## Schedule of all Presentations

Mathematics

Irina Shablinsky

#### Presentation Title

The Golden Ladder

#### Presentation Type

Oral Presentation

#### Abstract

The Golden Ratio is one of the better known irrational numbers, ϕ = (1+√5) / 2 or ca 1.6180339887… as an infinite decimal number. Some important geometric shapes using the Golden Ratio include the golden rectangle and the golden triangle and many interesting properties have been described for both. In this work, a new Euclidean structure called the golden ladder is introduced. The golden ladder was first created in visual software by applying the golden ratio to the diameters of tangent circles. For this work three recursive properties of the circumference and area have been proven. The golden ladder has been expanded to the third dimension, and it is possible to expand the definition to the nth dimension. The volume will be the property of interest in the third dimension. Additional interesting properties have been found for the golden ladder and are currently under investigation.

#### Keywords

the Golden Ratio, the golden ladder, Euclidean structures

#### Start Date

10-4-2015 9:30 AM

#### End Date

10-4-2015 11:00 AM

Holmes Hall 211

#### Share

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Apr 10th, 9:30 AM Apr 10th, 11:00 AM

The Golden Ladder

Holmes Hall 211

The Golden Ratio is one of the better known irrational numbers, ϕ = (1+√5) / 2 or ca 1.6180339887… as an infinite decimal number. Some important geometric shapes using the Golden Ratio include the golden rectangle and the golden triangle and many interesting properties have been described for both. In this work, a new Euclidean structure called the golden ladder is introduced. The golden ladder was first created in visual software by applying the golden ratio to the diameters of tangent circles. For this work three recursive properties of the circumference and area have been proven. The golden ladder has been expanded to the third dimension, and it is possible to expand the definition to the nth dimension. The volume will be the property of interest in the third dimension. Additional interesting properties have been found for the golden ladder and are currently under investigation.