Search
Subject Categories:
 Art (449)
 Asperger's (32)
 Blogging (10)
 China and the Han (9)
 eBay (3)
 Education (92)
 Fiction (28)
 Geography (27)
 History (37)
 Humor (46)
 Life (358)
 Mandalas (122)
 Mathematics (1,241)
 Mental Health (72)
 Music (43)
 Mysteries (16)
 Politics (120)
 Quotations (64)
 Religion (58)
 Satire (11)
 Science and Scientists (120)
 Follow RobertLovesPi.net on WordPress.com
MostViewed Posts, Recently:

Recent Posts
 A Second Type of Double Icosahedron, and Related Polyhedra
 Augmenting, and Then Reaugmenting, the Icosahedron, with Icosahedra
 The Double Icosahedron, and Some of Its “Relatives”
 Two Excellent Mathematical Websites
 The Compound of the Octahedron and the Small Stellated Dodecahedron
 A Zoo of Zonohedra
 Seven Different Facetings of the Truncated Icosahedron
 Four Symmetrohedra
 Some TenPart Polyhedral Compounds
 Augmenting the Dodecahedron with Great Dodecahedra
Explore RobertLovesPi By Topic
 Arkansas
 Art
 Asperger's
 astronomy
 atheism
 atheist
 chemistry
 chiral
 circle
 cluster
 compound
 cube
 cuboctahedron
 dodecahedron
 dual
 Education
 enneagon
 faceted
 faceting
 geometric
 geometrical
 geometrical art
 geometry
 Golden Ratio
 hexagon
 Humor
 humour
 icosahedron
 icosidodecahedral
 icosidodecahedron
 kite
 life
 mandala
 mandalas
 math
 mathematical
 mathematical art
 Mathematics
 music
 nonagon
 octagon
 octahedron
 op art
 pentagon
 physics
 politics
 polygon
 polyhedra
 polyhedral
 polyhedron
 president
 quotation
 quote
 religion
 rhombi
 rhombic dodecahedron
 rhombicosidodecahedron
 rhombic triacontahedron
 rhombus
 school
 science
 snub dodecahedron
 star
 stellated
 stellation
 symmetry
 tessellation
 tetrahedron
 tiling
 triangle
 Trump
 truncated icosahedron
 USA
 words
 zonohedron
Hit Counter
 329,512 hits
Tag Archives: Golden Ratio
Deliberately Difficult to Watch
I’ve never tried this before: create a rotating polyhedral image which is difficult to watch, using disorienting effects, such as the rotation of the images of spirals on the rotating faces. The spiral is made of golden gnomons (obtuse triangles with … Continue reading
Posted in Art, Mathematics
Tagged Art, difficult to watch, geometrical, geometry, Golden Ratio, Golden Spiral, great rhombicosidodecahedron, hard to watch, mathematical, Mathematics, polyhedra, polyhedron
9 Comments
The Second of Dave Smith’s “Bowtie” Polyhedral Discoveries, and Related Polyhedra
Dave Smith discovered the polyhedron in the last post here, shown below, with the faces hidden, to reveal how the edges appear on the back side of the figure, as it rotates. (Other views of it may be found here.) … Continue reading
A Euclidean Construction of a Golden Rectangle in Which All Circles Used Have Radius One or Two
There is more than one way to construct a golden rectangle using the Euclidean rules, but all the ones I have seen before use circles with irrational radii. This construction, which I believe to be new, does not use that shortcut, … Continue reading
Posted in Mathematics
Tagged compass, construction, Euclidean, Euclidean tools, geometry, Golden Ratio, Golden Rectangle, irrational number, Mathematics, phi, rational number, straight edge, straightedge, tau
Leave a comment
The Golden Ratio: Working from a Definition to Find a Value
I found the image above through the Wikipedia article on the golden ratio. After using what appears above to define the golden ratio, the article then reveals its exact and approximate values. Later, the writers of the article do show … Continue reading
Posted in Mathematics
Tagged 1.618, calculation, golden mean, Golden Ratio, golden section, phi, show work, tau, Wikipedia
2 Comments
A Regular Decagon, Decomposed into Golden Triangles and Golden Gnomons
The golden triangles, in yellow, are acute isosceles triangles with a leg:base ratio which is the golden ratio. Golden gnomons, shown in orange, are related, for they are obtuse isosceles triangles where the golden ratio shows up as the base:leg … Continue reading
Posted in Mathematics
Tagged decagon, geometry, golden gnomon, Golden Ratio, golden triangle, Mathematics
Leave a comment
A Golden Tessellation
This tessellation can be viewed in at least two ways: it can be seen as being composed of overlapping octagons which are equilateral, but not equiangular — or it can be viewed as a periodicallyrepeating pattern of golden gnomons, as … Continue reading
Posted in Mathematics
Tagged geometry, golden gnomon, Golden Ratio, golden triangle, Mathematics, tessellation, tiling
Leave a comment