R3 – Multiplication Links to Rotation and Rotication – Part 2
R3 Multiplication Link between Formulae: The R3 multiplication and rotication formulae also demonstrate how multiplication links to rotication. The post on multiplication use of trigonometry gives the formula for multiplication as: Part 1 of this post shows how the rotication formula can be rewritten in terms of Opposite Value types as: The multiplication calculations below […]
R3 – Multiplication Links to Rotation and Rotication – Part 1
Introduction: This post starts with a description of long multiplication in R3. It then describes the R3 multiplication links to rotation and rotication and how the different operations move a point. Long Multiplication Calculate (5^ + 7iv + 2j^)*(4v + 6iv + 4jv) = (20^ + 30iv + 66jv) by long multiplication and using the R3 multiplication table. For example: 4v […]
R3 – Quaternion Comparison
Comparison of Wave Number and Quaternion Multiplication Tables: An earlier post makes a detailed comparison of the Wave Number Multiplication table and the Quaternion Multiplication table. The only difference occurs when Quaternions are multiplied together, as in i*i, = -1, but in R3, 1^*1^ = 1^. In R3, multiplying 1^ and 1^ = 1^ and multiplying 1^ and 1v = 1v, leaving the operand […]
R3 – Return and Orthogonal Rules
Rotation: In this post, we delve into the Return and Orthogonal rules of rotation within the three-dimensional space R3. These principles are foundational to understanding the universal rules governing rotations, especially in contexts like Wave Numbers, where rotation operations play a crucial role. A rotation in R3 involves moving a point from one position to […]
R3 – Rotation Ball
Use a Tennis Ball as a Rotation Prop: A physical prop helps to understand 3d rotation. There are many digital 3d spheres on-line. They limit the user experience as they are only in 2d. It is difficult to find a physical 3d sphere to help with understanding rotation. A major requirement is to be able […]
Quantum – Circuits – Bellagio – Part 1
Seven qubits, q0 to q6, make up the Quantum Bellagio Circuit. The primary qubits are q0, q2, q3 and q4. The Haadamard gates put these into superposition producing 24 = 16 parts in the mega qubit. Consequently, the rest of the qubits are dependent qubits. Each part from 1 to 16 of the mega […]
R2 – Rotation – Roticvision
What is R2 Roticvision? The R2 roticvision operation is the inverse of rotication. As seen in an earlier post, rotication requires an amount of rotation, an axis and a starting point to calculate the new location of a point. In contrast, roticvision requires a current point, an axis and an original starting point that are […]
R2 – Rotication
This post defines the new concept of the R2 rotication operation. It also provides examples. What is Rotication in R2? The R2 rotication operation is supported by the facts expressed in its axiom definition of operations. Rotication is a two-step operation. The first part of the operation is the same as rotation and results in a […]
Running the Bellagio Circuit
Running a Quantum Circuit Quantum computers are analogue computers. In effect, this means that they are subject to physical errors each time a quantum circuit runs. As a result, quantum programs are run many times to ensure accurate results. Measurement of the qubits causes the qubits in the mega qubit to collapse to one of […]
Quantum – Circuits – Bellagio – Part 1 – Continued
In the previous post, the Quantum Bellagio Haadamard gates created a mega qubit of 16 multipart qubits. As a result, it setup all possible combinations of k, k‾ ,m and m‾ . Following this, the rest of part 1 of the circuit programs the problem constraints and then tags the solutions. Changes to Mega Qubit […]