Right Triangle Research Articles

Design Microstrip Antenna Using Particle Swarm Optimization

In this work, particle swarm optimization algorithm (PSO) models have been built for the design of microstrip antennas in various forms such as rectangular and equilateral triangle antenna. The analysis problem can be defined as to obtain resonant frequency for a given dielectric material and geometrical structure. This approach has a few advantages: giving a clearer and simpler representation of the problem, and totally avoiding binary encoding and decoding so as to simplify software programming. The antenna designed using PSO is implemented using Microwave Office software 7.1 produced in 2007.

Associations of dietary macronutrient composition with cardiometabolic health: data from the National Health and Nutrition Examination Survey (NHANES) 1999–2014

Abstract Background Human nutrition is a leading modifiable risk factor for the prevention of cardiometabolic diseases. However, most nutritional research focuses on the role of specific nutrients rather than compositional analysis of the diet. Purpose We aimed to assess the association of dietary macronutrient composition with various markers of cardiometabolic health. Methods This study was undertaken using 24-hour food recall data from the National Health and Nutrition Examination Survey from years 1999–2014 (n=36,637). Participants included both males and females ≥20 years of age (49.8±18.3 years; 53% Female). Caloric outliers for males (<800 kcal/day or >4200 kcal/day) and females (<600 kcal/day or >3500 kcal/day) were removed from the analysis (n=1844). Cardiometabolic health markers were collected via mobile examination center and included triglycerides (n=16,444), total cholesterol (n=31,155), LDL cholesterol (n=15,798), HDL cholesterol (n=33,435), blood pressure (n=34,121), body fat percentage (n=4269), body mass index (n=35,187), glucose (n=17,208), insulin (n=16,273), oral glucose tolerance test (n=8280), and HbA1c (n=27,288). Associations of dietary macronutrients with cardiometabolic health markers were assessed using 3-dimensional general additive models (Protein; Carbohydrate; Fat) with adjustment for age, sex, misreporting, ethnicity, education level, household income, physical activity, alcohol intake, and smoking. Response surfaces on right-angled mixture triangles were generated as predictions from absolute macronutrient intake at the 50th percentile of total energy intake. Macronutrient intakes were transformed to a percentage of energy to visualize and interpret associations compositionally. Results There was a complex 3-way interactive non-linear association of macronutrient composition with lipid profile (Figure A-D; all p<0.04), blood pressure (Figure E-F; all p<0.001), body fat percentage (Figure G; p<0.001), body mass index (Figure H; p<0.001), and all markers of glycemic control (Figure I-L; all p<0.001). Diets comprised of high protein coupled with low fat were associated with higher triglycerides but generally more favorable total cholesterol, blood pressure, and body fatness. Conversely, diets composed of high protein coupled with high fat were associated with higher HDL cholesterol but worse total cholesterol, body fatness, body mass index, and glycemic control. Conclusions These findings display a complex relationship between dietary macronutrient composition and cardiometabolic health. Future research is needed to evaluate how dietary source and quality may modify the observed associations. Funding Acknowledgement Type of funding sources: Private company.

A Concretization on the Algebraic Proof of Pythagorean Theorem Using the Similarity of Right-angled Triangles

A Concretization on the Algebraic Proof of Pythagorean Theorem Using the Similarity of Right-angled Triangles

Extended Angle Sum and Difference Identity Rules for Scalene Triangles

The present article extends the applicability of the angle sum and di erence identity rules sin(A±B) and cos(A±B) beyond the particular case of a right-angled triangle into the general case of scalene triangles as sin*(A±B,γ) and cos*(A±B,γ), adding the e ect of independently varying both the reference angle α = A±B and the obtuse angle γ. Accompanied by appropriate theorems and proofs, the mathematical end result are four updated equations that supersede the traditional expressions sin(A±B) = sin(A)cos(b)± cos(A)sin(B) and cos(A±B) = cos(α)cos(B) \mp sin(A) sin(B), where the conventional sin(α) and cos(α) functions are replaced by the [already proven] extended versions sin*(α,γ) and cos*(α,γ) enclosing modifications including two angles α and γ. An open-source program scripted in Octave is provided for the verification of the derived expressions, including plotting the geometric results as a figure for both the cases of angle summation and subtraction.

Simultaneous axial and radial swelling studies from 2D stereozoom images of tablet compacts composed of superdisintegrants.

Swelling-based disintegration is considered important for drug release from tablets and can be modified with excipients called tablet disintegrants. Swelling of tablets occurs axially and radially, and most researchers have observed both these events separately using 2D images. In the current work, we have studied these events simultaneously instead of separately under a stereozoom microscope for tablet compacts composed of high proportions of disintegrants (sodium starch glycolate, SSG and croscarmellose sodium, CCS), using water as the disintegrating medium. A hypothesis is proposed for the measurements of radial and axial swellings from a single 2D image, as horizontal lengths based on trigonometric functions for a right-angle triangle. All predicted axial and radial lengths (as per proposed hypothesis) are found validated with respect to vernier calliper measurements for dry-tablet compacts with a minute error of 3.809%. The axial swelling is approximately fivefolds more than that of radial swelling on the basis of normalised lengths. No particular trend can be spotted exclusively in favour of a superdisintegrant; however, the CCS-based tablets have shown higher swelling as compared to SSG-based tablets. From the current studies, it is evident that both axial and radial dimensions are obtainable from single 2D stereozoom images and can be successfully implemented for swelling studies of tablets.

Geometric approach to the proof of Fermat’s last theorem

A geometric approach to the proof of Fermat’s last theorem is proposed. Instead of integers a, b, c, Fermat’s last theorem considers a triangle with side lengths a, b, c. It is proved that in the case of right-angled and obtuse-angled triangles Fermat's equation has no solutions. When considering the case when a, b, c are sides of an acute triangle, it is proved that Fermat's equation has no entire solutions for p>2. The numbers a=k, b=k+m, c=k+n, where k, m, n are natural numbers satisfying the inequalities n>m, n<k+m, exhaust all possible variants of natural numbers a, b, c which are the sides of the triangle.
 The proof in this case is carried out by introducing a new auxiliary function f(k,p)=kp+(k+m)p–(k+n)p of two variables, which is a polynomial of degree in the variable . The study of this function necessary for the proof of the theorem is carried out. A special case of Fermat’s last theorem is proved, when the variables a, b, c take consecutive integer values. The proof of Fermat’s last theorem was carried out in two stages. Namely, all possible values of natural numbers k, m, n, p were considered, satisfying the following conditions: firstly, the number (np–mp) is odd, and secondly, this number is even, where the number (np–mp) is a free member of the function f(k, p).
 Another proof of Fermat’s last theorem is proposed, in which all possible relationships between the supposed integer solution of the equation f(k, p)=0 and the number corresponding to this supposed solution are considered.
 The proof is carried out using the mathematical apparatus of the theory of integers, elements of higher algebra and the foundations of mathematical analysis. These studies are a continuation of the author's works, in which some special cases of Fermat’s last theorem are proved

Comparison of Temperature and Light Distributions Around Nano-Resistors in SSI-LEDs

A recent optoelectronic device termed the Solid-State Incandescent LED (SSI-LED) was discovered by Kuo’s group in 2013 [1]. The device is made by subjecting a MOS Capacitor of transparent gate material and appropriate high-k properties to dielectric breakdown, which results in the formation of numerous nano-scale conduction paths called nano-resistors (NRs). Due to its extremely small cross-sectional area, NRs display high current densities for relatively small voltages applied across the device. Consequently, the high current densities yield high local temperatures that approach black body radiation and allow NRs to undergo incandescence, where white light is emitted from the top surface through the transparent gate electrode by thermal excitation of electrons. Since the heat generated from Joule heating is contained within the NRs, a large temperature drop occurs over the surrounding volume as the heat flux transitions from nanoscale to microscale, keeping the whole device at a much lower temperature. The light emission from the SSI-LED is similar to that of an incandescent lamp where a spectrum of a wide range of wavelengths is produced in contrast to the narrow band light emitted from the conventional pn junction-structured LED. Therefore, SSI-LEDs are suitable for natural light or white light applications [2].It is desirable to have a direct comparison of emitted light intensity, temperature, and current density profiles of not just single NRs, but of NRs with various layouts to quantify the interaction of these variables. Earlier simulations using COMSOL Multiphysics have produced temperature and current density distributions without any accompanying light intensity study [3]. Using the python simulation framework developed earlier, these variables were studied in COMSOL Multiphysics for 3 NRs arranged as a right-angled triangle, 4 NRs as a square, and 5 NRs in the shape of a '+' sign. The effect of mesh quality on the temperature and current density distributions was also quantified. Since the current density profile is highly dependent on the relative positions of the NRs, the mesh quality has a noticeable effect on the temperature surrounding the NRs. In accordance with theoretical calculations, there is a direct relationship between the current density as well as the temperature and light intensity. The resultant light intensity profiles qualitatively match experimental observations and offers a degree of validation at near screen distances. Near the circumference at the surfaces of the NRs, the current density is high [4].Figure 1(a) shows the arrangement of NRs which are all of 10 nm radius with NR centers separated from adjacent NR centers by 40 nm. Fig. 1(b) shows the light intensity (in log10 scale) of the same patterns at a distance of 1 nm above the gate electrode surface, where the light is emitted from the blackbody radiation with corresponding the CCT to the NR at the top surface. Fig. 1(c) is the temperature of the gate electrode surface for the same set of NR patterns. Blue regions have higher temperature and white regions are close to room temperature. The temperature on the gate electrode surface blends to form a distribution that resembles individual NRs, when in fact, the observed temperature is for the pattern as a whole. The possible reason for this is that temperature is distributed in terms of sinusoidal waves according to the solution of the heat equation and is largely diffused when measured at the gate electrode surface, while the light intensity distribution obtained from the Stefan-Boltzmann law and inverse square law, varies with the 4th power of temperature close to the gate and shows a significantly steeper curve with individual NRs still distinct.More detailed comparisons of the temperature and light distributions will be shown in the presentation.1. Y. Kuo and C.-C. Lin, Appl. Phys. Lett., 102, 031117 (2013).2. Y. Kuo, 2014 IEEE International Electron Devices Meeting, 4.7.1-4.7.4 (2014).3. A. Shukla and Y. Kuo, ECS J. Solid State Sci. Technol., 9, 065017 (2020).4. K. Natarajan and Y. Kuo (To be published). Figure 1

Pizza Sharing Is PPA-Hard

We study the computational complexity of computing solutions for the straight-cut and square-cut pizza sharing problems. We show that finding an approximate solution is PPA-hard for the straight-cut problem, and PPA-complete for the square-cut problem, while finding an exact solution for the square-cut problem is FIXP-hard and in BU. Our PPA-hardness results apply even when all mass distributions are unions of non-overlapping squares, and our FIXP-hardness result applies even when all mass distributions are unions of weighted squares and right-angled triangles. We also prove that decision variants of the square-cut problem are hard: the approximate problem is NP-complete, and the exact problem is ETR-complete.

A mathematical approximation in the physical sciences

The business of making mathematical approximations in the physical sciences has a long and noble history. For example, in the earliest days of pyramid construction in ancient Egypt it was necessary to approximate lengths required in construction, especially when they involved irrational numbers. Similarly, surveyors in early Greece seeking to lay out profiles of right-angle triangles or circles on the ground invariably ended up making approximations regarding measurements of required lengths, as indeed is the case today. Practitioners have always faced the problem of having to decide when parameters in theory have been met satisfactorily in the practice of measurement. Further, before the advent of hand-held calculators, students in schools in the UK would have been very familiar with the approximation 22/7 for the transcendental number π, obtained perhaps by comparing (as this author did) the measured circumferences of many laboriously drawn circles of different sizes with their diameters. Despite the advent of sophisticated calculating devices and facilities, such as computers and spreadsheets, the practice of making approximations is still much in evidence in theoretical work in fields associated with physical phenomena. Such approximations often result in formulae that are easy to use and remember, and moreover can produce theoretical results that support directly, or otherwise, results from measurements. In this respect, the practical mathematician does not have to seek results to many decimal places when measurement facilities allow for accuracy to only a few. The purpose of this Article is to illustrate this point by discussing an example drawn from the realms of antenna theory, relating to the performance of a dipole antenna. It is not the purpose here to delve into the derivation of dipole theory, but to extract the relevant information and show how useful mathematical approximations can be employed to simplify a relationship between parameters of interest to an antenna engineer. To this end, it will first be necessary to introduce some antenna concepts that might be new to the reader.

Effect of Anisotropy on the Quality of Laser Cutting Corner of CFRP Plate

Abstract Carbon fiber reinforced polymer (CFRP) composites are widely used in the aerospace field because of their outstanding performance. Laser is an effective method for CFRP composite processing. However, there are corner errors and obvious thermal damage in laser corner cutting, which affect the cutting quality. This article mainly describes the corner error and thermal damage behavior, and the effect of anisotropy of nanosecond UV laser when cutting different corners of CFRP plates. Select six corner angles to perform a full factorial experiment with a right-angled triangle hole cutting under the horizontal and vertical baselines and different laser repetition rates. The results show that there are obvious corner errors and heat affected zone (HAZ) and matrix recession (MR) in laser corner cutting. The corner error always shows that the cut-in error is smaller than the cut-out error (28.06% on average), and the cut-in error and HAZ decrease with the increase of the corner angle, but the difference between the cut-in and the cut-out error increases with the increase of the corner angle. In vertical baseline cutting, the corner error can be reduced to a certain extent, but the HAZ (average 38.42%) is seriously increased, and the thermal damage of linear cutting under a large pulse repetition rate is increased. The large laser repetition rate increases the thermal damage due to the increase of the overlap rate of adjacent pulses but has less effect on the corner error, especially the cut-in error.

A Dual Orthogonal Fed Monopole Antenna for Circular Polarization Diversity

A monopole antenna with circular polarization diversity and high isolation is proposed in this paper. The proposed antenna consists of two bent monopole antennas and a partial ground plane. Two monopole antennas are implemented on opposite planes with respect to the ground plane. The ground plane is a right-angled isosceles triangle, and the antenna is located at one end of the ground plane. Circular polarization (CP) characteristics are obtained using this structural asymmetry. In the proposed structure, the resonant frequency at S11 is controlled by the antenna length, and the null frequency at S21 (isolation) is controlled using the bending angle of the monopole and the distance between the two antennas. From the measured results, the CP operating bandwidth of the proposed antenna is 13.8% (1.76–2.02 GHz). The measured isolation is –50 dB at the resonant frequency and –20 dB within the operating bandwidth.

Quantum signatures of chaos in relativistic quantum billiards with shapes of circle- and ellipse-sectors* *Dedicated to the memory of Fritz Haake. Fritz introduced me (Barbara) into the field of quantum chaos. He supervised my diploma and doctoral thesis and since then has been a mentor, friend and helpful advisor during all the stages of my scientific career. I take his

According to the Berry–Tabor conjecture, the spectral properties of typical nonrelativistic quantum systems with an integrable classical counterpart agree with those of Poissonian random numbers. We investigate to what extend it applies to relativistic neutrino billiards (NBs) consisting of a spin-1/2 particle confined to a bounded planar domain by imposing suitable boundary conditions (BCs). In distinction to nonrelativistic quantum billiards (QBs), NBs do not have a well-defined classical counterpart. However, the peaks in the length spectra, that is, the modulus of the Fourier transform of the spectral density from wave number to length, of NBs are just like for QBs at the lengths of periodic orbits of the classical billiard (CB). This implies that there must be a connection between NBs and the dynamic of the CB. We demonstrate that NBs with shapes of circle- and ellipse-sectors with an integrable classical dynamic, obtained by cutting the circle and ellipse NB along symmetry lines, have no common eigenstates with the latter and that, indeed, their spectral properties can be similar to those of classically chaotic QBs. These features orginate from the intermingling of symmetries of the spinor components and the discontinuity in the BCs leading to contradictory conditional equations at corners connecting curved and straight boundary parts. To corroborate the necessity of the curved boundary part in order to generate GOE-like behavior, we furthermore consider the right-angled triangle NB constructed by halving the equilateral-triangle NB along a symmetry axis. For an understanding of these findings in terms of purely classical quantities we use the semiclassical approach recently developed for massive NBs, and Poincaré–Husimi distributions of the eigenstates in classical phase space. The results indicate, that in the ultrarelativistic limit these NBs do not show the behavior expected for classically chaotic QBs.

Distribution of shear fragments classified by morphology

In studies on metal shell under internal explosive loading, unlike brittle metals, ductile metals usually exhibit shear fracture. Existing literature mostly focuses on slip fracture caused by unidirectional shear fracture, in fact, the shell fractures in the two directions of maximum shear stress, making morphology of the fragments diversified, considering fragment morphology in the distribution may achieve a better description. In previous studies, Poisson mixtures and Weibull mixtures model are only used for fragment distribution statistics as a functional form, and parameters (weight coefficient and distribution modulus) in the function lack physical process description. In this paper, an experimental study on the fragmentation of 50SiMnVB steel shell under TNT internal explosive loading was carried out. Through the observation and analysis of recovered fragments, the shear fragments with cross-sections of parallelogram, right-angled trapezoid, and isosceles right-angled triangle are divided into three types: A, B, and C. According to “A-type fragments created by the parallel through-the-thickness fractures, B-type and C-type fragments created by interaction of intersecting fractures,” the morphological parameters of fragments in the distribution model were derived, including fragment size (width, length, thickness, mass, etc.), shape parameters, and weight coefficient. Weibull mixture distribution model is used to describe the distribution of the total fragments, whereas Weibull distribution is used to describe the distribution of each type of fragment. Through the comparison of theoretical calculations and experimental data, the applicability of the theoretical model in the field of “shear fracture of ductile steel shell under internal explosive loading” is verified.

The Right Triangle as the Simplex in 2D Euclidean Space, Generalized to n Dimensions

The purpose of the research is to show that the general triangle can be replaced by the right-angled triangle as the 2D simplex, and this concept can be generalized to any higher dimensions. The main results are that such forms do exist in any dimensions; meet the requirements usually placed on an n-dimensional simplex; a hypotenuse and legs can be defined in these shapes; and a formula can be given to calculate the volume of the shape solely from the legs by a direct generalization of the Pythagorean Theorem, without computing the Cayley-Menger determinant.

Dimensions and proportions of the rock-cut tombs at the Eastern Field of the Giza Necropolis

The dimensional and proportional analysis of rock-cut tombs on a wide range of material has been done before, but has remained unanswered as to the possible causes of their size and proportions. This study based on 79 rock-cut tombs on the Eastern field of the Giza necropolis has attempted to identify the reasons for the proportions and sizes of tomb chapels, and possible ways of their plan preparation during construction. The analysis showed that there was no single universal scheme – the size and proportions of each chapel were set depending on their filling – the presence or absence of a pictorial decoration and the number of burial shafts. Thus, analysis has shown a marked difference between the tombs built first on rocky areas from about the middle of V dynasty with a broad pictorial program, and the tombs that appeared later, containing almost no decorations. The former have a chapel width of 5–6 royal cubits and proportions in the range 1/1.1–2.7, while the width of the latter are mostly between 3–5 royal cubits and have a markedly more elongated chapel length – with proportions 1/2.1–3.5. For tombs, in which only a false door was originally planned from the decoration, the proportions were set according to the intended number of burials. Whereas tombs with decoration require space in front of the walls, and therefore a different width and proportions of the chapel. The possible use in the plan preparation during construction of a number of chapels of not only the best known Egyptian rectangular triangle 3:4:5, but also a triangle 5:12:13.

Substantiating the pulse method for determining the time parameter of fire detectors with a thermoresistive sensing element

This paper substantiates the pulse method for determining the time parameter for fire detectors with a thermoresistive sensing element ‒ the time constant. The method is based on using the Joule-Lenz effect, which manifests itself when an electric current pulse passes through the thermoresistive sensing element of fire detectors. Thermal processes in such a sensing element are described by a mathematical model that belongs to the class of equations of mathematical physics. The solution to the differential equation of this class was derived using the Hankel integral transformation and is represented as a series relative to the Bessel functions. The resulting solution is used to construct a mathematical model of a thermoresistive sensing element in the form of a transfer function, which takes the form of the transfer function of the inertial link. To trigger the thermoresistive sensing element of fire detectors, a single pulse of electric current in the shape of a rectangular triangle is used. The integral Laplace transformation was applied to mathematically describe the response of a thermoresistive sensing element to the thermal effect of such a test influence. To obtain information about the time parameter of fire detectors with a thermoresistive sensing element, the ratio of its output signals is used, which are measured in the a priori defined moments. A two-parametric expression was built to determine the time parameter of fire detectors; a verbal interpretation of the pulse method to determine it was provided. The implementation of this method ensures the invariance of the time parameter of fire detectors with a thermoresistive sensing element relative to the amplitude of a single pulse of an electric current, as well as relative to the parameter that is included in its transfer coefficient.

RECONSTRUCTION OF THE TWO VARIABLES DISCONTINUOUS FUNCTION BY DIFFERENT INFORMATION OPERATORS USING TRIANGULAR ELEMENTS

The paper examines methods for constructing mathematical models of two variables discontinuous functions using various information about them: one-sided values at points and one-sided traces along a given system of lines. The case is considered when the domain of the required function is triangulated by right-angled triangles. If interpolation or approximation methods are used, then for their construction the values of the function at given points must be given; if we use interlination methods, then traces of the desired function along a given system of lines. In this work, we construct a discontinuous interpolation and approximation splines for approximating a discontinuous function of two variables with given one-sided values in a given system of points (in our case, at the vertices of right-angled triangles), and prove theorems on the estimation of the approximation error by constructed discontinuous structures. In the paper a discontinuous interlination spline, which uses completely different information about the discontinuous function, namely one-sided traces along a given system of lines (in our case, along the sides of right-angled triangles) is also built. Interlination of functions can find wide application in the aircraft and automobile body design automation; when receiving and processing the results of sonar and radar, when solving problems of computed tomography, in digital signal processing and in many other areas. In the paper theorems on the integral form and an estimate of the approximation error by the constructed discontinuous interlination operator are also proved. Computational experiments that compare the results of the approximation of a discontinuous function of two variables by different information operators using triangular elements are presented. In the future, it is planned to apply the constructed operators of discontinuous approximation and interlination to solve a two-dimensional problem of computed tomography with a significant use of the inhomogeneity of the internal structure of the body, which must be reconstructed.

Analysis of student errors in solving comparative trigonometry problems of right-angled triangles based on watson's criteria

This study aims to analyze the location of students' errors in problem solving and the causal factors based on Watson's criteria. This type of qualitative descriptive research, with the subject of three students of class X AKL 1 taken based on certain considerations according to the criteria or can be called purposive sampling technique. Data collection techniques include direct observation in schools, interviews with subjects and documentation. Triangulation techniques used for data analysis include data reduction, presentation and conclusion drawing. From the results of the analysis, it was found that four types of errors were located inimproper procedures, indirect manipulation, missing data and missing conclusions. The cause of the error is students lack understanding of material concepts, being careless in reading questions, forgetting formulas, being in a hurry, and new factors are found, namely students use other paper to write down the completion steps. The results of the study can explain in detail the errors made by students in solving problems, so that it can minimize the occurrence of similar errors and improve the learning process of mathematics.

Optimizing the strength of the Bourdon effect by varying the triangle arrangement.

The Bourdon illusion refers to the perceived bentness of the straight collinear edges when two right-angled triangles are placed apex to apex. We studied this illusion using a cancellation method. In the first of three experiments, we manipulated the apex angle, with six different angles ranging from 4° to 45°. Results indicated that the Bourdon illusion is strongest when the angle is around 12°. In the second experiment, we compared four scalene triangles with a right-angled triangle. The angular shift was most salient when the shape corresponded to a right-angled triangle. In the third experiment, the patterns were created by varying the size of one right-angled triangle while holding the size of the second right-angled triangle constant. Results indicated that the Bourdon illusion was strongest when both right-angled triangles were of equal size. Our data suggest that the Bourdon illusion depends critically upon the specific arrangement of shapes in the display.

Kinetics of DPPH\u2022 scavenging by bacterioruberin from Haloferax alexandrinus GUSF-1 (KF796625)

This is the first account of the kinetics of free radical scavenging by bacterioruberin obtained from cells of Haloferax alexandrinus GUSF-1(KF796625), grown at optimum conditions of 25% NaCl, pH 7, 42 °C, 150 rpm in NaCl Tryptone yeast extract medium and light. Bacterioruberin separated from methanolic extract displayed characteristics absorption peaks at 368, 386, 463, 492 and 525 nm and gave an m/z value of 740.4 (C50H76O4) in Liquid Chromatography-Mass Spectroscopy validating its purity. Bacterioruberin (13 µM) decolorized and decayed 0.2 mM 1,1-diphenyl-2-picrylhydrazyl radicals (DPPH•) monitored at 517 nm and reached a steady state within 30 min. An EC50 of 6.50 µM ± 0.27 (4.81 µg/mL ± 0.2) was deduced for the 0.2 mM DPPH•-bacterioruberin reaction using the GraphPad Prism 9 statistical software and employing the right-angled triangle technique. The study also revealed a comprehensive information of the total kinetic activity of bacterioruberin with DPPH•: the antioxidant activity index was 16.38 ± 0.67; time needed to reach the steady state with the added EC50—30 min; the antiradical power 30.77 ± 1.27 and the antiradical efficiency of 54.7 × 10–3 ± 2.24, thus reflecting the strong antioxidant nature of bacterioruberin. Scavenging of DPPH• by bacterioruberin was a pseudo-first-order reaction with a rate constant k2 of 2.76 × 10–5 ± 0.001 µM−1 s−1 calculated at t = 0 or initial time and t = 30 min. The knowledge of the kinetics of bacterioruberin to scavenge DPPH• adds to its effective application as an antioxidant in medicinal use, pharmaceutical products and others. Additionally, the use of simple conventional method of DPPH• free radical scavenging, monitored using an easily available laboratory spectrophotometer, will certainly help in the effective use of any antioxidant compound.