at the unveiling of PORTALXII shows the spiral shaped walkway from above.
Spiral/Helix
While "spiral" and a "helix" are distinct as technical terms, a helix is sometimes described as a spiral in non technical usage. The two primary definitions of a spiral are provided by the American Heritage Dictionary:[1]
a. A curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point.
b. A three-dimensional curve that turns around an axis at a varying distance while moving parallel to the axis.
b. A three-dimensional curve that turns around an axis at a varying distance while moving parallel to the axis.
The first definition is for a planar curve that extends primarily in length and width, but not in height. A groove on a record[2] or the arms of a spiral galaxy (a Logarithmic spiral) are examples of a spiral.
The second definition is for the 3-Dimensional variant of a spiral, for example a conical spring (device) can be described as a spiral whereas a cylindrical spring or strand of a DNA are examples of a helix.[1]
The length and width of a helix typically remain static and do not grow like on a planar spiral. If they do, then the helix becomes a conic helix. You can make a conic helix with an Archimedean or equiangular spiral by giving height to the center point, thereby creating a cone-shape from the spiral.[3]
Ammonite/Nautilis
The study of spirals in nature have a long history, Christopher Wren observed that many shells form a logarithmic spiral. Jan Swammerdam observed the common mathematical characteristics of a wide range of shells from Helix to Spirula and Henry Nottidge Moseley described the mathematics of univalve shells. D’Arcy Wentworth Thompson's On Growth and Form gives extensive treatment to these spirals. He describes how shells are formed by rotating a closed curve around a fixed axis, the shape of the curve remains fixed but its size grows in a geometric progression. In some shell such as Nautilus and ammonites the generating curve revolves in a plane perpendicular to the axis and the shell will form a planar discoid shape. In others it follows a skew path forming a helico-spiral pattern.