Spirals | Archimedes | Squaring the circle
The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. It is the locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation with real numbers a and b. Changing the parameter a moves the centerpoint of the spiral outward from the origin (positive a toward θ = 0 and negative a toward θ = π) essentially through a rotation of the spiral, while b controls the distance between loops. From the above equation, it can thus be stated: position of particle from point of start is proportional to angle θ as time elapses. Archimedes described such a spiral in his book On Spirals. Conon of Samos was a friend of his and Pappus states that this spiral was discovered by Conon. (Wikipedia).
The Archimedean Spiral | Visually Explained (animation code also explained)
This is a video explaining what is so extraordinary about Archimedes, and the geometric things he did back in the BC. This is a partial explanation of the topic, and a partially explaining the code. Timecodes: 0:00 - Intro 0:11 - Archimedean Spirals 3:40 - The Exhaustion Method 5:38 - Ma
From playlist ManimCE Tutorials 2021
Device for milling Archimedean spiral groove 1
Combination of bevel gear satellite drive and nut-screw one.
From playlist Mechanisms
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/MYI
From playlist 3D printing
Archimedes Spiral Gear Mechanism
This unusual gear mechanism is based around an Archimedes Spiral. Tim was given it by a friend, who made it using 3D printing. Happy New Year to you all from everyone at Grand Illusions!
From playlist Engineering
The green and orange wheels of Archimedean grooves are identical. The green one is input. The pink pin slides in both grooves and in a straight slot of a immobile bar. The slot is on the line connecting axes of the two wheels. Two wheels rotate in the same direction with the same speed, li
From playlist Mechanisms
The green and orange coaxial wheels of Archimedean grooves are identical. The pink pin slides in both grooves and in a straight slot of a fixed bar. The two wheels rotate in opposite directions with the same speed. Pitch of the Archimedean groove must be big enough to prevent possible jam.
From playlist Mechanisms
The green and orange cams have different Archimedean profiles (pitches p1 and p2, p1 = 2.p2). The green one is input. Two cams rotate in opposite directions with different speeds, like in a drive of two gears of different tooth numbers. Transmission ratio = 1/2. Pitch of the Archimedean p
From playlist Mechanisms
The green and orange wheels of Archimedean grooves are identical. The green one is input. The pink pin slides in both grooves and in a straight slot of a fixed bar. If the bar is perpendicular to the line connecting axes of the two wheels at its middle point, two wheels rotate in opposite
From playlist Mechanisms
Instrument for drafting spiral 1
The orange nut-wheel, by revolving about the fixed central point, describes a spiral by moving along the screw threaded axle either way, and transmits the same to drawing paper on which transfer paper is laid with colored side downward. The obtained spiral is not an Archimedean one.
From playlist Mechanisms
Squaring the Circle with the Archimedean Spiral (animated visual proof)
This is a short, animated visual proof that we can square the circle IF we use the Archimedean spiral. Unfortunately, this is not a solution to the squaring the circle problem from antiquity because that requires it to be done with only a straightedge and compass. #mathshorts #mathvideo
From playlist Pi
Trisect an Angle with Archimedean Spiral (visual proof)
This is a short, animated visual proof demonstrating how to trisect any angle using the Archimedean spiral. #manim #math #mathshorts #mathvideo #trisect #trisectangle #impossible #geometry #chords #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #i
From playlist Geometric Constructions
Polar Equations Using Desmos: The Spiral
This video explains how to explore the polar equation of the spiral using desmos.com. http://mathispower4u.com
From playlist Graphing Polar Equations
Marjorie Wikler Senechal - Unwrapping a Gem - CoM Apr 2021
If the celebrated Scottish zoologist D’Arcy W. Thompson (1860 – 1948) could have met the near-legendary German astronomer Johannes Kepler (1571 – 1630), what would they talk about? Snowflakes, maybe? It is true that both men wrote about their hexagonal shapes. But they both wrote about Arc
From playlist Celebration of Mind 2021
Mechanism for drawing heart shape 1
Input: green shaft to which a cam and a crank are fixed. The crank traces a heart-shaped curve (in pink). Angular position between the Archimedean cam and crank must be as shown in the video (0 deg.) or 90 deg. The cam profile consists of 4 sections. Each one is an Archimedean spiral of eq
From playlist Mechanisms
The golden spiral | Lecture 13 | Fibonacci Numbers and the Golden Ratio
How to construct a golden spiral inside a golden rectangle. Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1
From playlist Fibonacci Numbers and the Golden Ratio
What is the Archimedes’ Principle? | Gravitation | Physics | Don't Memorise
We can bet you've heard about the Archimedes' principle at least once in your life. But do you know what it really means? Watch this video to find out. To get access to the entire course based on Gravitation, enroll here - https://infinitylearn.com/microcourses?utm_source=youtube&utm_med
From playlist Physics