About: Viviani's theorem   Sponge Permalink

An Entity of Type : owl:Thing, within Data Space : 134.155.108.49:8890 associated with source dataset(s)

This proof depends on the readily-proved proposition that the area of a triangle is half its base times its height—that is, half the product of one side with the altitude from that side. Let ABC be an equilateral triangle whose height is h and whose side is a. Let P be any point inside the triangle, and u, s, t the distances of P from the sides. Draw a line from P to each of A, B, and C, forming three triangles PAB, PBC, and PCA. and thus u + s + t = h.

AttributesValues
rdfs:label
  • Viviani's theorem
rdfs:comment
  • This proof depends on the readily-proved proposition that the area of a triangle is half its base times its height—that is, half the product of one side with the altitude from that side. Let ABC be an equilateral triangle whose height is h and whose side is a. Let P be any point inside the triangle, and u, s, t the distances of P from the sides. Draw a line from P to each of A, B, and C, forming three triangles PAB, PBC, and PCA. and thus u + s + t = h.
sameAs
dcterms:subject
dbkwik:math/proper...iPageUsesTemplate
abstract
  • This proof depends on the readily-proved proposition that the area of a triangle is half its base times its height—that is, half the product of one side with the altitude from that side. Let ABC be an equilateral triangle whose height is h and whose side is a. Let P be any point inside the triangle, and u, s, t the distances of P from the sides. Draw a line from P to each of A, B, and C, forming three triangles PAB, PBC, and PCA. Now, the areas of these triangles are , , and . They exactly fill the enclosing triangle, so the sum of these areas is equal to the area of the enclosing triangle. So we can write: and thus u + s + t = h.
Alternative Linked Data Views: ODE     Raw Data in: CXML | CSV | RDF ( N-Triples N3/Turtle JSON XML ) | OData ( Atom JSON ) | Microdata ( JSON HTML) | JSON-LD    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 07.20.3217, on Linux (x86_64-pc-linux-gnu), Standard Edition
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2012 OpenLink Software