170 projects · experiments and explanations

Physics and mathematics in motion

A point moves left–right and up–down at the same time. Change the ratio between their rhythms and watch an equation become a drawing. Then continue into light, gravity, geometry and probability.

The complete collection ↓

x = sin(2πfₓt)y = sin(2πfᵧt + φ)

Ideal harmonic motions without friction; the axes show relative displacement, from −1 to +1. The figure is not a planetary orbit.

Lissajous figures2 : 3

Above: horizontal motion. At right: vertical motion. The larger point combines them.

Phase difference 90°Time 2,00 s

Horizontal frequency: 0.25 Hz. Vertical frequency: 0.375 Hz. The motion repeats after eight seconds.

01 / Physics and mathematics

A circle and a line can have the same frequencies.

At a 1:1 ratio, with equal amplitudes, a 90° phase difference gives a circle. At 0°, it gives a line. What changes is when each motion reaches its extreme. The shape tells us about the relationship between two signals.

Inside a note — An instrument for curious ears ↗The room sings back ↗What a sound looks like ↗

1:1 · 0°

1:1 · 90°

02 / Physics and mathematics

Some ratios close the curve.

When the frequency ratio is rational, the two motions return together to their initial state. At 1:√2, there is no finite common period. Here you see only the first 32 seconds of that curve, calculated at screen precision.

Why no piano can be perfectly in tune ↗The 23-Cent Comma ↗The 7 frieze patterns: every repeating border is one of seven, stitch your own ↗Are all 17 in the Alhambra? Count them yourself ↗

1 : √2

03 / Physics and mathematics

Light can preserve the trace of a motion.

The photograph preserves a light trace based on Lissajous figures. In an oscilloscope, two signals can control the two axes of one point. An instrument displays measured signals; the model above displays the chosen equations.

How many molecules are in a glass of water? Brownian motion and Avogadro's number, measured by you ↗A Slinky Starts Falling from the Top ↗My rainbow: every observer sees different drops ↗

Red and green light traces photographed against black — Light trace, 2020. Photograph by Dietmar Rabich / Wikimedia Commons · CC BY-SA 4.0. Resized and converted to WebP.

04 / Physics and mathematics

From an equation to things you can try.

An equation can describe a sound, a fall or the odds in a game. The experiments below show the assumptions behind a calculation and where it can be compared with a measurement. The collection also covers geometry, exponential growth, cryptography and statistics.

How a train steers without a steering wheel ↗How many times can a sheet of paper be folded? The stack from 42 folds reaches the Moon, the paper would span the Milky Way ↗Three shuffles won’t hide a card ↗You pick first. I pick second. ↗How Marian Rejewski broke Enigma: a working machine and his mathematical attack ↗

Why does it move?How big is it?What are the odds?

Physics and mathematics · 170 projects

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170 projects

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Motion, forces and heat
Cluj under the lid: the winter nights when it is warmer on the mountain than in the city
On 34.5% of the winter nights measured by the Cluj weather balloon between 1957 and 2012, the air at 1,500 m above sea level was warmer than the air at ground level. Every night, on the real relief, up to 2025. In Romanian and English.
Light, space and time
Halley’s Comet: where it is now, and its whole 75-year orbit from 1986 to 2061
Halley’s Comet passed the far point of its orbit on 8 December 2023 and is heading back to the Sun, which it rounds on 28 July 2061. The page follows the whole orbit by scroll, 1986 to 2061, on NASA JPL positions: of 27,563 days, the comet spends 78 closer to the Sun than Earth is and 35 years farther out than Neptune. With a year of birth it shows where the comet was then and how old you will be when it returns.
Light, space and time
Falling into a black hole: what the sky looks like on the way in
A fall into a black hole seen through the faller’s own eyes. Each point of the picture is a ray of light followed through curved space with the equations of general relativity, over NASA’s map of 1.7 billion stars. At the horizon the black disc is 84° across and covers 13% of the sky; the rest is still stars. At Sagittarius A* the fall from the horizon to the centre takes 28 seconds.
Waves and sound
How a train steers without a steering wheel
A train wheel is shaped like a cone, and the shape does the steering. Push a wheelset sideways, watch the wave about ten metres long it draws, then test the idea with two cups.
Geometry and scale
How many times can a sheet of paper be folded? The stack from 42 folds reaches the Moon, the paper would span the Milky Way
An A4 sheet folds six times in one direction, the record is 12, and 42 folds would take the stack to the Moon but need a strip 107,052 light-years long. You fold the sheet yourself, then ask for more paper and watch the bill grow fold by fold, by Britney Gallivan's formula.
Light, space and time
The birthday sky: the Moon, planets and the Sun's constellation
What was in the sky on the day you were born? Pick a date and a place and get the sky chart: Moon phase, planets above the horizon, sunrise and sunset, plus the constellation the Sun was really in — not the magazine sign, because of precession. All computed in your browser.
Light, space and time
The solar system at 1:10 billion: Neptune would be 450 m from the Sun
If the Sun were 14 cm across, Earth would be a 1.3 mm bead 15 m away, Jupiter at 78 m, Neptune at 450 m. Pin the Sun on your street and walk to each planet, with Voyager 1 on the same map and a printable class sheet. No textbook picture fits to scale.
Motion, forces and heat
How fast are you moving? Earth's spin, orbit, galaxy and the CMB
You sit still, yet Earth carries you along: spin, orbit, galaxy and cosmic background. Pick a place and see all four speeds on a single ruler.
Motion, forces and heat
How long does it take to fall through the Earth?
Find your town, see where its tunnel comes out on the other side, and start the race of two fallers: one through the textbook uniform Earth, one through the real Earth. Which wins, and by how much?
Motion, forces and heat
Skip a stone across a lake. How many bounces can you make?
A game that follows the laws of physics: skip a stone across a drawn lake and count the bounces. What matters (tilt, spin, speed), what a Latin author wrote about the same game about 1,800 years ago, and the world record: 88 bounces.
Waves and sound
The Earth rang like a bell for weeks
After the earthquake of 26 December 2004, which with the tsunami it set off killed or left missing 227,898 people, the whole planet vibrated like a bell. Hold a button to hear a month of the real record played back 500,000 times faster while a globe takes the shape of each tone; the Earth's breath, 0.05 mm every 20½ minutes, was recorded in Romania too.
Waves and sound
The 52 Hz whale, ‘the loneliest in the world’, and the blue whales singing ever deeper since 1963
What US Navy hydrophones heard from 1989 to 2004, and what is not known about the 52 Hz whale. From 1963 to 2019 the song of northeast Pacific blue whales dropped by a third; type your birth year and hear a NOAA recording played at that year's note and at the 2019 note. In Romanian and English.
Motion, forces and heat
Big Ben’s clock is adjusted with old pennies: the Great Clock of Westminster, and what one coin does to its day
UK Parliament says one old penny on the Great Clock’s pendulum makes it gain 0.4 seconds a day. Slide the coin along the 4.4-metre rod to see where it speeds the clock, where it does nothing and where it slows it; then let the days run, hear the hour strike in a real recording and make a card of your tray.
Motion, forces and heat
How many molecules are in a glass of water? Brownian motion and Avogadro's number, measured by you
Catch real one-micron beads filmed in water under a microscope, one by one, and their tremble gives you the number of molecules in a mole, as in Jean Perrin's 1908 experiment. What Robert Brown actually saw, what Einstein predicted, the path without a tangent, your glass of water. In Romanian and English.
Motion, forces and heat
How does a hailstone get that big? Ride one through the storm
Pick the size of the hail you remember and see how fast it fell and how hard it hit. Then grow a stone in an updraft, cut it in half, and learn what is known — and what is not — about anti-hail rockets. In Romanian and English.
Waves and sound
The 1977 earthquake, over today's red-dot buildings
Follow the 1977 wave across a 3D map of Bucharest, see the damage recorded for each square kilometre and search today's seismic-risk list. The historic record describes map squares, not what happened to any one building.
Light, space and time
Drag the sky back 640 million years and watch the Moon change
The Moon moves away 38.3 mm a year, almost as fast as your fingernails grow. Drag the sky back through time and see the Sun and Moon at their size then, with a shorter day and different eclipses; every number is marked measured, counted in rock or calculated.
Physics of the body
Older Than Earth: which stars made you?
Nearly every atom in your body is older than the Earth: about 63 in 100 are primordial hydrogen, older than the stars. Follow one gold atom from the Big Bang to you, weigh your own stardust, and find where gold comes from. In Romanian and English.
Light, space and time
Where Light Dies
From the sunlit surface to 10,935 metres down: five ocean zones, the red light that dies first, the 2004 giant squid, the Titanic at 3,800 metres and the three crews that touched the bottom of the Mariana Trench — a scrolling descent, in Romanian and English.
Motion, forces and heat
Their last breath is in your next one
Breathe out and watch your breath travel around the Earth on the real winds. Then find out how many molecules from the breath of someone you have lost enter you with every breath. In Romanian and English.
Physics of the body
Bats aren't blind, but they hunt by ear. Find the moth by its echo
Hear a pipistrelle's call 10 times slower, so you can hear it at all, and find a moth in the dark by its echo. Then a whole attack, slowed down, the moth that hears the bat from 30 metres, and where the 1,000-mosquitoes-an-hour myth comes from. In Romanian and English.
Waves and sound
What a sound looks like
A brass plate computed from real physics, strewn with sand. Bow it or sing to it, and the sand runs onto the lines that stand still, as it did for Ernst Chladni in 1787. Then find eight of his figures. In Romanian and English.
Light, space and time
The last colour of a soap bubble
A soap bubble painted only with the physics of light: every colour comes from the thickness of the film. Watch it drain until it turns black, then set Newton's words from 1704 beside the colours computed today. In Romanian and English.
Motion, forces and heat
The church Gaudí hung from the ceiling
Gaudí designed the Colònia Güell church upside down, from string and sacks of shot. Hang the weights, turn the model over and walk into the crypt that gravity drew. In Romanian, English, Spanish and Catalan.
Light, space and time
It is raining through you right now
Your screen becomes a detector: see the cosmic-ray muons crossing it, about 17 a second through your body. Then climb 15 km to where one proton becomes a cascade, watch relativity on two clocks, the pyramid of Khufu x-rayed and the neutrinos that arrive through the Earth at night. And how to see them at home. In Romanian and English.
Geometry and scale
Are all 17 in the Alhambra? Count them yourself
Researchers found 11, 12, 13, 14 or all 17 ways to repeat a pattern in the Alhambra, by different rules. Choose whose examples you trust and which rules you accept, and count for yourself. In Romanian and English.
Motion, forces and heat
Can you weigh an element no one has ever seen?
In 1871 Mendeleev left gaps in the periodic table and described gallium, scandium and germanium in advance. Work out the element in the “?72” box from its neighbours, then see what Winkler measured in 1886, who was right about gallium, and how many elements were known in the year you were born. In Romanian and English.
Light, space and time
Measure the Earth with a pencil
At your local noon, a pencil's shadow shows how far you are from the Equator; two shadows in two towns give the size of the Earth, as for Eratosthenes. Your exact noon, a class mode and what the ancient sources say. In Romanian and English.
Geometry and scale
How many ancestors did you have in the year 1000?
The places in your family tree double every generation. By the year 1000 they need billions of people, in a Europe of about 36 million. Put your grandparents' towns on the map, follow your ancestors generation by generation and compare them with a classmate's. In Romanian and English.
Physics of the body
The middle of your eye is made of carbon from the air of the year you were born
Nuclear tests in the 1950s and 60s nearly doubled the carbon-14 in the air, and every human body kept the mark. Put your family's birth years on the curve and see which year each part of you is made of: lens, tendon, heart, blood. In Romanian and English.
Probability and rules
Three shuffles won’t hide a card
Shuffle a new deck three times, push one card into the middle and find it yourself from the threads the shuffles leave behind. Then see why mathematicians say “seven”. In Romanian and English.
Motion, forces and heat
The prime meridian: voted in 1884, moved 102.5 metres, and your own noon
Zero longitude at Greenwich as a scroll scene: your own true noon today, worked out for where you are, the 1884 vote, the 102.5 metres between the courtyard line and the zero in use today, crossed by the sun in 0.35 seconds, and the minute to step outside and look at your shadow.
Motion, forces and heat
Thousands of starlings, no leader: how they turn as one
Each starling keeps track of just six or seven neighbours, near or far. Play the falcon over a live flock of thousands, watch a turn sweep through at 20 to 40 metres a second, and find out where to see a murmuration.
Physics of the body
Most of your atoms are 13.8 billion years old: where each part of your body was made
Six in ten of your atoms are hydrogen from the Big Bang. Your oxygen came from exploding giant stars, much of your carbon from dying stars, half the calcium in your bones from exploding white dwarfs, your iodine from colliding neutron stars. Set your weight and watch your body come apart.
Motion, forces and heat
Jump into a hole through the Earth
A straight tunnel through the centre of the Earth and a fall of 38 minutes 11 seconds, computed from the PREM model: you get heavier on the way down, the trip splits into three equal thirds, and from Bucharest you come out in the South Pacific. With a real-time fall, antipode globes and straight tunnels between cities, in English and Romanian.
Geometry and scale
How Marian Rejewski broke Enigma: a working machine and his mathematical attack
An exact Enigma that decrypts a real German message from 7 July 1941, then Rejewski's attack run on your device: the doubled key, the loops the cables cannot change and the 105,456-row catalogue, built in seconds. Plus the codebreakers' passage through Romania in 1939.
Light, space and time
Why is the night sky dark? Olbers' paradox and the light that has not reached us yet
If the stars went on for ever, the sky would blaze like the Sun. A forest where every line of sight hits a tree, a sky filling with suns, three centuries of wrong answers, and the 13.8-billion-year-old light that covers the whole sky, invisibly.
Light, space and time
When the sun really reaches you: sunrise and sunset behind the mountains for any place in Romania
Almanac sunrise assumes a flat horizon. Calculated from the terrain for every day of the year: at Băile Herculane on 21 December the sun only clears the mountains at 10:54; 6.7 million people live where the terrain takes at least half an hour of sun on the shortest day.
Motion, forces and heat
Which mountains you can see from your town: a panorama computed from the terrain for anywhere in Romania
Type a town and see which peaks rise above its horizon and how far away they are. More than half of Romanians live where a peak over 2,000 m would be in view; from the Retezat you can see Bulgaria, from the Apuseni the Tatras.
Motion, forces and heat
Nine seconds between the flash and the thunder. How far away was it?
Divide the seconds by three for kilometres, and heard thunder means the storm can strike. With a map of your town.
Motion, forces and heat
The space station flies over your house. Here is when to look up
You can see it with the naked eye, like a very bright star. Pick your town for the next passes, to the minute.
Light, space and time
The northern lights have been seen from Romania. How many times since records began?
Three times in three years: November 2023, May 2024, January 2026. Since 1932, 23 storms have reached Kp 9.
Light, space and time
The Plough didn't look like this 100,000 years ago
100,000 years ago the Plough's bowl gaped almost twice as wide. Drag time across the sky, watch Polaris lose the pole, and meet the people who looked up then.
Physics of the body
All the DNA in you would reach the Sun and back. How many times?
About 21 times: 6.2 billion kilometres of DNA in 3 trillion nucleated cells. Guess first, then redo the sum with your own numbers and learn why the 600-trips myth no longer stands.
Motion, forces and heat
The cloud above you weighs as much as 80 elephants
An ordinary summer cloud gathers about 500 tonnes of water, as much as 80 bull elephants, and still does not fall. Weigh your own cloud, with your own weight on the scales, and learn what holds it up.
Light, space and time
The farthest thing people have ever made is a day away, even for light
Romanian is one of the 55 languages on Voyager 1's golden record. On 18 November 2026 the craft reaches one light-day from Earth, a moment with three different dates depending on how you measure it. The story, from the tour that was never made to the instruments going out.
Light, space and time
When will the sky go dark at noon over your town?
Pick the nearest town and see every solar eclipse it gets from 1900 to 2100: which were total, how much Sun was left each time, and when the next shadow comes.
Light, space and time
How old is sunlight: 8 minutes across space, 170,000 years inside the Sun
Light flies eight minutes to reach you, but its energy wandered inside the Sun for 170,000 years. A random-walk simulation, a race with a neutrino, and eight true-or-false sentences.
Motion, forces and heat
The water bear survived open space. A 37-degree day kills it
Dried out, the water bear spent ten days in the vacuum of space and woke after over 30 years frozen. Awake, it dies at 37 degrees. Measure yourself against it, to scale, and play with its limits.
Motion, forces and heat
What a raindrop looks like: sphere, bun, mid-air breakup
No raindrop looks like a teardrop: small it is a sphere, large a flattened bun falling at 31 km/h, and the giants break up in mid-air. Pick a diameter, see the shape and speed, then play eight true-or-false sentences.
Geometry and scale
Pizza Size Comparison — Which Pizza Is Worth More? Calculator
A 40 cm pizza is not 25% bigger than a 32 cm one. It is 56.25% more pizza. Unless the price grows by at least that much, the large one is the better deal.
Motion, forces and heat
What do HB, 2B, 4B and 2H mean on a pencil?
H is hard and pale, B is soft and black, and the number says how much. A 20-grade scale, from 9H to 9B, with HB in the middle.
Motion, forces and heat
Why Phone Batteries Die in the Cold
Phone batteries do not lose electrical charge in the freeze: the electrolyte thickens, internal resistance surges tenfold, and the processor cuts off power to prevent critical voltage collapse.
Light, space and time
The other side of the Moon: why it looks so different, and who has landed there
Turn a globe of the Moon and watch the dark seas almost disappear: they cover 30% of the near side and 2% of the far side. With a map of crust thickness, the South Pole–Aitken basin, the places where Chang’e 4 and Chang’e 6 landed, and what the first samples brought back from there say.
Motion, forces and heat
Your climate has moved — Marius Comper
Compare your Romanian locality’s summers with Europe in 1971–1990. An interactive ERA5 atlas of temperature and rainfall.
Physics of the body
The Clock Inside Your Inner Ear
Spin in a chair and stop dead: you feel a rotation that isn't there. Keep turning instead, and the sensation disappears entirely — an interactive physical model of the inner ear shows why, and how a pilot ends up in a graveyard spiral believing they're flying straight.
Motion, forces and heat
Where does the rain here go? — The path of rain
At Arad, the Mureș flows west: through the Tisza, then into the Danube and the Black Sea. Search for a river or pick a place to follow the water, then discover the land that feeds it.
Waves and sound
Inside a note — An instrument for curious ears
Take a sound apart. Shape its harmonics, see the waveform, and listen to the same pitch change character.
Motion, forces and heat
The North That Moves
A compass for the wandering north magnetic pole: 36 kilometres in one year, a NOAA/BGS model, and two norths that separate over time.
Light, space and time
We Never See the Planets
A planet becomes visible through the light it removes. Move a planet across a star and see the signal, then choose a real world from NASA's archive.
Motion, forces and heat
Pocket gravity
Hold and drag the sky to bend 1,800 orbits. Try to tear the ring apart — then let gravity gather it again.
Light, space and time
How Small Is the Present?
The only “now” you can be sure of is the point where you stand. At any distance, the present is a window no signal can close, and one step moves it.
Probability and rules
You pick first. I pick second.
Choose one of three dice and play against the house. All average 5, yet each beats another more often. Open the table and check every outcome.
Probability and rules
Would you open the shortcut?
Open a road in an imaginary town and see why 65 minutes can become 80. Then change the traffic until the shortcut starts to help.
Probability and rules
No Dice: Can You Actually Be Unpredictable?
Press 0 or 1 across 20 rounds. An 8-state automaton tries to guess your every choice before you press.
Physics of the body
The Falling Ruler: Can you catch it in mid-air?
Five drops test how fast the brain converts visual motion into mechanical grip. Each catch leaves a stamped mark on the ruler's body.
Motion, forces and heat
Can You Find the Center of Gravity?
Five asymmetrical silhouettes test human intuition against static rotational moments. Touch the plate to see if it balances or topples.
Geometry and scale
Where Does the Beam Emerge?
Five rounds test subjective vision against Euclidean geometry. Fire a laser through an opaque wall and measure the V1 angular distortion.
Geometry and scale
Can you eyeball a perfect square?
The width is fixed at 200 mm. Raise the top edge until the rectangle looks like a perfect square. On each round, the master caliper gauge drops over the slab and measures your error.
Motion, forces and heat
Through the Tunnel: Can You Catch the Exit?
Five rounds test how the brain projects the velocity of an invisible mark. The point freezes instantly on trigger, revealing the signed error in milliseconds.
Geometry and scale
Same Tile or Mirror?
Eight pairs of blue tiles, four matching and four mirrored, in the same order for everyone. Instant verdicts, final score at the end.
Geometry and scale
Can You Find the Center of the Circle?
Five geometric shapes wait on the drafting board. Tap where you think the exact center is, and the compass needle measures your error in millimetres.
Physics of the body
Sixty-Six Times: Oxygen Held by Haemoglobin
Haemoglobin's binding capacity is about 66 times the dissolved fraction at 100 mmHg. Without haemoglobin, about 82 L/min would be only the theoretical minimum scale of flow required.
Geometry and scale
Can you set the angle to exactly 90 degrees?
Rotate the blade until you believe it forms a perfect right angle. Then drop the steel square and measure your error in tenths of a degree.
Waves and sound
The Speed of Sound
From Yakutsk to Bangkok, sound gains 6.83% in speed — nearly a full second over every 5 kilometres.
Geometry and scale
No Spirit Level: Can You Level a Beam by Eye?
Level the beam and release the ball. Gravity measures your eyes' angular tilt.
Physics of the body
Ninety Millimetres of Mercury: The Calf's Second Heart and the Pressure Drop in the Ankle
When you stand motionless, the column of blood raises ankle pressure to 90 millimetres of mercury. Six to seven steps bring it down towards approximately 25 millimetres, while sustained walking maintains a 20–25 millimetre plateau.
Motion, forces and heat
A Slinky Starts Falling from the Top
The top falls, the bottom stays almost stationary for about 0.27 seconds, and the centre of mass descends by an ideal 35.8 centimetres.
Motion, forces and heat
Why Buttered Toast Always Lands Butter-Side Down
180° at 0.75 metres, ordinary table height; it would take almost 3 metres for 360° and a butter-up landing.
Geometry and scale
How one square metre becomes A4
A0 has a nominal area of 1 m², while its published 841 × 1,189 mm dimensions leave a gap of 51 square millimetres. Four halvings yield A4, and the 1:√2 ratio preserves the shape.
Physics of the body
Twenty Minutes for a Bubble: The Biophysics of Knuckle Cracking and the Cavitation Refractory Period
Under >60 N tensile force, synovial pressure falls to −2.5 bar and the cavity appears in <310 ms. MRI supports cavity formation, while the 2018 model leaves a role for partial collapse open; the ~20-minute clock is illustrative.
Physics of the body
Your Ear Has Its Own Amplifier
The quantitative biophysics of the active cochlear amplifier: how 12,000 outer hair cells leverage a 150 mV transmembrane gradient to oscillate nanomechanically at over 20,000 Hz, generating otoacoustic emissions and the Tartini phantom tone (2f1 - f2).
Physics of the body
The Body Stands Like an Inverted Pendulum
In quiet standing, the ankle keeps correcting an unstable pendulum. In a no-correction model, a 0.5° sway grows to 5° in 0.72 seconds at the default height of 1.75 m.
Physics of the body
One Volt per Centimetre: The Skin's Epithelial Battery and the Electric Field That Heals Wounds
Skin maintains a 20–50 mV potential; a wound collapses local resistance and creates a 100–200 V/m field that mechanically steers keratinocytes to the cut long before chemical gradients can diffuse.
Physics of the body
Fifty Grams in the Skull
Submerged in 140 millilitres of fluid, the brain sheds 97% of its effective weight through buoyant force, while deep sleep unleashes a hydraulic tide that purges cellular waste.
Physics of the body
Tens of Picoamperes in the Dark
In darkness, rod ion channels remain open; a 20 pA illustrative model shows why light can reduce energy consumption by more than 75% in mammalian rods.
Physics of the body
Walking is controlled falling
In walking, the body passes over the stance foot like an inverted pendulum and recovers about 65% of external mechanical energy. Measure your walk and see where its Froude number lands.
Physics of the body
Pupil squared
The pupil can widen from 2 to 8 millimetres: fourfold in diameter, sixteenfold in opening area. The geometry is simple; the retina adapts separately.
Physics of the body
One Kilogram at Arm's Length
At the same mass, distance from the elbow can change torque tenfold. Play with mass, distance, and angle, then see what static force would balance the object at the biceps.
Physics of the body
Seven Milliseconds Behind the Head: The Biophysics of the Vestibulo-Ocular Reflex and Why Your Eyes Beat Any Gimbal
While the cortical visual system needs 150 milliseconds to process motion, the inner ear vestibulo-ocular reflex rotates the eyes in the opposite direction in just 7 milliseconds through the fastest neural arc in the human body.
Physics of the body
Why You Don't Deafen Yourself Talking
The quantitative biophysics of the stapedius reflex: anticipatory activity observed during vocalisation and frequency-dependent filtering in the middle ear. The simulator uses 20 decibels as an explicit model example.
Physics of the body
Thirteen Nanometres: The Biophysics of Fingerprints and the Nanoscale Limit of Touch
A static touch on the skin resolves two separate pins only when spaced at least 1.6 millimetres apart. Yet the moment a fingertip slides laterally, epidermal friction ridges convert microscopic surface relief into a 250 Hz shear wave, allowing the detection of surface grooves just 13 nanometres high.
Physics of the body
Five Hundred and Eighty Calories per Gram: The Extreme Biophysics of Sweat and the Human Heat Engine
Why humans are Earth's greatest endurance coolers in the heat: the biophysics of water phase transition, 1,343-watt cooling power, and the dripping sweat paradox.
Physics of the body
Two Millinewtons per Metre: The Surface Tension of Lungs and the 480-Million-Bubble Paradox
If human lungs were lined with pure water, all 480 million alveoli would collapse immediately. A 2.5-gram lipid film reduces surface tension to 2 mN/m at expiration.
Physics of the body
One and a Half Watts: The Hydraulic Mechanics of the Human Heart
A pump displacing 7.6 tonnes of fluid daily operates at a mechanical output of just 1.33 watts and a total metabolic power of 7.4 watts.
Physics of the body
Nine Degrees Under Your Fingertip: Why Metal Feels Colder Than Wood
From the same 20 °C starting point, the skin interface reaches 20.6 °C on aluminium and 29.2 °C on wood; the idealised 8.65 °C gap comes from an effusivity ratio of almost 67 to 1.
Physics of the body
Ten Oscillations a Second: The Hand's Physiological Tremor
In a human centrifuge experiment, resonant mechanics predicted 99% of postural-tremor peak frequency. The phone used for measurement adds inertia and changes the observed spectrum.
Physics of the body
Seven Hundred Newtons on the Molar: The Biomechanics of the Bite and Enamel's 100-Atmosphere Strength
Although the human jaw operates as a Class III lever with a mechanical disadvantage at the incisors (150–250 N), back at the second molar bite force surges to 700–900 N (70–90 kgf). Concentrated onto just a few square millimetres, contact stress exceeds 150–300 MPa (over 1,500 atmospheres — higher than the Mariana Trench), resisted without fracture by enamel's decussating prism architecture.
Physics of the body
Ten Microseconds Between the Ears: How the Brain Computes Sound Location
The human brainstem detects sound arrival disparities down to 10 microseconds (3.4 mm in air) using axonal delay lines and coincidence detector neurons in the medial superior olive.
Physics of the body
Sixty kilograms a day? How much ATP your body really makes
Your body holds only 50–100 grams of ATP, yet remakes 36–47 kg of it a day at 2,000 kcal. Turn the machine that makes it with your finger, and find out where the famous 21,000 rpm comes from.
Physics of the body
Half a Millimetre per Second: Why Blood Nearly Stops in the Capillaries
At a resting cardiac output of 5.0 L/min, Q = A × v gives about 185 mm/s in the aorta and 0.19–0.24 mm/s across the capillary bed. Systemic oxygen exchange depends on tissue, metabolism, diffusion distance and flow distribution.
Physics of the body
Forty-Three Dioptres: Why We See Completely Blurred Underwater and Where the Eye's True Lens Really Is
The eye's true lens is the cornea's curvature in air. That is why a dive mask restores sharp vision with completely flat glass.
Physics of the body
Nine Photons in the Dark: The Quantum Limit of Human Vision
Hecht estimated the visual threshold at 5–14 absorbed photons; 9 is representative. Modern intact-rod experiments estimate about 2,000 cGMP molecules hydrolyzed per R*, while the roughly 1 pA measurement came from toad rods.
Physics of the body
One Million to One: The Stomach's Impossible Acid Gradient
At the parietal-cell apical membrane, the H⁺/K⁺-ATPase produces one of the steepest proton gradients known in mammalian tissue: from pH 7.40 in the cytosol to pH 1.40 in the secretory canaliculus, or one million to one. The mucus-bicarbonate barrier is 200 µm thick.
Physics of the body
Eight Nanometres per Step: Kinesin's Invisible March
To haul cargo across one metre of axon, delivery accumulates the kinematic equivalent of 125 million 8-nm steps through coordinating kinesin relays. While free diffusion would exceed 150,000 years, in vivo fast axonal transport completes delivery in 2.5–5 days.
Physics of the body
Forty Millimetres on the Back, Two on the Fingertip
On the index fingertip we resolve two points 1.6 millimetres apart, but on the back they must be spread 42 millimetres apart to avoid fusing. The back compresses space by 26 times due to mechanoreceptor density and cortical magnification.
Physics of the body
Ten Picometres in the Eardrum
If sound struck inner ear fluid directly, 99.89% of energy would bounce off like a wall. To bridge the impedance mismatch, evolution built a mechanical three-bone lever that amplifies pressure over 22-fold — enabling the eardrum to detect vibrations of just 10 picometres.
Physics of the body
Ten Million Volts per Metre
A human cell maintains a resting potential of just 70 millivolts. Yet because this voltage drops across a lipid bilayer only 7 nanometres thick, the transverse electric field reaches 10,000,000 V/m — over three times the dielectric breakdown threshold of a lightning strike in air.
Waves and sound
Thirty-Nine Bits per Second
The 17-language mean is 39.15 bits per second, but languages differ, from 33.8 to 45.9. The rate varies less than syllable speed or information per syllable.
Motion, forces and heat
The Clay That Never Cools
In 1900, the Tube was 14°C. After 125 years of braking, 500 GWh of annual heat have saturated the clay mantle, turning the earth into a 30°C radiator.
Light, space and time
The Heat per Kilogram
The Sun sheds 0.19 mW/kg; powering a 10 W LED bulb requires 52 tonnes of solar matter.
Physics of the body
Thermodynamics of the Tongue and Blood: Butter and Margarine
Butter melts at 34°C on the tongue, while industrial margarine melts at 44°C like wax: 150 years of chemistry, gastronomy, and clinical trials.
Motion, forces and heat
34 Hours and 17 Minutes: The Floor Under the Pendulum
If you let a pendulum swing freely in Bucharest, its plane completes a full rotation in 34 hours and 17 minutes.
Motion, forces and heat
Five Hundred Tonnes in a Clear Sky
A standard 1 km³ cumulus cloud holds 500 tonnes of liquid water. Dispersal into 119 quadrillion droplets caps settling speed at 1.2 cm/s, allowing rising thermal currents to support the entire mass.
Light, space and time
The Horizon That Lies
150 km to the Bucegi Mountains, only 43 km of curvature reserve — the air is the culprit.
Waves and sound
Two Notes in the Mouth
Vocal folds produce only a raw drone: what we hear as speech is a chord of two frequencies. In “i”, the gap spans over 3 octaves; from “u” to “i”, the second frequency triples; and Romanian anchors two central vowels along the midline.
Waves and sound
The Deep Ocean Highway
At one thousand metres depth, the ocean forms a natural waveguide carrying sound across global basins. In 1991, a tone emitted near Antarctica was recorded in Bermuda, 18,200 kilometres away.
Waves and sound
Fifty Beats per Second
The power socket dictates time for millions of microwave and radio clocks. In 2018, a 113 GWh shortfall stole 346 seconds (5m 46s) from 400 million people without causing a single blackout.
Geometry and scale
The Tree That Closes
By generation 30, a family tree requires 1,073,741,824 ancestors, while Earth held only 320 million people in 1100 AD. Travel through 40 generations on the ancestry spindle.
Motion, forces and heat
Smell does not fit in one word
Choose up to three words from an olfactory catalogue and see how many molecules carry them together.
Waves and sound
The 23-Cent Comma
Why every piano lies to your ear.
Motion, forces and heat
The Dandelion and the Ring in the Air
Turn a solid disk into a dandelion pappus and watch the gaps between its filaments maintain a separated vortex ring. At its measured porosity, the pappus produces more than four times as much drag per unit projected area as the solid reference disk.
Motion, forces and heat
Nine Drops in a Century
At room temperature it shatters like glass under a hammer. Under decadal gravity, it flows as a liquid 230 billion times more viscous than water. In 99 years, only nine drops have fallen from the University of Queensland funnel.
Motion, forces and heat
The charged drop sharpened before impact
A saltwater drop slid over an insulator, formed a cone near copper, and left local defects after 3,000 charged impacts. The neutral control stayed smooth.
Physics of the body
Seven Metres per Second: Why the Pulse at Your Wrist Is Not the Blood Flowing
When you take your pulse, you feel an elastic shockwave travelling 35 times faster along the arterial wall than the blood itself.
Physics of the body
Eleven Joules at the Heel
An in-vivo study measured 11.3 J of propulsive recoil at 3.5 m/s; the historical 35 J figure is 3.1 times larger, but it does not describe the same measurement.
Motion, forces and heat
The Cat Without a Push
A cat can turn its paws down after changing shape in mid-air. Angular-momentum conservation still holds, and the two-segment model shows where the net rotation comes from.
Waves and sound
Why spaghetti snaps into three
Dry spaghetti usually breaks into at least three pieces under simple bending. Twist can quench the cascade because the torsional wave unloads energy faster.
Waves and sound
A Wet Mouse Shakes 30 Times a Second
A Labrador shakes at about 4.5 Hz and a brown bear at 4 Hz. The stroboscopic plate links that rhythm to the acceleration needed to release water from fur.
Geometry and scale
Can you cut the ribbon exactly in half?
Touch the spot where you would cut. The ribbon straightens and shows the difference at once.
Geometry and scale
The Paradox of Romania's Coastline
Drag the ruler and watch the compass measure Romania's real coastline; the length recalculates live.
Motion, forces and heat
Why Sink Water Ignores the Hemispheres
A sink drains in thirty seconds. Earth's rotation needs nearly three hours of stillness to dominate the water's motion.
Probability and rules
The Dunning-Kruger chart, explained — how a famous psychology chart draws itself
The chart behind the Dunning-Kruger effect can be reproduced from pure random numbers. An interactive simulator shows the mechanism, and a 2026 paper says the truth runs the other way.
Waves and sound
Why no piano can be perfectly in tune
Twelve pure fifths miss the C seven octaves up by 23.46 cents. Tune a fifth by ear, climb twelve like it, and hear where Pythagorean, meantone and equal tuning hid the difference.
Probability and rules
The Micromort Hall of Fame
A leaderboard of documented survivors, ranked by incident-conditioned paper micromorts.
Geometry and scale
Why the Copier Always Says 141%
The enlarge button on any photocopier, from A4 to A3, reads 141%. That number is the square root of two, and it is why paper sizes A0 through A10 can keep halving forever without ever changing shape. An interactive explorer of ISO 216 geometry.
Physics of the body
Eighty Milliseconds: Why Consciousness Lives in the Past
To synchronize instantaneous light with sluggish sound and asynchronous nerve impulses, the brain delays conscious perception by 80 milliseconds. An interactive exploration of temporal biophysics.
Probability and rules
Romania's direct public purchases and Benford's law
Nearly 600,000 direct purchases each quarter follow Benford's law, while the legal cap remains clear in the amounts. SEAP data from 2022–2024 shows what the method can tell us, plus a tool for checking your own numbers.
Light, space and time
Sixteen Minutes
The sun reaches its true noon up to sixteen minutes before or after twelve o'clock on your clock. Only four days a year do the two match exactly.
Light, space and time
A Hundred Times Rarer
The Moon has 5,185 confirmed impact craters wider than 20 kilometres. Earth, despite taking more hits per square kilometre, has only 52. An explorer with 70 real craters, from 200 years old to 2.229 billion years old.
Waves and sound
The Ninth Bell Needs Eight Days Without a Pause
Eight tower bells can ring in 40,320 different orders, with no repeats allowed. One team has ever rung the complete list without a break, in 1963, over almost eighteen hours. One more bell would take over eight straight days.
Waves and sound
How long in the microwave at a different wattage? 600–1100W converter
Enter the label power and time plus your oven power and get the converted time, including why −20% becomes +25%.
Motion, forces and heat
The bridge that taught a country engineering: Cernavodă 1895
Fetești–Cernavodă 1890–95: Saligny, 4,087.95 metres, the longest bridge complex in Europe. Caissons, Gerber consoles, the silver rivet and the 15-locomotive test.
Motion, forces and heat
North Is Not a Place
An interactive explainer about the gap between north on a map and north in a compass needle.
Light, space and time
When the Sun Disappears: An eclipse atlas
A multidisciplinary atlas of what a total solar eclipse reveals about nature, minds, societies, institutions and knowledge.
Light, space and time
The 1961 eclipse in Bucharest: two minutes under cloud
The eclipse was total in Bucharest on 15 February 1961, but cloud hid totality from the ground. Newspapers, scientific reports and Romanian archives preserve observations made on the ground and from the aircraft.
Light, space and time
My rainbow: every observer sees different drops
A rainbow appears when sunlight, water drops, and your eyes line up in a precise geometry. Move the observer and see which drops send light towards you.
Waves and sound
The Same Year. Two Measures.
17,373 earthquakes in the USGS snapshot. The same year looks crowded by count and concentrated by energy.
Light, space and time
Urban shadow
An interactive view of daylight: choose a city, move the hour, and watch the sun, building, and shadow reshape the same day.
Light, space and time
The light that left
Choose a year and see the stars whose light set out for Earth then. 8,714 stars from HYG 4.1 form an interactive map of the sky.
Waves and sound
Twenty-Seven Seconds, Then Silence
27 leap seconds kept the world's clocks aligned with Earth between 1972 and 2016. None since: the planet has entered a decade spinning faster, on average, than any other on direct record, and 5 July 2024 is the shortest day ever measured. In October 2026, in Versailles, delegates will vote on Draft Resolution C, which would make UTC continuous from 20 May 2027 before a negative leap second becomes necessary.
Waves and sound
Before the S-wave
The P–S window matters when the next action was decided beforehand.
Motion, forces and heat
A Tiny Star, Built by Hand
An interactive guide to fusion energy with a kids mode, field atlas, plant cutaway, plasma-control game, reactor tradeoff game, fuels, materials and caveats.
Motion, forces and heat
Seizing Iran's Uranium: The Physics of an Impossible Operation
A visual analysis of the impossible operation of locating, suppressing, accessing and evacuating enriched uranium from Iran.
Probability and rules
Same Ballots, Three Winners
The same 9 ballots. Three real rules. Three winners.
Waves and sound
The room sings back
Walls give a room notes of its own. Where you listen changes how loud each mode sounds.
Probability and rules
Loto 6/49: the draws are close to random, the numbers people play are not
All 2,376 official draws up to 1 October 2026, put to the test: the balls, overdue numbers and the winning entries.
Physics of the body
The faintest sound you can hear moves your eardrum less than an atom
Go down into your own body, order of magnitude after order of magnitude: from a candle seen kilometres away, through two needles on the skin, a red cell and a 10-nanometre turbine, down to an atom. At every step, a measurement from 43 other pages.
Motion, forces and heat
How does a hummingbird hover?
Pause one wingbeat to see how a hummingbird holds its position above a flower. Real photographs, an interactive explanation and the research behind it.
Motion, forces and heat
Romania's time: what time was it in Iași at Bucharest noon
When Bucharest read noon, Iași already read 12:06 and Craiova only 11:51. Pick a city, slide the year across 1891 and watch four local noons become a single railway time.
Light, space and time
Travelling near the speed of light: fly to Andromeda in one lifetime
Accelerate at 1 g, the pull you feel standing on Earth, and in 28 years and 7 months aboard you reach the Andromeda galaxy. Fly there through a sky of 85,611 catalogued stars and watch two clocks for home: the one that runs in Earth’s frame, and the latest light from Earth that has caught up with you.
Light, space and time
What was the Moon on the night you were born? Find your birth Moon
On the night you arrived, the Moon had a shape. Put in your birthday and the sky turns back to it, then find out when it returns.
Probability and rules
The will to gamble: games of chance through history, from knucklebones to slot machines
You get 100 coins and carry them through history: knucklebones, the gambling hall of the Arthaśāstra, the ball machine at Constantinople's Hippodrome, the Chevalier de Méré's bets, Dostoevsky's roulette and a modern slot built from its technical sheet. Plus the brain, young men, Romania and today's 2.3 billion gamblers.
Geometry and scale
The 7 frieze patterns: every repeating border is one of seven, stitch your own
Stitch a motif in cross-stitch and see it repeated every way a border can repeat. By shape, there are seven, and it has been proved there is no eighth. Try to find one. In Romanian and English.
Light, space and time
After sunset, the sky is blue for a different reason
A sky computed from the physics of air, for your place and evening. Scroll and the Sun sinks to the stars; take out the ozone and the blue hour turns yellow.
Light, space and time
The evenings the sun sits on Ceaușescu's palace
Seen from Alba Iulia Square, the setting sun comes down exactly onto the top of Bucharest's Palace of the Parliament on 29 March and 13 September. Look up your street and see the evenings the sun sets or rises at its end, in a view drawn from the city's real buildings.
Waves and sound
Rhythmic applause: why an audience claps in unison, and why the beat falls apart
A theatre audience claps in time with no conductor. Clap along with a simulated hall of 300 people and find out why the beat appears only when people clap more slowly, and why it breaks.
Waves and sound
Krakatoa 1883 and Tonga 2022: the air wave, town by town
A globe of the Krakatoa (1883) and Hunga Tonga (2022) air waves around the Earth, with the hour each passed any town, checked against barograph records.
Motion, forces and heat
Who measured the universe?
Henrietta Leavitt found the relation between a Cepheid’s period and brightness, but did not measure distances. Plot the 25 stars in Table I and follow how Hertzsprung and Hubble turned the relation into a cosmic distance scale.
Motion, forces and heat
Sibiu’s three-stage rocket — Conrad Haas’s notebook
Explore Conrad Haas’s drawing and a 3D cutaway, then decide which casings to leave behind in an experiment about rocket mass.

About the collection

The collection includes every project classified as physics and related work on geometry, probability, cryptography and biophysics. Categories group reading questions. The opening figure computes two ideal harmonic oscillations with equal amplitudes and frequencies a/8 and b/8 Hz; it does not show measurements of a physical system.

Reviewed 2026-10-15 · Collection as text

Sources

University of New South Wales — Lissajous figures
Two perpendicular oscillations; frequency ratio and phase difference.
OpenStax — University Physics, 15.1: Simple harmonic motion
Dietmar Rabich — Lissajous-Figur, 2020
CC BY-SA 4.0 photograph, resized and converted to WebP.