; circular-section formula's limits mapped.

Discovers resistance changes with strain.

Dijon experiments make roughness part of the law.

Stress-state earth pressure theory; Ka in closed form.

Brown & Sharpe gauge — the geometric series adopted as AWG.

AWG standardizes the copper in the denominator.

Early analysis of pipe-surge pressure (circa).

Rechargeable lead-acid cell.

Photographs oscillatory spark discharge — theory confirmed.

Fahrenheit-sized absolute scale for engineering.

Lead-acid rechargeable cell; the 12 V series string to come.

Double bridge extends null measurement to milliohms.

Four-terminal (Kelvin) sensing removes lead error.

Field equations predict EM waves at the speed of light.

Deadliest US maritime disaster — steam's cost made plain.

Proposes the 2/3-power law.

Patents wire-reinforced concrete — planters first, structures soon after.

Reinforced concrete patented — steel goes into the pour.

Whirling speed identified — and supercritical running wrongly forbidden.

Shock jump conditions from thermodynamics.

Field-energy formulation — ½LI² formalized.

Coins 'radian' at Queen's College Belfast.

Dimensionless resistance coefficient (circa).

'Theory of Sound' founds engineering vibration analysis.

Preferred-number series — geometric sizing of standard parts.

Coaxial cable patented.

Coaxial line patented.

Equivalent-circuit theorem — the divider's output impedance.

Skin effect derived for spherical conductors.

Dye-filament experiment finds the transition criterion.

Manganin — the near-zero-tempco resistance alloy.

Energy flux of the EM field — S itself.

Coins 'torque' for twisting effort in machinery.

Twisted rebar patent; reinforced concrete becomes buildable in America.

Twisted rebar patent — mechanical bond by geometry.

Temperature dependence of equilibrium — the exponential form.

Operational circuit analysis normalizes the conductance view.

Operational calculus makes filter math tractable.

Transmission-line theory — reflections quantified.

General conductor case; the effect named and tamed.

Closed-core practical transformer.

Cone clutch on the first automobiles.

Names and formalizes inductance; reactive behavior theorized.

AC distribution demo at Great Barrington — the grid begins.

Coins 'impedance' for AC opposition.

Generates and measures radio waves — λf = c confirmed on a lab bench.

Transmission-line theory explains velocity factor in cables.

Resonant circuits generate and detect radio waves.

AC resistance of practical conductors quantified.

Measures EM oscillation periods experimentally.

The dipole — the first antenna.

Independent derivation — the Rankine-Hugoniot relations.

Schlieren photograph of a bullet's shock wave.

Photographs supersonic shock waves; identifies the speed ratio.

Commercial venturi meter for waterworks.

Commercial venturi meter — flow becomes a billable number.

Photographs shock waves; the sonic ratio gets its physics.

Ionic dissociation theory — concentration becomes physical chemistry.

The dipole — radio's first and reference antenna.

The converging–diverging nozzle goes supersonic.

The watt adopted as the unit of power, honoring Watt.

Tangent-modulus theory extends buckling past the elastic range.

Runs turbine shafts above critical on flexible spindles.

Presents the formula that takes his name.

The joule named in Joule's honor.

The watt named as the unit of power.

Activation energy and the rate equation.

AC instrument era forces peak-vs-RMS bookkeeping.

Monolithic reinforced-concrete frame system — column, beam, and slab as one.

Complex/phasor method tames AC calculation.

Portable precision instruments make shunt measurement standard practice.

Complex phasor method — reactance becomes arithmetic.

US customary units legally defined from the meter.

'Impedance' paper — complex Z formalized.

Phasor method makes RLC arithmetic routine.

Empirical formula for critical speeds of loaded shafts.

Argon discovered from a 0.5% density anomaly.

AC power transmission wins; RMS becomes the lingua franca.

Invar discovered — near-zero expansion alloy.

Radioactivity discovered in uranium salts.

Capacity vs. discharge-rate law.

Patents syntonic (tuned) wireless telegraphy.

Propeller cavitation discovered at sea; first cavitation tunnel.

First NEC — wire size becomes a safety regulation, circa.

First NEC; drop guidance enters wiring practice, circa.

ΔP = ρ·a·Δv established on Moscow's mains.

Patents the hollow-block molding machine — the CMU is born.

Transatlantic radio makes path loss an engineering question.

Over-the-horizon mystery starts propagation science.

Wind-tunnel lift measurements replace bad tables.

Mass vs weight separated; g₀ = 9.80665 m/s² fixed.

Litre tied to 1 kg of water — off by 28 ppm.

Balloon soundings discover the tropopause and stratosphere.

Systematic ball-bearing load-capacity experiments.

Circulation condition at the trailing edge.

General theory of hydraulic transients.

Exponential decay law and transmutation theory — the half-life.

Measures pressure along a Laval nozzle — theory confirmed (circa).

The rocket equation published, with liquid fuel proposed.

11.2 km/s framed as spaceflight's price of exit.

Exhaust velocity identified as rocketry's key metric.

Ton of refrigeration standardized from melting ice.

Göttingen program makes supersonic flow an engineering science.

Force coefficients normalized by q — modern aerodynamic bookkeeping (circa).

Boundary-layer theory explains why Re governs.

Boundary layer explains where drag comes from.

Block-making machinery industrializes; blocks become a commodity.

Multi-plate oil-bath clutch developed.

Lift = ρVΓ — the circulation theorem.

First observation of electroluminescence (SiC).

Coated stick electrode makes structural arc welds possible.

Ideal aggregate gradation curve published.

Electroluminescence observed in silicon carbide.

Oblique-shock θ-β-M theory in his dissertation under Prandtl.

Coins the name 'Reynolds number'.

A15 standardizes reinforcing bars; the numbered size system follows.

Rational psychrometric formulae — air conditioning gets its chart.

Wind-tunnel C_d measurements; the drag crisis found.

First ready-mixed concrete delivered — the cubic yard becomes a commodity.

International Annealed Copper Standard fixes ρ = 1.7241 µΩ·cm.

Coins Q for coil quality at Western Electric (published usage 1920s).

Boiler & Pressure Vessel Code — hoop stress becomes law.

Industry standard reference conditions emerge (circa).

Convective heat-transfer theory; LMTD framework matures (circa 1910s).

Rubber V-belt invented — the compact machine drive.

Pump test standards make efficiency claims comparable.

Standards body that codified NPSH practice.

Torque wrench invented for NYC water-main flange bolts.

Lifting-line theory — finite wings computed.

Torque wrench patented — tightening becomes a number.

Water–cement ratio law; aggregate science enters mix design.

Whirling rotor theory — self-centering above resonance explained.

First premeditated free-fall parachute jump — V_t survived by design.

'A Method of Reaching Extreme Altitudes' — measured nozzle efficiency.

The multivibrator — two-state RC timing circuits.

Multivibrator circuits, including the one-shot.

Image-parameter network design matures.

Two-port image design formalized.

Nobel Prize for Invar and precision metrology.

Image-parameter design; matching becomes systematic.

Systematic matched-network (pad/filter) synthesis.

Pad synthesis equations in modern form.

Roughness coefficient tied to physical wall texture.

'Die Rakete zu den Planetenräumen' — the German school begins.

The book that made orbital mechanics a movement.

Define the Transmission Unit (TU), replacing 'miles of standard cable' with a clean log ratio.

First international standard atmosphere for aviation.

Load–life exponent and statistical bearing life at SKF.

Standard atmosphere fixes T(h) — Mach from altitude becomes arithmetic.

Cavitation similarity number σ (circa).

Transmission Unit replaces miles-of-standard-cable.

Single dry-plate clutch standardizes the modern form.

Proves the minimum-energy two-impulse transfer.

Erdbaumechanik — modern soil mechanics, effective stress, and the limits of the classics.

468/f enters amateur canon.

First liquid-fuel rocket flight, Auburn, Massachusetts.

First liquid-fuel flight — Isp leaves the test stand.

Negative feedback, sketched on a ferry-ride newspaper.

TU renamed the decibel, honoring Alexander Graham Bell.

Standardizes the resistor color code.

Sampling rate theorem groundwork.

Decibel adopted; the 10·log/20·log power-voltage pair standardizes.

Measures thermal noise in resistors.

Derives kTB from thermodynamics.

Quartz crystal clock — Q as a timekeeping technology.

First structural welding code — throat stress made law.

'Vibration Problems in Engineering' — the working handbook.

The TU renamed the decibel.

Broadband coax system — the modern cable.

Curvature correction factor for helical spring stress.

Names the Mach number.

Nautical mile fixed at 1852 m; 'Mach number' named.

Broadband coaxial transmission system.

Maximally flat filter paper starts modern filter design.

'Strength of Materials' canonizes modern practice.

Torsion design practice standardized in the classic texts.

C90 standardizes load-bearing CMU dimensions and strength.

First commercial microwave link, Calais–Dover — clearance becomes engineering.

Effective-earth-radius (4/3) refraction model.

Systematic airfoil families catalogue C_L for designers.

Interference measurement standardizes on field-strength/µV language.

'Mechanical Vibrations' and the tuned damper canon.

Quantum-tunneling theory of electrical breakdown in solids.

US licensing regime; ERP becomes broadcast's yardstick.

Transition-state theory explains the barrier.

'Theory of Elastic Stability' — the working engineer's reference.

12C welded storage-tank standard; gauging becomes contractual (later API 650).

12C welded tank standard — steel verticals standardized.

Patents PCM — digitized analog signals.

Formulas for Stress and Strain — the compilation on every stress engineer's shelf.

Bonded strain gauge makes the bridge the universal sensor front end.

Bonded wire strain gauge, invented independently at Caltech and MIT.

The Smith chart — reflection made graphical.

Implicit transition formula for f.

Smith chart — L-network design as geometry.

F-correction charts for multi-pass exchangers.

50 Ω standardized as the loss-power compromise, circa.

Summing amplifier for the M9 gun director — the op-amp's war job.

First shell-and-tube exchanger standards.

Duty balance formalized on every exchanger datasheet.

3–15 psi live-zero signaling standardizes process control.

Ultrasonic reflectoscope — sound speed becomes an NDT tool.

The etched printed circuit board.

Rigorous antenna theory explains the shortening factor.

Standardized RG-series cables and connectors.

Moving-target indication — Doppler goes operational.

Brittle fracture of welded ships forces the toughness revolution.

Noise-figure convention fixes T₀ = 290 K.

Noise figure defined; 290 K reference set.

Cascade formula — first-stage dominance proven.

'Mechanical Springs' — the standard design text.

The Moody chart — f at a glance.

Geostationary orbit proposed for communications.

R-value insulation rating popularizes L/k commerce (circa).

The Friis transmission formula — FSPL formalized.

Transmission formula — the budget's physics.

50 Ω becomes the RF impedance — fixing the 107 dB offset.

Helical antenna; the practical-antenna era.

Isotropic-referenced link budgets — EIRP's home turf.

'Properties and Uses of Thermistors' — the modern NTC component.

Resolves the inelastic column paradox.

Stressed-volume fatigue theory of rolling contact.

First piloted supersonic flight — the relations flown.

Mach 1.06 flown — the ratio becomes a milestone.

First level supersonic flight — Mach 1 crossed.

Quantization noise analysis — the 6.02N + 1.76 dB line.

Quantization noise law — the forward direction.

Joule adopted for heat — the calorie officially deprecated.

Sampling theorem formalized.

Radiocarbon dating — the half-life as a clock.

*Antennas* — the beamwidth-gain approximation canonized.

TD-2 transcontinental microwave relay; path profiling standardized.

Etched-foil gauges bring precision manufacture to the bridge arm.

International color-code standard (now IEC 60062).

K2-W — the first commercial op-amp.

Microstrip introduced.

IEC 63 standardizes the E-series, circa.

Gyrobus — flywheel-powered public transport.

Report 1135 tabulates the isentropic-flow relations.

Report 1135 charts the θ-β-M relation for working engineers.

Original current-capacity charts (later MIL-STD-275).

Silicon junction diodes show stable reverse breakdown — 'zener' diodes, circa.

Crest factor becomes a shaker-system spec.

Current-loop transmitters replace air lines.

The equation, staged, reaches orbit with Sputnik.

First artificial satellite proves the arithmetic.

Commercial SCR — hard switching, and the snubber's job, arrives.

1 ft = 0.3048 m exactly; the conversion becomes exact.

First spacecraft to reach Earth escape velocity.

International yard: 1 in = 25.4 mm exactly.

1 lb = 0.45359237 kg exactly.

The hertz adopted as the SI unit of frequency.

SI adopted — m³/h and L/s standardized.

The watt enshrined in the new SI.

API 650 — the modern welded storage-tank standard.

First practical visible LED (red, GaAsP).

Satellite links make dB-column budgeting standard practice.

First practical visible (red) LED.

Three-op-amp differential topology in common use.

Cryogenic first stages exploit the formula for radio astronomy.

Hydrogen-LOX flies — chemical Isp near its ceiling.

A 3.5 K unexplained noise temperature = the cosmic microwave background.

SR-71 inlets stage oblique shocks to fly Mach 3.2 efficiently.

First geostationary satellite.

GTO — the Hohmann transfer as commercial routine.

Litre restored to exactly 1 dm³.

µA709 monolithic op-amp; the IC era begins.

Conformal-mapping analysis of strip lines.

Near-Hohmann trajectory reaches Mars.

4–20 mA standardized.

First US RF exposure standard.

8410 network analyzer moves matching from slotted lines to screens.

Max-q design point governs the Moon rocket's structure.

Pogo suppression — water hammer meets rocketry (circa).

AD520 — first monolithic instrumentation amplifier.

The pascal adopted as the SI unit of pressure.

Designs the 555 under contract to Signetics.

555 designed at Signetics — monostable mode built in.

Bandgap reference — precision moves on, zeners keep the simple jobs.

NE555 released — timing becomes a three-part bill of materials.

NE555 ships; 1.1·R·C enters every databook.

'Optimum Snubbers for Power Semiconductors' formalizes the design.

Closed-form design equations — the ones in this card.

±1% parts make E96 the working series, circa.

U.S. Standard Atmosphere 1976 — still the working reference.

Rigorous long-form bolt torque–preload equation published.

Explicit f formula — the one this card evaluates.

Voyager budgets prove the method across the solar system.

VDI 2230 systematizes bolted-joint calculation.

ISO 281 standardizes the L10 rating life.

Off-line SMPS makes the HV bulk cap the energy reservoir, circa.

Rectifier-fed bulk caps make NTC inrush discs ubiquitous, circa.

HEXFET power MOSFETs — faster edges, same RC medicine.

Synchronous (toothed) belts mature, adding exact ratios to belt drives.

ISO 5167 standardizes orifice metering worldwide (first edition).

Speed of light fixed by definition at 299,792,458 m/s.

Metre redefined via the speed of light.

HART overlays digital comms on the analog loop.

Commercial lithium-ion changes the budget.

Li-ion 18650 commercialized — S×P becomes everyone's math.

AD620 sets the modern G = 1 + 49.4k/Rg convention.

Blue GaN LED — white light, Nobel 2014.

High-brightness blue GaN LED — white lighting unlocked.

Digitizer testing standardized; ENOB defined operationally.

ATX spec writes ~17 ms hold-up into every PC supply.

Modern refit of the Magnus constants used here.

The compliance-calculation handbook this card mirrors.

IPC-2221 generic design standard carries the classic curves.

Mars Climate Orbiter lost to a lbf·s vs N·s mix-up.

ADC test methods make ENOB the honest-resolution metric.

IPC-2152 replaces them with measured modern data.

Kelvin redefined via the Boltzmann constant.

Kilogram redefined via the Planck constant.