Helical Path
Helical Path - Related Videos
01:22
Mean free path and Mean free time
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2025
Consider the gas molecules in a cylinder. They move in a random motion as they collide with each other and change speed and direction. The average of all the path lengths between collisions is known as the "mean free path." The mean free path varies inversely with the density of the molecules because when there are more molecules inside a volume, they have a greater chance of colliding with each other, thus reducing the mean free path. Additionally, the mean free path is inversely related to...
01:21
Path Between Thermodynamics States
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2023
Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1: In the first process for path A to C, the gas is kept at constant temperature T. It undergoes an expansion from volume V1 to V2. The work done by an ideal gas is expressed as Substituting for pressure as nRT/V from the ideal gas equation and integrating the terms, the work done by an ideal gas at constant temperature is obtained as In the second process, for path A to B, the...
12:24
Helical Organization of Blood Coagulation Factor VIII on Lipid Nanotubes
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Cited by 9 •
2014
We present a combination of Cryo-electron microscopy, lipid nanotechnology, and structure analysis applied to resolve the membrane-bound structure of two highly homologous FVIII forms: human and porcine. The methodology developed in our laboratory to helically organize the two functional recombinant FVIII forms on negatively charged lipid nanotubes (LNT) is described.
09:22
Self-assembling Morphologies Obtained from Helical Polycarbodiimide Copolymers and Their Triazole Derivatives
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2017
Here, we present a protocol to prepare and visualize secondary structures (e.g., fibers, toroidal architectures, and nano-spheres) derived from helical polycarbodiimides. The morphology characterized by both atomic force microscopy (AFM) and scanning electron microscopy (SEM) was shown to depend on molecular structure, concentration, and the solvent of choice.
07:26
Foraging Path-length Protocol for Drosophila melanogaster Larvae
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Cited by 18 •
2016
We provide a detailed protocol for a Drosophila melanogaster foraging path-length assay. We discuss the preparation and handling of test animals, how to perform the assay and analyze the data.
FAQs
The radius r controls the distance of each point from the central axis, so changing it enlarges or contracts the circular part of the motion. The parameter p controls how far the curve advances axially as t changes and therefore determines the pitch. Together, r and p establish the helix’s scale, spacing, and spatial orientation.
The cosine and sine terms coordinate the point’s circular movement in perpendicular x and y directions. At the same time, the linear term in z produces axial advancement. Combining periodic trigonometric behavior with linear change creates a curve whose horizontal position repeats while its height continues to change, linking planar trigonometry to three-dimensional geometry.
Curvature describes how strongly the path bends, while spatial orientation indicates how the curve is positioned relative to its axis. The radius influences the size of the circular bending, and the axial parameter changes how quickly the curve rises between turns. Examining both quantities helps distinguish tightly wound paths from more extended helical forms.
Begin by assigning values to r and p, then evaluate x, y, and z for selected values of t. Comparing these points reveals the circular progression and axial advance. Calculus and vector geometry can then be applied to study changing position and the curve’s spatial behavior, providing a systematic analysis rather than relying only on a sketch.
Helical paths model trajectories in which motion combines repeated circular behavior with steady advancement along an axis. The same geometric framework supports descriptions of screw motion, spring shapes, and spiral structures. In each case, the parameters provide a compact way to relate the visible form of the path to its mathematical dimensions and orientation.
The parametric form gives mathematics a precise language for representing spatial motion and geometry. Trigonometric functions describe the repeating component, while vector geometry and calculus support analysis of position, direction, and curvature. These tools make helical paths useful as idealized models for physical trajectories, mechanical screw motion, springs, and related engineering structures.