Collection
From sequences to loans: arithmetic and geometric growth, savings plans, annuities, compounding within the year and perpetuities.
Apps
An arithmetic sequence as a staircase of base a and blocks d: recursively step by step (asking down to step 1, then hopping up, one moon per hop) vs. explicitly aₙ = a + (n−1)·d. Up to step n there are n − 1 hops; a ghost block refutes "a + n·d".
FinanceTry it
Sequence versus series as a staircase and a tower: the steps aₖ = a + (k−1)d stand at the bottom, above them steps 1 … n fly up and stack into the tower sₙ = a₁ + … + aₙ. The tower tops form a sequence again (partial sums), base n·a and increase d·(n−1)n/2 can be coloured, plus the little Gauss and a geometric mode. Refutes "sₙ is the value in year n".
FinanceTry it
Arithmetic and geometric sequences as bar pairs in three lecture scenarios: output with +d or +p %, straight-line vs. declining-balance depreciation, simple vs. compound interest. A difference bracket and a quotient bracket at the selected year, two type-test cards whose flat track reveals the type, slide exercises with solutions and a quiz. Refutes "declining-balance depreciation eventually reaches zero".
FinanceTry it
Sₙ = 1 + q + … + qⁿ⁻¹ as bars: times q, one slot along, subtract – the middle cancels, only qⁿ and 1 remain. Six scrubbable steps to Sₙ = (qⁿ − 1)/(q − 1), the case q = 1, q < 1 and a savings-plan link.
FinanceTry it
A savings plan with a constant instalment: each instalment as a tower on its payment date, the interest staircase and little Gauss n(n+1)/2 for simple interest, the geometric series Kₙ = E·q·(qⁿ−1)/(q−1) with compounding, in advance and in arrears, balance, present value and building savings.
FinanceTry it
Same payment, shifting split: interest and principal per year, balance Rₙ = S qⁿ − A(qⁿ − 1)/(q − 1), interest line S(q − 1), annuity and term with formulas, in arrears and in advance, linear repayment for comparison.
FinanceTry it
What happens when the bank credits interest several times a year? The balance grows as a staircase of interest pieces, each slightly larger than the last. An interest stack compares m = 1 with m periods and shows the small extra. The second card plots the effective annual rate p_eff = 100(1 + p/(m·100))^m − 100 against m: it rises but levels off at the continuous-compounding limit 100(e^{p/100} − 1). Slide example (€1000, 6 %, 10 years) and Bernoulli's limit e. Refutes "monthly gives 12 times as much" and "p_eff grows without bound".
FinanceTry it
Monthly payments with annual interest credit: interest strips as a Gauss staircase, equivalent annual deposit and remaining balance for withdrawals over n years.
FinanceTry it
How long does capital last? Balance, interest and withdrawal per period, the perpetuity a = K(q − 1) and the term N = ln(A/(A − S(q − 1)))/ln q with its vertical asymptote, last withdrawal, yearly or monthly, in advance and in arrears.
FinanceTry it
The sum 1 + 2 + … + n as a staircase of cubes: a copy turned by 180° completes it to an n × (n+1) rectangle with equally high columns. With Gauss’s pairs up to 100, upper limit n − 1 (slide 8) and the arithmetic series sₙ = n/2·(a₁ + aₙ) (slide 9).
Visual proofsTry it
Annuity, linear and bullet loans for the same debt: interest and principal per year, balance as a staircase, interest = p/100 · area beneath it, total paid and present value (S for all at i = p), comparison rate i, slide 10 with the arithmetic interest sequence.
FinanceTry itCollections
Planning and steering projects: the iron triangle, stakeholders, network diagrams, earned value, schedule risk, team size, Kanban and waterfall against Scrum.
8 appsOpen collection
Reading the traces: burial mounds in section, radiocarbon dating, settlements in the landscape and the tomb of Tutankhamun.
5 appsOpen collection
Why robot arms are heavy, how six axes guide a hand and how control holds the load.
4 appsOpen collection
Tables, keys, joins, groups and subqueries you can touch: how a database really reads.
7 appsOpen collection
Generative AI in strong images: what it can do, how it writes, why it convinces, how to use it well and where to take care.
7 appsOpen collection
Engine, brakes, high voltage, CAN bus and chassis: technology and diagnostics of the modern vehicle.
9 appsOpen collection
Heat in the city centre: heat islands, shade, trees and unsealing, using the old town of Reutlingen as an example.
5 appsOpen collection
Reading the small print, spotting subscription traps, placing risk figures and making texts understandable.
4 appsOpen collection
From equation to curve: initial values, linear equations, substitution and the worlds in which they apply.
7 appsOpen collection
Mean, median, mode, box plot and levels of measurement: descriptive statistics to try out.
9 appsOpen collection
From coordinates to the inverse: vectors, dot and cross products, linear equations and matrices in pictures.
12 appsOpen collection
Production principles, waste, one-piece flow, value streams, bills of materials and routing: how a factory is organised.
6 appsOpen collection
What the CRA requires of manufacturers: checking whether it applies, meeting reporting deadlines, keeping software bills of materials.
5 appsOpen collection
Reducing, common denominators, multiplying, dividing and mixed numbers: fractions step by step.
7 appsOpen collection
Proofs of special beauty to touch: Zagier's windmills, the museum guards and Buffon's needle.
3 appsOpen collection
How oscillations break down: coefficients, symmetry, phasor chains, the Gibbs phenomenon and the plucked string.
7 appsOpen collection
What happens inside the machine: objects, methods, operators, slicing and sorting in Python, visible step by step.
9 appsOpen collection
From the Patent Motor Car to the Z3: famous machines and experiments cut open in 3D.
11 appsOpen collection
Keyboard, intervals, scales, chords, the circle of fifths and groove: music theory you hear and play.
9 appsOpen collection
How sound is made and shaped: synthesizers and samplers, envelopes and overtones, waveforms and timbre, voice and orchestra, room acoustics and sound scenography — all audible in your browser.
16 appsOpen collection
Staging space, sight, light, sound and paths: visitor flows, showcase lighting, room acoustics, sound islands, projection mapping and the pavilions of world expos to try out.
15 appsOpen collection
Mathematical questions open for decades, for which an AI model proposed solutions in 2026, as interactive apps: understand the problem, experience the result.
32 appsOpen collection
From neurons and gradients to transformers, RLHF and agents: machine learning you can touch.
44 appsOpen collection
DNA, replication, transcription, translation and cell division as explorable 3D models.
24 appsOpen collection
Perspective, ornament, structure and space: how art and architecture work with mathematics.
21 appsOpen collection
Hyperloop, autonomous vehicles, warehouses and conveyors: logistics as interactive simulation.
17 appsOpen collection
Heart, eye, voice, skeleton and nerves: the human body in 3D, layer by layer.
10 appsOpen collection
Monty Hall, Simpson, Berkson and base rates: where intuition fails us with numbers.
14 appsOpen collection
Planets, stars, black holes and space probes: the cosmos to explore.
10 appsOpen collection
Light switches for nerve cells, a telescope made of ice, mirror-image chemistry and interest rates: the 2026 Nobel Prizes to try out.
8 appsOpen collection
Planted participants, smoke in the room, one dollar for a lie and experimenters who are themselves the subjects: famous social psychology experiments to try yourself.
5 appsOpen collection
Relations, classes, orders, bijections, different infinities and topology: mathematics as the science of structure, hands-on.
11 appsOpen collection
Riemann, P vs NP, Poincaré and other great questions of mathematics, made tangible.
16 appsOpen collection
Counting, arithmetic and shapes: maths for beginners, playful and clear.
6 appsOpen collectionWant to use these apps in your courses? Let’s find out what works for you.
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