Welcome ~ Ask questions. Answer questions. Share your insights. Learn something new this year.

Topic RSS

Fibonacci series directly relates the tetrahedron to the pentagon

October 17, 2019

7:36 am

7:36 am

Bradley Grantham

Member

Members

Forum Posts: 3

Member Since:

October 17, 2019

October 17, 2019

Offline

November 18, 2019

11:04 am

11:04 am

Cindy

New Member

Members

Forum Posts: 2

Member Since:

April 3, 2018

April 3, 2018

Offline

That is interesting, but I'm not sure I understand fully.

Do you mean that, for instance, if the length of three edges is in proportions 3 : 5 : 8

then the new face would be a point of a 5 pointed star?

That seems counter-intuitive to me.

I can imagine that if the lengths were 3 : 3 : 5

that the new face might approximate a star point,

but "any three terms of the Fibonacci series" seems like it would often generate a new face

that was not an isosceles triangle, let alone a golden ratio one.

Perhaps I'm misunderstanding what you mean?

January 9, 2020

12:20 pm

12:20 pm

Bradley Grantham

Member

Members

Forum Posts: 3

Member Since:

October 17, 2019

October 17, 2019

Offline

I actually do mean 3:5:8 but the phi ratio gets closer the higher in the sequence one goes; the 3:5 triangle has the shorter side of the star( the side of a pentagon) while the 3:8 and 5:8 triangles -dont ask me HOW...wind up having equal lengths for the third sides of their triangles- the two diagonals of the pentagon, or the sides that form the "point" of the star

January 9, 2020

12:37 pm

12:37 pm

Bradley Grantham

Member

Members

Forum Posts: 3

Member Since:

October 17, 2019

October 17, 2019

Offline

March 7, 2021

10:22 am

10:22 am

Shem

New Member

Members

Forum Posts: 2

Member Since:

July 3, 2016

July 3, 2016

Offline

I'm going to actually try this with sticks and glue.

Make a tetrahedron.

Mark points 3 5 and 8 units down three edges.

Join them up with other sticks.

Examine the resulting triangle.

I agree with @Cindy that intuitively I would think you need two lengths the same

in order to get an isosceles triangle, so Im intrigued 🙂

I find it fascinating that once you have phi ratios in a form

then they tend to appear everywhere within it.

So if the lengths were phi ratio instead of Fibonacci then I guess the triangle

would be a perfect star point?

April 15, 2021

7:32 pm

7:32 pm

d0b123

New Member

Members

Forum Posts: 1

Member Since:

April 15, 2021

April 15, 2021

Offline

A logical way to better understand the isoceles triangle concept here is to imagine a tetrahedron of side length 8 standing on sand. Push one corner of the tetrahedron into the sand so that a side of length now = to 3 is standing vertically while one of the other two sides remains touching the surface at it's full length = 8. Push the final side down until it has length 5 above the sand surface. You now have a vertical Pythagorean triangle of sides 3,4,5 with the 3 side at 90 degrees to the horizontal and the 5 side (hypoteneuse) at an angle of 60 degrees to the 3 side (because they are two (part) sides of a tetrahedron, or the equilateral trianglular face of same).

Bisecting the 60 degree angle between the 3 and 5 lines intersects the 4 baseline at it's midpoint. If we draw a line (in the sand ! 😉 ) between the midpoint and the only uncovered side of length 8 where it just touches the sand we can see that there must be 2 equal length sides between the 3-8 and 5-8 points on the horizontal sand surface.

Just for interest (if anyone is still awake at this point?) the midline from the 4 baseline and the 8 side length point has a length of root 51 (square of 2 subtracted from square of root 55) or about 7.141 and the two equal line lengths are root 55 (8 squared - 3 squared) or about 7.416 and the shorter side = 4 as explained before.

The only snag is:

it's NOT a star point! The angle between the equal sides is approx 65 degrees not the 72 degrees in a star (360/5) while the short - long side ratio is approx 1.854 not Phi. 🙁

But it is definitely makes an isoceles triangle in the horizontal plane.

d0b123

May 5, 2021

11:18 am

11:18 am

Narada Dan Vantari

Byron Bay NSW Australia

Admin

Forum Posts: 60

Member Since:

October 23, 2012

October 23, 2012

Offline

Interesting explanation @d0b123

Definitely still awake,

(and counting tetrahedrons as they jump the fence).

Checkout the Universe's best Sacred Geometry store at http://www.SacredGeometrical.com

3D printed models and jewellery, sacred geometry clothing designs, and of course our lavishly illustrated book

'Understanding Sacred Geometry and the Flower of Life'

Forum Timezone: Australia/Sydney

Most Users Ever Online: 37

Currently Online:

Guest(s) 1

Currently Browsing this Page:

1 Guest(s)

1 Guest(s)

Top Posters:

Ginger Spirit: 19

Peter S: 12

jode: 5

Bradley Grantham: 3

Liara Covert: 2

Shem: 2

White Crow: 2

Luke Williams: 2

Cindy: 2

Firebird: 1

Member Stats:

Guest Posters: 3

Members: 956

Moderators: 0

Admins: 2

Forum Stats:

Groups: 1

Forums: 15

Topics: 48

Posts: 122

Newest Members:

BoyceNot, betflix98sr, CypForum, Delmardaf, mablexl4, silviajo2, Jeffreyrut, Richardphype, BadSantatfa, charleshicktwAdministrators: Narada Dan Vantari: 60, Ike: 2

© Simple:Press —