The Sand Reckoner
E156210
The Sand Reckoner is a treatise by Archimedes in which he develops a system for expressing extremely large numbers to estimate the quantity of sand that could fit in the universe.
All labels observed (5)
| Label | Occurrences |
|---|---|
| The Sand Reckoner canonical | 8 |
| On the Sand-Reckoner | 2 |
| Archimedes’ Sand Reckoner | 1 |
| Psammites (The Sand Reckoner) | 1 |
| The Sand Reckoner of Archimedes | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1358765 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: The Sand Reckoner Context triple: [Archimedes, notableWork, The Sand Reckoner]
-
A.
Almagest
The Almagest is an influential 2nd-century astronomical treatise by Claudius Ptolemy that systematically presents the geocentric model of the cosmos and provides mathematical tools for predicting planetary motions.
-
B.
Aristotle’s On the Heavens
Aristotle’s On the Heavens is an influential ancient Greek treatise that presents Aristotle’s cosmology and theories about the structure and motions of the universe.
-
C.
Euclides adauctus et methodicus
Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
-
D.
De revolutionibus orbium coelestium
De revolutionibus orbium coelestium is Nicolaus Copernicus’s seminal 1543 work that introduced the heliocentric model of the universe, fundamentally transforming astronomy and natural philosophy.
-
E.
Dialogue Concerning the Two Chief World Systems
Dialogue Concerning the Two Chief World Systems is Galileo Galilei’s influential 1632 work that presents and defends the Copernican heliocentric model through a comparative dialogue of astronomical theories.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: The Sand Reckoner Target entity description: The Sand Reckoner is a treatise by Archimedes in which he develops a system for expressing extremely large numbers to estimate the quantity of sand that could fit in the universe.
-
A.
Almagest
The Almagest is an influential 2nd-century astronomical treatise by Claudius Ptolemy that systematically presents the geocentric model of the cosmos and provides mathematical tools for predicting planetary motions.
-
B.
Aristotle’s On the Heavens
Aristotle’s On the Heavens is an influential ancient Greek treatise that presents Aristotle’s cosmology and theories about the structure and motions of the universe.
-
C.
Euclides adauctus et methodicus
Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
-
D.
De revolutionibus orbium coelestium
De revolutionibus orbium coelestium is Nicolaus Copernicus’s seminal 1543 work that introduced the heliocentric model of the universe, fundamentally transforming astronomy and natural philosophy.
-
E.
Dialogue Concerning the Two Chief World Systems
Dialogue Concerning the Two Chief World Systems is Galileo Galilei’s influential 1632 work that presents and defends the Copernican heliocentric model through a comparative dialogue of astronomical theories.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical treatise
ⓘ
work by Archimedes ⓘ |
| addressedTo |
Gelon II of Syracuse
ⓘ
linked to:
King Gelon II of Syracuse
|
| aimsTo | show that the number of grains of sand needed to fill the universe is finite and expressible ⓘ |
| alsoKnownAs |
Psammites
ⓘ
Psammitēs ⓘ |
| approximateDate | 3rd century BCE ⓘ |
| author | Archimedes ⓘ |
| contains |
estimates of the size of the Earth
ⓘ
estimates of the size of the Sun ⓘ estimates of the size of the universe ⓘ |
| critiques | earlier cosmological models ⓘ |
| dedicatedTo | King Gelon II of Syracuse ⓘ |
| describes | heliocentric model attributed to Aristarchus of Samos ⓘ |
| develops | Archimedean system of large numbers ⓘ |
| focusesOn |
cosmological size estimates
ⓘ
system for expressing extremely large numbers ⓘ |
| genre |
astronomy
ⓘ
mathematics ⓘ number theory ⓘ |
| hasApproximateUpperBoundFor | number of grains of sand that could fill the universe ⓘ |
| hasForm | letter ⓘ |
| historicalPeriod | Hellenistic period ⓘ |
| influencedBy | Aristarchus of Samos ⓘ |
| introducesConcept | orders of magnitude beyond myriads ⓘ |
| mainSubject |
estimation of the number of grains of sand in the universe
ⓘ
large numbers ⓘ notation for very large numbers ⓘ |
| mathematicalField |
arithmetical notation
ⓘ
combinatorics of large numbers ⓘ |
| originalLanguage | Ancient Greek ⓘ |
| originalTitle | Ψαμμίτης ⓘ |
| preservedIn | medieval manuscript tradition ⓘ |
| setting | Syracuse ⓘ |
| significance |
early systematic treatment of extremely large numbers
ⓘ
historically important in the development of number notation ⓘ source for ancient Greek astronomical estimates ⓘ |
| structure | prose exposition with mathematical arguments ⓘ |
| topic |
cosmological scale compared to human-scale quantities
ⓘ
finite expressibility of enormous quantities ⓘ |
| usesConcept |
grouping of numbers into periods
ⓘ
powers of 10 ⓘ |
| workOf | Ancient Greek mathematics ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: The Sand Reckoner Description of subject: The Sand Reckoner is a treatise by Archimedes in which he develops a system for expressing extremely large numbers to estimate the quantity of sand that could fit in the universe.
Referenced by (13)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: The Sand Reckoner
linked to: The Sand Reckoner
subject linked to:
King Gelon II of Syracuse
subject linked to:
King Gelon II of Syracuse
linked to: The Sand Reckoner
linked to: The Sand Reckoner
linked to: The Sand Reckoner