សិល្បៈ
សម្រស់ និង សុខុមាលភាព
សិប្បកម្ម
វប្បធម៌ និង ប្រវត្តិសាស្ត្រ
ការកម្សាន្ត
បរិស្ថាន
ម្ហូប និង ភេសជ្ជៈ
អនាគតបៃតង
វិស្វកម្មបញ្ច្រាស
SCHOOL PROJECTS
វិទ្យាសាស្ត្រ
កីឡា
បច្ចេកវិទ្យា
ប្រដាប់ដែលស្លៀក
Measuring Pi — Archimedes' Method of Squeezing a Circle Between Polygons
Pi is the ratio of any circle's circumference to its diameter — the same number for every circle. You can measure it roughly with a string, but around 250 BC Archimedes found it exactly, with no measuring at all. He trapped a circle between a polygon drawn just inside it and one just outside, then doubled the sides again and again until the two polygons closed in on the circle from both directions. With 96-sided polygons he proved pi lies between 3+10/71 and 3+1/7. This blueprint walks through both the string measurement and Archimedes' rigorous squeeze.
មធ្យម
2
ការណែនាំ
1
1
Understand what pi is
Understand what pi is
Pi is the ratio of a circle's circumference (the distance around) to its diameter (the distance across). It is the same for every circle, large or small. Its value begins 3.14159… and never ends or repeats.
2
2
Measure pi with a string
Measure pi with a string
Wrap a cord snugly around a round object and mark its circumference, then measure straight across for the diameter. Divide circumference by diameter — you will get about 3.14. Try several sizes; the ratio stays the same every time.
Tools needed:
Cotton Kitchen String3
3
See the limit of measuring
See the limit of measuring
A cord and ruler give only two or three good digits — small measuring errors spoil the rest. To pin pi down exactly you need geometry, not string. This is the leap Archimedes made.
4
4
Trap the circle between two polygons
Trap the circle between two polygons
Draw a circle, then a regular polygon just inside touching it and another just outside enclosing it. The circle's circumference must lie between the two polygon perimeters — smaller than the outer, larger than the inner.
Tools needed:
Red Alder Board
Chalk Line5
5
Start with hexagons
Start with hexagons
Begin with six-sided polygons — the easiest to draw, since a hexagon's side equals the circle's radius. Their perimeters already bracket pi between 3 and about 3.46. Good, but still loose.
6
6
Keep doubling the sides
Keep doubling the sides
Double the sides: 6 to 12 to 24 to 48 to 96. Each doubling makes both polygons hug the circle more closely, so the inner and outer perimeters squeeze together and the gap that must contain pi shrinks.
7
7
Reach Archimedes' bounds
Reach Archimedes' bounds
At 96 sides Archimedes proved pi is greater than 3+10/71 (about 3.1408) and less than 3+1/7 (about 3.1429). The true value 3.14159… sits right in that gap — found by pure reasoning, with no ruler touching the circle.
8
8
Go as far as you like
Go as far as you like
The doubling never stops: more sides give more digits of pi, as many as your patience allows. Archimedes' squeeze was the best method known for almost two thousand years, until calculus offered faster ones.
ឧបករណ៍ចាំបាច់
3- កន្លែងទុក
- កន្លែងទុក
- កន្លែងទុក
You can swap these in
Can't get one of the materials? Swap it for an equivalent — these work just as well.
- Instead of Chalk Line, try:
Drying Line
Nylon Monofilament Line (0.3mm, 50m)
Nylon Fret Line
Fishing Line (Monofilament) - Instead of Cotton Kitchen String, try:
Guitar String Set (Acoustic, Phosphor Bronze)
Violin String Set (Full Size, Synthetic Core)
Bow String
Recommended for this build
Products makers often use with builds like this one.
Dowel RodUsed together and in similar builds
Graphite Pencil SetFrequently used with this build's materials
PaperFrequently used with this build's materials
Desktop ComputerFrequently used with this build's materials
KnifeUsed in similar builds
Hand SawUsed together and in similar builds
Cardstock Assorted Pack (50 Sheets)Frequently used with this build's materials
CalculatorFrequently used with this build's materialsប្លង់ពាក់ព័ន្ធ
ប្លង់ទាំងនេះចែករំលែកចំណេះដឹង — បច្ចេកទេស សម្ភារៈ ឬគោលការណ៍
Related blueprints
Other builds that share materials, tools, or techniques with this one.
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Weaving a Rush Floor Mat — Simple Plaiting with Wetland Plantstextiles
Measuring How Far the Sun Is Compared to the Moon — Aristarchus' Half-Moon Method
Making Panpipes — A Row of Tuned Bamboo Tubes
Making Raw Apple Cider Vinegar by Wild Fermentationfermentation
Growing Sweet Potato Slips — Sprouting a Root into Many Plants
CC0 សាធារណៈ
ប្លង់នេះត្រូវបានចេញផ្សាយក្រោម CC0។ អ្នកមានសិទ្ធិចម្លង កែប្រែ ចែកចាយ និងប្រើប្រាស់ដោយមិនចាំបាច់សុំអនុញ្ញាត។
គាំទ្រអ្នកបង្កើតដោយទិញផលិតផលតាមរយៈប្លង់របស់ពួកគេ ដែលពួកគេទទួលបាន កម្រៃជើងសារអ្នកបង្កើត កំណត់ដោយអ្នកលក់ ឬបង្កើតកំណែថ្មីនៃប្លង់នេះ ហើយបញ្ចូលជាការតភ្ជាប់ក្នុងប្លង់របស់អ្នកដើម្បីចែករំលែកចំណូល។