Christiaan Huygens

How to use this course

Christiaan Huygens stands between Galileo Galilei and Isaac Newton. He found the first moon of Saturn and explained its ring, built the first pendulum clock and gave its complete mathematical theory, wrote the first printed book on probability, found the correct laws of elastic collision, derived the formula for centrifugal force, and proposed the wave theory of light that still carries his name. He did all of this in the language of Euclid and Archimedes, without the calculus that Newton and Gottfried Wilhelm Leibniz were inventing around him.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Huygens argued with similar triangles, proportions and limiting arguments in the style of Archimedes. The course states his results in modern notation and says where his own route differed.

Dates. The Dutch provinces of Holland and Zeeland used the Gregorian calendar in Huygens’s lifetime, so dates in this course are New Style unless marked otherwise. English dates of the same period, as in the Hooke and Newton modules, are usually Old Style, ten days behind.

Timeline

The Hague, 1629–1645

Christiaan Huygens was born in The Hague on 14 April 1629, the second son of Constantijn Huygens and Suzanna van Baerle. His father was secretary to successive Princes of Orange, a poet in Dutch and Latin, a composer and a friend of the leading minds of Europe. He corresponded with Marin Mersenne and knew René Descartes well. The family was rich, Calvinist and well connected. There were five children: Constantijn the younger (1628), Christiaan, Lodewijk (1631), Philips (1632) and Suzanna (1637). Their mother died in 1637, soon after Suzanna’s birth.

The boys were taught at home until the age of sixteen. The programme was broad and deliberate: Latin, Greek, French and Italian, music, drawing, logic, fencing and riding, and mathematics. Christiaan built mechanical models as a child and showed early skill in geometry. In 1644 his father engaged the mathematician Jan Jansz Stampioen as a tutor. Descartes, who visited the family, took an interest in the boy’s progress, and his Principia philosophiae and Géométrie shaped Huygens’s youth. Later in life Huygens rejected much of Descartes’s physics, but he kept the Cartesian demand that every effect have a mechanical cause.

Leiden and Breda, 1645–1655

In May 1645 Huygens entered Leiden University to study law and mathematics. On Descartes’s advice his mathematics tutor was now Frans van Schooten, the editor of the Latin edition of the Géométrie. Van Schooten taught him Descartes’s analytic geometry and the methods of François Viète and Pierre de Fermat, and remained his mathematical correspondent for years. In March 1647 Huygens moved to the newly founded Orange College at Breda, where his father was a curator. He left in August 1649 and joined a diplomatic mission of Henry, Duke of Nassau, to Denmark. He hoped to travel on to Stockholm to see Descartes, but the weather prevented it, and Descartes died there in February 1650.

In these years Mersenne began to set him problems by letter. Huygens showed that a chain hanging freely is not a parabola, as Galileo had suggested, and found how a weightless cord must be loaded to hang in a parabola. Mersenne called him a new Archimedes.

Huygens never practised law. His first publication, Theoremata de quadratura hyperboles, ellipsis et circuli (1651), exposed an error in the quadrature of the circle claimed by the Jesuit Grégoire de Saint-Vincent. De circuli magnitudine inventa (1654) gave new and sharper bounds for the ratio of circumference to diameter (Lesson 04). Between 1652 and 1656 he also worked out the rules of elastic collision, discovering that Descartes’s rules were wrong (Lesson 06), but he kept them in manuscript.

Around 1654 Christiaan and his brother Constantijn began to grind and polish their own telescope lenses, and Christiaan devised improved methods for doing so. The craft would give him his first fame.

Lenses, Saturn and the clock, 1655–1666

On 25 March 1655, with a telescope he and Constantijn had built, Huygens saw a faint star near Saturn that followed the planet. It was a moon, now called Titan, the first satellite found since Galileo’s four moons of Jupiter. He announced it in a short tract, De Saturni luna observatio nova, and hid a second claim in a Latin anagram. When he unscrambled it in Systema Saturnium (1659), it said that Saturn is girdled by a thin flat ring, nowhere touching the planet and inclined to the ecliptic. Galileo had seen Saturn with “ears” that came and went. Huygens explained the changes geometrically: because the ring is tilted, its appearance from Earth changes with the planet’s position in its 29½-year orbit, and twice in each orbit we see it edge on, when it nearly vanishes. Systema Saturnium also described an eyepiece micrometer for measuring small angles.

In 1655 Huygens made his first visit to Paris, where he heard of the correspondence between Blaise Pascal and Fermat on games of chance. Back in Holland he wrote De ratiociniis in ludo aleae, which van Schooten published in 1657 (Lesson 05).

The pendulum clock

Astronomy needed accurate time. Galileo had noticed that a pendulum’s swing takes nearly the same time whatever its amplitude, but nobody had used a pendulum to govern a working clock. Huygens began the project in December 1656. His design let a freely swinging pendulum regulate the verge escapement of a weight-driven clock, and he patented it in the Dutch Republic in 1657. The Hague clockmaker Salomon Coster built the first examples; the oldest surviving one, dated 1657, is in the Museum Boerhaave in Leiden. Good clocks of the day might drift by a quarter of an hour a day; Huygens’s by seconds. He described the design in the short tract Horologium (1658).

A circular pendulum is only approximately isochronous. In 1659 Huygens discovered the curve on which the period does not depend on amplitude at all, the cycloid, and how to make a pendulum bob follow it (Lesson 08). In the same year he derived the law of centrifugal force (Lesson 07). Both results went into the book of 1673.

Longitude and London

A clock that kept time at sea would solve the problem of longitude, and Huygens hoped his would. Sea trials began in the early 1660s with mixed results: the motion of a ship disturbs a pendulum. In 1661 he visited London, met John Wallis and Robert Boyle, saw Boyle’s air pump, and watched the Royal Society take shape. In 1663 he was elected a Fellow. By 1666 he was the most celebrated natural philosopher on the Continent, and Jean-Baptiste Colbert invited him to Paris to help found the new Académie royale des sciences.

Geometry before calculus: π and the hanging chain

For the general reader. Archimedes trapped π between the perimeters of polygons drawn inside and outside a circle. Huygens, at 25, found how to squeeze far more accuracy out of the same polygons by combining them cleverly. Forty years later he helped solve one of the first problems of the new calculus, the shape of a hanging chain, still using geometric methods.

Chords and arcs

For an arc of a circle let \(c\) be its chord and \(c'\) the chord of half the arc. Archimedes’s inequality \(2c'<s\) has an error of third order in the angle. Huygens proved in De circuli magnitudine inventa a bound that is accurate to fifth order.

Modern check. On the unit circle take the arc subtending angle \(2\alpha\): \(s=2\alpha\), \(c=2\sin\alpha\), \(c'=2\sin(\alpha/2)\). Taylor expansion gives

so the error is of fifth order and positive. Huygens’s own proof compares areas of inscribed triangles and segments in the manner of Archimedes. The practical meaning is that one step of polygon doubling, plus a one-third correction, does the work of several further doublings. This is an early instance of what is now called Richardson extrapolation: \(p_n=L-a/n^2+O(n^{-4})\), so \(p_{2n}+\tfrac13(p_{2n}-p_n)\) cancels the \(n^{-2}\) term.

The hanging chain

Galileo had suggested that a hanging chain forms a parabola. As a student Huygens showed it does not. A cord carries a parabola when the load is uniform per unit horizontal length, as for the deck of a suspension bridge. A free chain carries a load uniform per unit arc length. In 1690 the Basel mathematician Jacob Bernoulli posed the problem of the chain’s exact shape; in June 1691 the Acta Eruditorum printed solutions by Huygens, Leibniz and Johann Bernoulli. Huygens, who had named the curve catenaria in a letter to Leibniz, found its properties by geometric arguments; in modern form it is \(y=a\cosh(x/a)\).

Expectation and games of chance

For the general reader. What is a fair price for a gamble? Pascal and Fermat had discussed the question in private letters in 1654. Huygens turned their ideas into a short book, the first printed treatise on probability, built on one principle: a chance of winning something is worth exactly the stake that would buy you into a fair game with the same prospects. Today we call that worth the expected value.

The axiom

De ratiociniis in ludo aleae (1657) has fourteen propositions and ends with five problems for the reader. Huygens does not define probability. He defines the value of a chance by a fairness argument: if I have equal chances of getting \(a\) or \(b\), my chance is worth \((a+b)/2\), because with that stake I could set up a fair game with an opponent that pays me \(a\) or \(b\) with equal chance.

In modern terms, the value of a gamble with outcomes \(a_i\) of probability \(\pi_i\) is \(E=\sum_i\pi_ia_i\). Huygens’s word for it was expectatio in van Schooten’s Latin, the origin of the English term.

The problem of points

Two players stake equal sums on a game of several rounds, each round won by either player with probability \(\tfrac12\). The game stops early when one needs \(m\) more rounds and the other \(n\). How should the stake be divided? Huygens solves it by working backwards from positions whose value is known, the method of Pascal. Let \(e(m,n)\) be the first player’s share of a total stake of 1. Then

The gambler’s ruin

Huygens’s fifth problem came from Pascal by way of Pierre de Carcavi. Two players A and B throw three dice. When 11 comes up A gains a point from B; when 14 comes up B gains a point from A. Each starts with 12 points, and the first to lose all of them is ruined. What are their chances?

Derivation. Let \(u_k\) be A’s chance of winning when A holds \(k\) points. Conditioning on the next exchange, \(u_k=p\,u_{k+1}+q\,u_{k-1}\) with \(u_0=0\), \(u_{a+b}=1\). The characteristic roots are \(1\) and \(r\), so \(u_k=\alpha+\beta r^k\), and the boundary conditions give the formula. For \(a=b=n\), \(P_A=\frac{1-r^n}{(1-r^n)(1+r^n)}=\frac{p^n}{p^n+q^n}\).

The laws of collision

For the general reader. Descartes had given seven rules for what happens when two bodies collide, and most were wrong. Huygens replaced them with correct rules for hard, elastic bodies. His key move was to imagine the collision watched by a man standing on a boat drifting along a canal: the laws must look the same to him as to a man on the bank. This is the principle of relativity, used as a tool for the first time.

Hypotheses

Huygens worked on collisions from 1652, sent his results to the Royal Society in 1668 and printed a summary in the Journal des sçavans in 1669; Wallis and Christopher Wren sent the Society results at the same time. The full treatise, De motu corporum ex percussione, appeared only in 1703. Its main hypotheses are:

1. A body in motion continues in a straight line with constant speed unless something prevents it (inertia, from Galileo and Descartes).
2. Two equal hard bodies meeting head-on with equal and opposite speeds rebound with the same speeds reversed (symmetry).
3. The motion of bodies and their relative motions are to be judged relative to a frame that may itself be moving uniformly; the rules hold equally in any such frame (relativity: the boat).
4. A larger body striking a smaller one at rest gives it some motion and loses some of its own.

Derivation in Huygens’s style

For equal masses, the symmetric hypothesis says that \((+w,-w)\) becomes \((-w,+w)\). Now watch from a boat moving with velocity \(-V\): the velocities \(V+w\) and \(V-w\) become \(V-w\) and \(V+w\). Any pair \((u_1,u_2)\) has this form with \(V=(u_1+u_2)/2\), so equal bodies exchange velocities. For unequal masses Huygens went to the frame of the centre of gravity, \(V=(m_1u_1+m_2u_2)/(m_1+m_2)\), in which the velocities \(w_1,w_2\) satisfy \(m_1w_1+m_2w_2=0\). He argued that in this frame each body simply reverses its velocity: otherwise the common centre of gravity could be raised by the collision, which contradicts the principle that heavy bodies cannot raise their own centre of gravity by their own motions (Lesson 09). Transforming back gives

Rules 1–3 follow at once. Descartes had conserved the scalar sum \(\sum m|u|\), which fails. Huygens saw that the conserved “quantity of motion” must take direction into account, and that \(\sum mv^2\) is also conserved in elastic impact. Leibniz later made \(mv^2\), his vis viva, a central quantity of dynamics, partly on Huygens’s example.

Centrifugal force

For the general reader. Whirl a stone on a string and you feel it pull outward. In 1659 Huygens worked out exactly how strong that pull is: it grows with the square of the speed and falls with the radius of the circle. Newton later used the same formula, read inwards as a centripetal force, to connect the motion of the planets with the inverse-square law of gravity.

The derivation

Huygens imagined a body tied to a wheel turning uniformly. Released, it would fly off along the tangent. Seen by an observer turning with the wheel, it recedes from the circle as a falling body recedes from its starting point: in time \(t\) a body moving along the tangent at speed \(v\) is at distance \(\sqrt{r^2+v^2t^2}-r\approx v^2t^2/(2r)\) from the circle. This distance grows as the square of the time, the signature of a constant acceleration, here \(v^2/r\). The cord must therefore pull the body with a force that bears the same ratio to its weight as \(v^2/r\) to \(g\).

Huygens stated thirteen propositions on circular motion at the end of Horologium oscillatorium without proofs. Newton studied them closely.

The conical pendulum

A bob on a cord of length \(l\) moving on a horizontal circle of radius \(r\), with the cord at angle \(\theta\) to the vertical, is balanced when the horizontal and vertical components of the tension satisfy \(T\sin\theta=m\omega^2r\) and \(T\cos\theta=mg\). Then \(\omega^2=g/(l\cos\theta)=g/h\), where \(h\) is the height of the cone.

Huygens used this to design a clock governed by a conical pendulum, which runs smoothly rather than with ticks, and he showed how a bob kept on a paraboloid of revolution would be exactly isochronous for every radius.

The cycloid, the tautochrone and evolutes

For the general reader. A pendulum swinging on a circle keeps almost, but not quite, the same time whatever the size of its swing. Huygens found the curve for which the time is exactly the same: the cycloid, traced by a point on the rim of a rolling wheel. He then invented a theory of curves, evolutes and involutes, to show how to make a hanging bob follow a cycloid, by letting its cord wrap against two cycloidal plates.

The tautochrone

Take the cycloid generated by a circle of radius \(a\), inverted so that its lowest point is at the origin:

Its arc length from the bottom is \(s=\int_0^\theta 2a\cos(t/2)\,dt=4a\sin(\theta/2)\), and the height is \(y=2a\sin^2(\theta/2)=s^2/(8a)\).

Proof. Along the curve, \(\ddot s=-g\,dy/ds=-\frac{g}{4a}\,s\). This is simple harmonic motion with \(\omega^2=g/(4a)\), and every solution reaches \(s=0\) a quarter period after it starts from rest: \(\tfrac\pi2\sqrt{4a/g}=\pi\sqrt{a/g}\). Huygens proved it with a long sequence of geometric lemmas comparing descent along the cycloid with descent along a circle and with uniform motion, in the manner of Galileo’s Two New Sciences.

Evolutes and involutes

Unwind a taut thread from a curve \(C\): its end traces an involute of \(C\), and \(C\) is the evolute of the traced curve. Huygens proved the basic facts in Part III of Horologium oscillatorium:

So a pendulum of length \(l=4a\) hung from the cusp between two cycloidal “cheeks”, each half an arch of the cycloid generated by radius \(a\), wraps against them and its bob moves exactly on the cycloid of the theorem. Its period is \(2\pi\sqrt{l/g}\) for every amplitude. Part III also contains the rectification of curves: since the free thread has the length of the arc it has unwound, the arc length of the evolute is known. This gave Huygens the arc lengths of the semicubical parabola and of the cycloid, \(8a\) per arch.

In practice the cheeks gave less advantage than Huygens hoped, because friction and the flexing of the cord introduced errors of their own. Clockmakers kept small amplitudes instead. Huygens’s theory of evolutes outlived the clock: it is the theory of curvature in the plane.

The compound pendulum

For the general reader. A real pendulum is not a point on a weightless string. It is a rod and a heavy bob, or any rigid body swinging about an axis. Which simple pendulum swings in step with it? Marin Mersenne had asked the question in the 1640s and Descartes and Gilles Personne de Roberval had failed to answer it. Huygens solved it in Part IV of Horologium oscillatorium, and in doing so used, for the first time, the quantity now called the moment of inertia.

Huygens’s principle

Huygens took as his first hypothesis a principle he attributed to Evangelista Torricelli: if a system of heavy bodies starts from rest and moves under gravity, its centre of gravity cannot rise above its starting height. He added that if, at any moment, the bodies were separated and each turned upward with its acquired speed, their common centre of gravity would rise exactly to its original height. In modern terms this is conservation of energy for a rigid system, \(\tfrac12\sum m_iv_i^2=g\,M\,\Delta h_G\).

Derivation. Rotating through angle \(\phi\) from the lowest position raises the centre of gravity by \(h(1-\cos\phi)\). With angular velocity \(\dot\phi\), Huygens’s principle reads \(\tfrac12\dot\phi^2\sum m_ir_i^2+Mgh(1-\cos\phi)=\text{const}\). Differentiating, \(I_O\ddot\phi=-Mgh\sin\phi\), the equation of a simple pendulum of length \(I_O/(Mh)\). The parallel-axis relation \(I_O=M(k^2+h^2)\) gives the last form.

Indeed the new distance is \(h'=l-h=k^2/h\), and \(h'+k^2/h'=k^2/h+h=l\). In 1817 Henry Kater turned this into the reversible pendulum, the standard instrument for measuring \(g\) for a century.

A universal measure

For small swings the period is \(T=2\pi\sqrt{l/g}\). Huygens put it as a proportion: the time of one small swing is to the time of free fall through half the length as the circumference of a circle is to its diameter. He proposed the length of a pendulum beating seconds as a natural unit of length that any nation could reproduce. The proposal was revived in the debates that led to the metre in the 1790s; the metre was defined instead from a meridian of the Earth.

The wave theory of light

For the general reader. Huygens thought of light as a disturbance travelling through a fine invisible medium, like sound through air. His central idea is a construction: every point that the disturbance reaches becomes a small source of its own, and the new wavefront is the envelope of all these little waves. With it he derived the laws of reflection and refraction and explained the double image seen through a crystal of Iceland spar.

The construction

Huygens presented his theory to the Académie in 1678 and published it in 1690 as Traité de la lumière. He held that light travels with a finite speed, and reported Ole Rømer’s 1676–77 inference of that speed from the timing of the eclipses of Jupiter’s moon Io.

Refraction

A plane wave with speed \(v_1\) meets a plane interface at angle of incidence \(\theta_1\). Let the wavefront touch the interface at \(A\) at time 0, while its other end is still a distance \(v_1\Delta t\) from the interface, reaching it at \(B\) at time \(\Delta t\), so \(AB\sin\theta_1=v_1\Delta t\). By then the wavelet from \(A\) has radius \(v_2\Delta t\) in the second medium, and the refracted front is the tangent from \(B\) to it, so \(AB\sin\theta_2=v_2\Delta t\).

Light bends toward the normal on entering a denser medium because it travels more slowly there. Descartes and later Newton’s corpuscular theory required the opposite. The question was settled for Huygens by Léon Foucault’s measurement of the speed of light in water in 1850. With \(\theta_2=\pi/2\) the construction also gives total internal reflection beyond the critical angle.

Iceland spar

A crystal of calcite splits a ray into two. One, the ordinary ray, obeys the law of refraction. The other, the extraordinary ray, does not: it is refracted even at normal incidence. Huygens explained this by supposing that in the crystal there are two kinds of wavelet, spheres for the ordinary ray and spheroids of revolution about the crystal’s optic axis for the extraordinary ray. The envelope of spheroids is a plane, but the ray to the point of tangency is no longer perpendicular to it. His predictions for many cuts of the crystal agreed with measurement. He also noticed that the two rays from one crystal behave differently when passed through a second crystal turned about the ray, and confessed he could not explain it. The explanation, polarization of a transverse wave, came with Thomas Young and Augustin-Jean Fresnel in the 1810s.

Fresnel’s completion

Huygens’s wavelets had no wavelength and no phase, so his theory could not explain diffraction or interference, and he had no reason why the backward envelope should be ignored. In 1818 Fresnel combined the construction with the principle of interference: the field at a point \(P\) is the superposition of secondary wavelets with their phases. In the Fresnel–Kirchhoff form,

where \(s\) is the distance from \(Q\) to \(P\) and \(\chi\) the angle between the normal and the direction to \(P\). The obliquity factor vanishes in the backward direction, and Gustav Kirchhoff derived it in 1882 from the wave equation.

Paris and the Académie, 1666–1681

In 1666 Huygens moved to Paris as a founding member of Louis XIV’s Académie royale des sciences, with a royal pension and lodgings in the Bibliothèque du Roi. He was its most eminent member and helped shape its programme of collective experiment and observation. He worked on the vacuum pump, the pendulum clock and the theory of gravity, and in 1669 defended a version of Descartes’s vortex theory of gravity against objections from Roberval and Edme Mariotte.

From 1671 his assistant was the young Denis Papin, with whom he built an engine in which gunpowder exploded in a cylinder drove a piston, an ancestor of the internal combustion engine. In 1672 Gottfried Wilhelm Leibniz arrived in Paris on a diplomatic mission. Huygens directed his reading, set him problems such as the sum of the reciprocals of the triangular numbers, and guided him until 1676, the years in which Leibniz invented his calculus. In the same years Huygens criticized Newton’s new theory of colours, at first without understanding it.

The Dutch War made his position delicate. In 1672 Louis XIV invaded the Dutch Republic, whose new stadtholder, William III of Orange, was the prince his family had served for generations. Huygens stayed in Paris. In 1673 he published Horologium oscillatorium, his masterpiece, with a fulsome dedication to Louis XIV.

In 1675 Huygens devised a watch regulated by a spiral balance spring. He sought a French patent, and the announcement provoked Robert Hooke, who claimed he had invented spring regulation years before; the dispute embittered relations with the Royal Society for a time. Huygens fell seriously ill in 1670, again in 1676, when he spent two years in The Hague and studied Iceland spar, and again in 1679 and 1681. In 1681 he left Paris for the last time. After Colbert’s death in 1683 and with the growing hostility to Protestants in France that culminated in the revocation of the Edict of Nantes in 1685, he did not return.

Hofwijck, death and legacy, 1681–1695

Back in Holland, Huygens worked on a marine clock for the Dutch East India Company, ground very long-focus lenses with Constantijn for aerial telescopes without tubes, and built a planetarium driven by clockwork whose gearing used continued fractions to approximate the planetary periods. In 1686 he wrote a manual in Dutch, Kort onderwijs, on finding longitude with clocks, and corrected the results of the Company’s trial voyage to the Cape of Good Hope. His father died in 1687, aged 90, and in 1688 Christiaan made the family’s country house, Hofwijck at Voorburg, his home.

In 1689, after William III had become king of England, Huygens made a third visit there. He met Newton on 12 June 1689, and they discussed Iceland spar and motion in resisting media. Huygens admired the Principia but rejected an attraction acting at a distance without mechanical cause. In 1690 he published the Traité de la lumière together with the Discours de la cause de la pesanteur, which proposed a vortex mechanism for gravity and gave his estimate of the flattening of the Earth (Exercise 7.2). He corresponded with Leibniz on the new calculus, which he came to accept late in life, and solved the catenary problem in 1691.

His last book, Cosmotheoros, speculated on life on the planets and the size of the universe. He estimated the distance to Sirius by comparing its brightness with that of the Sun. He died in The Hague on 8 July 1695, aged 66. He never married. He was buried in the Grote Kerk in The Hague, in an unmarked grave like his father’s. Constantijn published Cosmotheoros in 1698, and the Opuscula postuma of 1703 contained the collision treatise and De vi centrifuga.

Legacy

• Timekeeping: the pendulum clock remained the most accurate timekeeper until quartz clocks in the 1930s. The spiral balance spring still regulates mechanical watches.
• Mechanics: the relativity principle in collisions, conservation of momentum and of \(\sum mv^2\) in elastic impact, centrifugal force, the moment of inertia and the theory of the physical pendulum. Newton acknowledged his debt in the Principia.
• Mathematics: evolutes, involutes and curvature; the first printed treatise on probability and the concept of expectation, which Jacob Bernoulli reprinted and annotated in Ars conjectandi (1713).
• Optics: the Huygens–Fresnel principle, the foundation of diffraction theory, and the two-lens Huygens eyepiece.
• Astronomy: Titan and the ring of Saturn. The European Space Agency’s Huygens probe, carried by Cassini, landed on Titan on 14 January 2005.
• Editions: the Dutch Society of Sciences published his complete works, the Œuvres complètes, in 22 volumes between 1888 and 1950.

Connections

People linked to Christiaan Huygens across this collection. A name without a link has no page here yet. See Christiaan Huygens in the network of all 337 lives →

Teachers and advisors

• Frans van Schooten 1645-1647

Students

• Gottfried Wilhelm Leibniz 1672-1676

Influenced by

• Blaise Pascal
• Evangelista Torricelli
• Galileo Galilei
• Ibn al-Haytham
• Marin Mersenne 1646-1648
• René Descartes

Influenced

• Abraham de Moivre
• Alexis Clairaut
• Augustin-Jean Fresnel
• Edmond Halley
• Jacob Bernoulli
• Thomas Young
• William Hyde Wollaston
• Étienne-Louis Malus

Colleagues and collaborators

• Christopher Wren
• Gilles Personne de Roberval 1666-1675
• Giovanni Domenico Cassini 1669-1681
• Isaac Newton 1672-1695
• Johann Bernoulli 1691
• John Wallis
• Ole Rømer
• Pierre de Fermat 1656-1659
• Robert Boyle
• Denis Papin 1671-1675

Rivals

• Robert Hooke 1665-1695

Family

• Constantijn Huygens
• Constantijn Huygens Jr.

Also mentioned in this life

• Archimedes
• Euclid
• Léon Foucault
• Johannes Kepler
• Gustav Kirchhoff
• François Viète

Fields

• mechanics 27 lives
• optics 38 lives
• astronomy 50 lives
• probability theory 23 lives
• geometry 32 lives

On CoursesHub

• Pascal & Probability · History of Mathematics
• Wave Optics · Optics & Photonics
• Classical Mechanics

Sources and further reading

Biography

1. J. J. O’Connor and E. F. Robertson, Christiaan Huygens, MacTutor History of Mathematics.
2. Christiaan Huygens, Wikipedia (with extensive references).
3. C. D. Andriesse, Huygens: The Man Behind the Principle, Cambridge University Press, 2005.
4. H. J. M. Bos, Huygens, Christiaan, in Dictionary of Scientific Biography, vol. 6, Scribner, 1972.
5. J. G. Yoder, Unrolling Time: Christiaan Huygens and the Mathematization of Nature, Cambridge University Press, 1988.
6. H. Aldersey-Williams, Dutch Light: Christiaan Huygens and the Making of Science in Europe, Picador, 2020.

Works and science

1. C. Huygens, Œuvres complètes, 22 vols., Société hollandaise des sciences, 1888–1950.
2. C. Huygens, The Pendulum Clock or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks, transl. R. J. Blackwell, Iowa State University Press, 1986.
3. C. Huygens, Treatise on Light, transl. S. P. Thompson, Macmillan, 1912. Project Gutenberg.
4. Horologium Oscillatorium, Wikipedia.
5. Huygens–Fresnel principle, Wikipedia.
6. A. Hald, A History of Probability and Statistics and Their Applications before 1750, Wiley, 1990 (chapter on De ratiociniis).
7. M. Born and E. Wolf, Principles of Optics, Cambridge University Press, 7th ed., 1999 (Huygens–Fresnel and Kirchhoff theory).
8. R. Dugas, A History of Mechanics, Dover, 1988 (Huygens on collision and the compound pendulum).