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Euclid's Algorithm — Find the Biggest Shared Measure with Paper Strips
A hands-on maths project: cut two paper strips of different lengths and repeatedly lay the shorter along the longer to find their greatest common measure -- Euclid's 2,300-year-old algorithm, done with your hands. A Python cell checks your answer, and a compendium shows why this simple recipe still runs inside computers.
Anfänger
30 minutes
Anweisungen
1
1
The greatest common measure
The greatest common measure
The greatest common divisor of two numbers is the largest number that divides both. Around 300 BC Euclid found a beautiful way to get it without factoring. You will do it as he did -- as lengths.
2
2
Cut two strips
Cut two strips
Cut two strips of card, one 48 cm and one 18 cm (or any two lengths). The greatest common divisor is the longest ruler-length that measures BOTH strips a whole number of times.
Materialien für diesen Schritt:
Cardstock Assorted Pack (50 sheets)1 StückBenötigte Werkzeuge:
Sharp Scissors
Steel Ruler (30cm)3
3
Lay the short along the long
Lay the short along the long
Lay the 18 cm strip along the 48 cm strip as many whole times as it fits (twice, reaching 36), and mark the leftover (12 cm). Now repeat with the two smaller lengths: fit 12 into 18 once, leftover 6. Fit 6 into 12 exactly twice, no leftover. The last non-zero leftover, 6 cm, is the answer -- it measures both original strips exactly.
4
4
Check it
Check it
Loading Jupyter Notebook...
Benötigte Werkzeuge:
Desktop Computer
Calculator5
5
Compendium: the oldest algorithm still running
Compendium: the oldest algorithm still running
What your strips reveal. (1) Each step replaces the longer length with the leftover, and it works because any length dividing both strips also divides the leftover. (2) It is astonishingly fast -- its very worst case is consecutive Fibonacci numbers, and even then it takes only a handful of steps for huge numbers. (3) The same idea reduces fractions to lowest terms (divide top and bottom by their GCD). (4) It is one of the oldest algorithms still in daily use, running billions of times a day inside the RSA encryption that protects online banking and messaging.
Materialien
1- Platzhalter
Benötigte Werkzeuge
4- Platzhalter
- Platzhalter
- Platzhalter
- Platzhalter
You can swap these in
Can't get one of the materials? Swap it for an equivalent — these work just as well.
- Instead of Paper, try:
Mulberry Bark Paper
Yoshino Filtering Paper (Fine Grade)
Tissue Paper (acid-free)
Acid-free Tissue Paper
Cotton Wrapping Paper
Litmus Paper - Instead of Desktop Computer, try:
Path Planning Computer - Instead of Graphite Pencil Set, try:
Notebook and Pencil
Carpenter's Pencil Set (24-Pack) - Instead of Sharp Scissors, try:
Small Sharp Scissors - Instead of Calculator, try:
Carbon Footprint Calculator Kit - Instead of Steel Ruler (30cm), try:
Measuring Ruler
Recommended for this build
Products makers often use with builds like this one.
Weft Yarn (Cotton)Frequently used with this build's materials
Warp Yarn (Cotton)Frequently used with this build's materials
HoneyFrequently used with this build's materials
Wicker Harvest BasketFrequently used with this build's materials
Fire StarterFrequently used with this build's materials
Distilled WaterFrequently used with this build's materials
Cotton Kitchen StringUsed together and in similar builds
Measuring Tape 3mUsed together and in similar buildsVerwandte Blueprints
Diese Blueprints teilen Wissen — Techniken, Materialien oder Prinzipien
Related blueprints
Other builds that share materials, tools, or techniques with this one.
Al-Khwarizmi's Algebra — Complete the Square with Paper Tiles
Mulching — Covering the Soil to Save Water and Feed It
Regrowing Vegetables from Their Bases — Free Greens from Kitchen Scraps
Building a Voltaic Pile — The First Battery and the Birth of Steady ElectricityELECTRONICS
Perfect Numbers — Find the Numbers That Equal Their Own Parts
Building a Counterweight Trebuchet — The Medieval Siege Engine That Toppled Castlesengineering
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