Meningkatkan Pemahaman Siswa tentang Teorema Pythagoras dengan Kotak Musik Spiral Theodorus

The background of this journal is because of the low understanding level of students regarding the Pythagoras theorem. It is visile from the inability of students in deciding the Hypotenuse on right triangle and students often see the Pythagoras theorem formulas as a same. Even though both formulas may not be the same, they must firstly be defined what does it mean a,b,c. Writer is interested in solving those problems by using Spiral Theodorus music box as instructional media. The basic concept that writer use during the making of this media is to connect the Pythagoras concept with Spiral Theodorus. It is because writer think Spiral Theodorus use Pythagoras concept. This musix box can be used everyday by students so that the more often student used and see the Spiral Theodorus music box, the more they will increase their understanding about Pythagoras theorem. Keywords: Pythagoras, Kotak Musik Spiral Theodorus

Culturally Responsive Teaching: Connecting Mathematics to Art (pp. 7--17)

The author presents an activity designed to help preservice mathematics teachers begin to understand how they can make their lessons more culturally responsive by connecting content to everyday contexts while incorporating students’ interests and culture in their teaching

Spreading entanglement through pairwise exchange interactions

The spread of entanglement is a problem of great interest. It is particularly relevant to quantum state synthesis, where an initial direct-product state is sought to be converted into a highly entangled target state. In devices based on pairwise exchange interactions, such a process can be carried out and optimized in various ways. As a benchmark problem, we consider the task of spreading one excitation among $N$ two-level atoms or qubits. Starting from an initial state where one qubit is excited, we seek a target state where all qubits have the same excitation-amplitude -- a generalized-W state. This target is to be reached by suitably chosen pairwise exchange interactions. For example, we may have a a setup where any pair of qubits can be brought into proximity for a controllable period of time. We describe three protocols that accomplish this task, each with $N-1$ tightly-constrained steps. In the first, one atom acts as a flying qubit that sequentially interacts with all others. In the second, qubits interact pairwise in sequential order. In these two cases, the required interaction times follow a pattern with an elegant geometric interpretation. They correspond to angles within the spiral of Theodorus -- a construction known for more than two millennia. The third protocol follows a divide-and-conquer approach -- dividing equally between two qubits at each step. For large $N$, the flying-qubit protocol yields a total interaction time that scales as $\sqrt{N}$, while the sequential approach scales linearly with $N$. For the divide-and-conquer approach, the time has a lower bound that scales as $\log N$. With any such protocol, we show that the phase differences in the final state cannot be independently controlled. For instance, a W-state (where all phases are equal) cannot be generated by pairwise exchange.Comment: 6 pages, 3 figure

On the stability of classical orbits of the hydrogen ground state in Stochastic Electrodynamics

de la Pe\~na 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics are stable. Though the Cole-Zou 2003 simulations support the stability, our recent numerics always lead to self-ionisation. Here the de la Pe\~na-Puthoff argument is extended to elliptic orbits. For very eccentric orbits with energy close to zero and angular momentum below some not-small value, there is on the average a net gain in energy for each revolution, which explains the self-ionisation. Next, an $1/r^2$ potential is added, which could stem from a dipolar deformation of the nuclear charge by the electron at its moving position. This shape retains the analytical solvability. When it is enough repulsive, the ground state of this modified hydrogen problem is predicted to be stable. The same conclusions hold for positronium.Comment: 18 pages latex, 1 figur

Classification of Low Velocity Impactors Using Spiral Sensing of Acousto-Ultrasonic Waves

The non-linear elastodynamics of a flat plate subjected to low velocity foreign body impacts is studied, resembling the space debris impacts on the space structure. The work is based on a central hypothesis that in addition to identifying the impact locations, the material properties of the foreign objects can also be classified using acousto-ultrasonic signals (AUS). Simultaneous localization of impact point and classification of impact object is quite challenging using existing state-of-the-art structural health monitoring (SHM) approaches. Available techniques seek to report the exact location of impact on the structure, however, the reported information is likely to have errors from nonlinearity and variability in the AUS signals due to materials, geometry, boundary conditions, wave dispersion, environmental conditions, sensor and hardware calibration etc. It is found that the frequency and speed of the guided wave generated in the plate can be quantized based on the impactor\u27s relationship with the plate (i.e. the wave speed and the impactor\u27s mechanical properties are coupled). In this work, in order to characterize the impact location and mechanical properties of imapctors, nonlinear transient phenomenon is empirically studied to decouple the understanding using the dominant frequency band (DFB) and Lag Index (LI) of the acousto-ultrasonic signals. Next the understanding was correlated with the elastic modulus of the impactor to predict transmitted force histories. The proposed method presented in this thesis is especially applicable for SHM where sensors cannot be widely or randomly distributed. Thus a strategic organization and localization of the sensors is achieved by implementing the geometric configuration of Theodorous Spiral Sensor Cluster (TSSC). The performance of TSSC in characterizing the impactor types are compared with other conventional sensor clusters (e.g. square, circular, random etc.) and it is shown that the TSSC is advantageous over conventional localized sensor clusters. It was found that the TSSC provides unbiased sensor voting that boosts sensitivity towards classification of impact events. To prove the concept, a coupled field (multiphysics) finite element model (CFFEM) is developed and a series of experiments were performed. The dominant frequency band (DBF) along with a Lag Index (LI) feature extraction technique was found to be suitable for classifying the impactors. Results show that TSSC with DBF features increase the sensitivity of impactor\u27s elastic modulus, if the covariance of the AUS from the TSSC and other conventional sensor clusters are compared. It is observe that for the impact velocity, geometric and mechanical properties studied herein, longitudinal and flexural waves are excited, and there are quantifiable differences in the Lamb wave signatures excited for different impactor materials. It is found that such differences are distinguishable only by the proposed TSSC, but not by other state-of-the-art sensor configurations used in SHM. This study will be useful for modeling an inverse problem needed for classifying impactor materials and the subsequent reconstruction of force histories via neural network or artificial intelligence. Finally an alternative novel approach is proposed to describe the Probability Map of Impact (PMOI) over the entire structure. PMOI could serve as a read-out tool for simultaneously identifying the impact location and the type of the impactor that has impacted the structure. PMOI is intended to provide high risk areas of the space structures where the incipient damage could exist (e.g. area with PMOI \u3e 95%) after an impact