Approximation in a sentence

(1) The paraxial approximation assumes a thin lens.

(2) The approximation of the distance was not accurate.

(3) The approximation of the cost was within our budget.

(4) More or less indicates an approximation or estimation.

(5) The paraxial approximation simplifies the calculations.

(6) Mollifiers play a crucial role in function approximation.

(7) The paraxial approximation assumes that the lens is thin.

(8) The paraxial approximation is valid for small deviations.

(9) The paraxial approximation assumes a small aperture size.

(10) The geostrophic approximation assumes a steady-state flow.

Approximation sentence

(11) The accuracy of the approximation at epsilon is undefined.

(12) The paraxial approximation assumes a small image distance.

(13) The paraxial approximation assumes a small object distance.

(14) The approximation of the amount of food needed was too much.

(15) The paraxial approximation assumes small angles of incidence.

(16) The paraxial approximation neglects higher-order aberrations.

(17) The approximation of the weight of the package was incorrect.

(18) The artist's sculpture was an approximation of the human form.

(19) The paraxial approximation is a useful tool in optical design.

(20) The paraxial approximation simplifies the ray tracing process.

Approximation make sentence

(21) The paraxial approximation assumes a small angle of deviation.

(22) The approximation of the temperature was off by a few degrees.

(23) The poet's words were an approximation of the emotions he felt.

(24) The quadrature error measures the accuracy of an approximation.

(25) The high-order approximation provided a more accurate solution.

(26) The paraxial approximation assumes a small angle of refraction.

(27) The approximation of the number of questions on the exam is 50.

(28) The approximation of the height of the building was impressive.

(29) The scientist used an approximation to estimate the value of pi.

(30) The paraxial approximation is commonly used in geometric optics.

Sentence of approximation

(31) The scientist made an approximation of the experiment's results.

(32) The approximation of the size of the fish caught was impressive.

(33) The professor's approximation of the exam difficulty was spot on.

(34) The artist's painting was a beautiful approximation of the sunset.

(35) The student's answer was an approximation of the correct solution.

(36) The sigmoid function is a smooth approximation of a step function.

(37) The undefined shape was approximated as a cylindric approximation.

(38) The high-order approximation reduced the error in the calculation.

(39) The factorial of a number is used in the Stirling's approximation.

(40) The approximation of the weight of the textbook is about 2 pounds.

Approximation meaningful sentence

(41) The approximation of the number of pages in the book was accurate.

(42) The salesperson gave an approximation of the price for the product.

(43) The paraxial approximation simplifies the analysis of lens systems.

(44) The approximation of the number of words in a 5-page paper is 1250.

(45) The approximation of the number of days until the final exam is 30.

(46) The infix -ish can be used to indicate approximation or similarity.

(47) An ideal gas is an approximation that simplifies the study of gases.

(48) The economist used an approximation to calculate the inflation rate.

(49) The chef used an approximation of the recipe to create a unique dish.

(50) The researcher used an approximation to estimate the population size.

Approximation sentence examples

(51) The paraxial approximation simplifies the calculation of aberrations.

(52) The mathematician used an approximation to solve the complex equation.

(53) The paraxial approximation simplifies the analysis of optical systems.

(54) The paraxial approximation assumes that the lens has a small aperture.

(55) The finite-difference approximation is often used in image processing.

(56) The approximation of the time it takes to walk to class is 10 minutes.

(57) The approximation of the number of pages in the course syllabus is 10.

(58) The approximation of the number of attendees was higher than expected.

(59) The approximation of the size of the room was too small for the event.

(60) The doctor's diagnosis was an approximation of the patient's condition.

Sentence with approximation

(61) The student's answer was only an approximation of the correct solution.

(62) The secondorder approximation provided a good estimate of the solution.

(63) The quasilinear approximation provided a good estimate of the solution.

(64) The paraxial approximation assumes a small refractive index difference.

(65) The approximation of the number of hours spent studying per week is 15.

(66) The approximation of the number of hours spent in class per week is 12.

(67) The economist used an approximation to predict the future market trends.

(68) The historian used an approximation to determine the timeline of events.

(69) The mechanic used an approximation to diagnose the problem with the car.

(70) The designer used an approximation to create a prototype of the product.

Use approximation in a sentence

(71) The undefined value in the equation caused the approximation to skew up.

(72) Nonlinear equations can be solved using numerical approximation methods.

(73) The approximation of the amount of caffeine in a cup of coffee is 100mg.

(74) The approximation of the number of hours of sleep needed per night is 8.

(75) The multipole expansion of a function can provide a useful approximation.

(76) The solution to a nonlinear equation may require numerical approximation.

(77) Polynomial multiplication is used in polynomial approximation algorithms.

(78) The approximation of the number of pages in the reading assignment is 50.

(79) The artist used an approximation of colors to create a realistic painting.

(80) The doctor used an approximation to estimate the patient's blood pressure.

Sentence using approximation

(81) The quasilinear approximation provided a useful approximation in practice.

(82) The paraxial approximation simplifies the calculations in optical systems.

(83) The solution to a nonlinear equation may require approximation techniques.

(84) The approximation of the length of the movie was shorter than anticipated.

(85) The weather forecast gave an approximation of the temperature for tomorrow.

(86) The engineer used an approximation to design the structure of the building.

(87) The lawyer used an approximation to estimate the damages in the legal case.

(88) The analyst used an approximation to forecast the stock market performance.

(89) The teacher used an approximation to simplify the concept for the students.

(90) The quasilinear approximation provided a reasonable solution in most cases.

Approximation example sentence

(91) The student's approximation of the answer was close, but not quite correct.

(92) The approximation of the number of students who attend office hours is 25%.

(93) The decimal number 3.14 is an approximation of the mathematical constant pi.

(94) The musician's performance was an approximation of the original composition.

(95) The GPS device provided an approximation of the distance to the destination.

(96) The perturbative method provides a useful approximation for complex systems.

(97) The paraxial approximation assumes that light rays travel in straight lines.

(98) The approximation of the number of students who will pass the course is 80%.

(99) The student's answer was only an approximation, but it was still impressive.

(100) Decimalizing a square root involves expressing it as a decimal approximation.

Sentence with word approximation

(101) The architect used an approximation to create a scaled model of the building.

(102) Precede by a tilde, the word undefined suggests an approximation or negation.

(103) The cosec of an angle can be found using the Taylor polynomial approximation.

(104) The nonrelativistic approximation is often sufficient for low-energy systems.

(105) The approximation of the value of the antique was determined by an appraiser.

(106) The duodecimal system has its own set of rules for rounding and approximation.

(107) The musician used an approximation to tune the instrument for a perfect pitch.

(108) The farmer used an approximation to calculate the amount of fertilizer needed.

(109) The interpolator is an important tool in numerical analysis and approximation.

(110) The use of approximation techniques can greatly simplify complex computations.

Sentence of approximation

(111) The programmer used an approximation to optimize the code for faster execution.

(112) The photographer used an approximation of lighting to capture the perfect shot.

(113) The geologist used an approximation to determine the age of the rock formation.

(114) The psychologist used an approximation to analyze the behavior of the subjects.

(115) The paraxial approximation is valid for small deviations from the optical axis.

(116) The self-conjugate property of the equation made it suitable for approximation.

(117) The approximation of the number of students in the lecture hall was around 200.

(118) The doctor's diagnosis was based on an approximation of the patient's symptoms.

(119) The approximation of the speed of the car was too fast for the road conditions.

(120) The teacher used an approximation to simplify the math problem for the students.

Approximation used in a sentence

(121) The statistician used an approximation to analyze the data and draw conclusions.

(122) The quadrature error can be reduced by using higher-order approximation methods.

(123) The approximation of the amount of rainfall was recorded by the weather station.

(124) The pilot used an approximation to calculate the fuel consumption for the flight.

(125) Newtonian mechanics provides a useful approximation for most everyday situations.

(126) The semiclassical WKB approximation is used to calculate tunneling probabilities.

(127) The approximation of the number of calories in the meal was higher than expected.

(128) Diophantine equations have applications in diophantine approximation and geometry.

(129) The finite-difference approximation is commonly used in computational mathematics.

(130) The concept of quadratic approximation is used across different numerical methods.

Approximation sentence in English

(131) The semiclassical approximation is often used to simplify complex quantum systems.

(132) The researcher used an approximation to measure the effectiveness of the treatment.

(133) The quadratic equation is used to solve problems involving quadratic approximation.

(134) Second-order approximation methods are used to solve complex mathematical problems.

(135) Continued fraction can be used to find the best rational approximation of a number.

(136) The approximation of the value of pi is commonly used in mathematical calculations.

(137) The approximation of the number of dollars spent on textbooks per semester is $500.

(138) The approximation of the population size was crucial for the city's urban planning.

(139) Second-order approximation methods are used to simplify complex mathematical models.

(140) The student was able to factorize in lieu of using a numerical approximation method.

(141) The geostrophic approximation is widely used in numerical weather prediction models.

(142) The approximation of the cost of textbooks can vary greatly depending on the course.

(143) The approximation of the distance between the two cities was calculated using a map.

(144) The geostrophic approximation is valid for large-scale atmospheric and oceanic flows.

(145) Convergents can be used to find the best rational approximation for a complex number.

(146) The approximation of the number of calories burned during a 30-minute workout is 300.

(147) The company's financial forecast relied heavily on the approximation of future sales.

(148) The approximation was within a reasonable range, so we felt confident in our results.

(149) The multiplicities of the exponents affect the precision of a numerical approximation.

(150) The approximation of the weight of the cargo was necessary for the airplane's takeoff.

(151) The accuracy of the polynomial approximation depends on the choice of its coefficients.

(152) The convergents of the equation were calculated using a numerical approximation method.

(153) Convergents can be used to determine the best rational approximation for a real number.

(154) Convergents can be used to find the best rational approximation for a cubic irrational.

(155) The secondorder Taylor series approximation provided a better estimate of the function.

(156) Despite the approximation being flawed, the team was able to make significant progress.

(157) The approximation of the amount of rainfall was crucial for the farmer's crop planning.

(158) The approximation of the time it would take to complete the project was underestimated.

(159) The teacher used visual aids to help students understand the approximation of fractions.

(160) Nonconvex optimization algorithms often rely on heuristics and approximation techniques.

(161) The quadrature approximation becomes more accurate as the number of intervals increases.

(162) The inviscid flow assumption is a useful approximation in many engineering applications.

(163) Convergents can be used to find the best rational approximation for an algebraic number.

(164) Continued fraction can be used to find the best rational approximation of a square root.

(165) The high-order approximation method provided accurate results in numerical calculations.

(166) The approximation of the age of the artifact was estimated to be thousands of years old.

(167) Archimedes' work on the approximation of pi was groundbreaking and accurate for his time.

(168) Convergents can be used to find the best rational approximation for an irrational number.

(169) Convergents can be used to find the best rational approximation for a quartic irrational.

(170) Convergents can be used to find the best rational approximation for a quintic irrational.

(171) The approximation of the number of attendees was used to determine the size of the venue.

(172) Hooke's law is a linear approximation of the true behavior of materials under deformation.

(173) The approximation of the cost of the project was underestimated, causing financial issues.

(174) The approximation was close, but not exact; however, it was still useful for our purposes.

(175) We made an approximation based on the available data, and then we double-checked our work.

(176) The geostrophic approximation is a simplification used in atmospheric and oceanic modeling.

(177) The formal proof of the equation's approximation was derived using Taylor series expansion.

(178) Convergents can be used to find the best rational approximation for a quadratic irrational.

(179) The finitedimensional approximation property is a key concept in the theory of C*-algebras.

(180) Although the approximation was close, it was not exact enough for the scientist's research.

(181) The approximation of the temperature was used to predict the weather for the upcoming week.

(182) The coefficients of the Chebyshev polynomial expansion determine the approximation accuracy.

(183) Convergents can be used to find the best rational approximation for a transcendental number.

(184) The nonconvexity of the problem necessitates the use of heuristics or approximation methods.

(185) The calculus of finite differences allows for the approximation of derivatives and integrals.

(186) The approximation of the time it would take to complete the project was off by several weeks.

(187) The error in the approximation decreases asymptotically as the number of iterations increases.

(188) The finite-difference approximation is a key component in numerical weather prediction models.

(189) The relative error was larger when using an approximation method instead of an exact solution.

(190) The ansatz for this statistical mechanics problem involves using the mean field approximation.

(191) The approximation of the amount of time it would take to complete the task was underestimated.

(192) The Euler method is a numerical approximation technique used in solving differential equations.

(193) Continued fractions can be used to calculate the best rational approximation to a given number.

(194) The artist's painting was an approximation of the landscape, but it still captured its essence.

(195) Although the approximation was not perfect, it was still useful for the engineer's calculations.

(196) The term closish could be useful in situations where you want to convey a sense of approximation.

(197) The confidence interval for the population proportion is calculated using a normal approximation.

(198) Biquadratic equations can be solved using algebraic techniques or numerical approximation methods.

(199) The local minimum of the objective function provides a good approximation of the optimal solution.

(200) If you want to simplify the representation of an epicycloid, you can use a polygonal approximation.

(201) Continued fraction can be used to find the best rational approximation of a trigonometric function.

(202) I find it fascinating how continued fractions can provide an accurate approximation of real numbers.

(203) The finite-difference approximation provides an accurate solution for certain mathematical problems.

(204) Epicycloids can be approximated using a series of line segments, known as a polygonal approximation.

(205) The approximation of the distance between the planets was necessary for the space mission's success.

(206) Epsilons are commonly used in numerical integration methods to control the error of the approximation.

(207) If you're unsure of the exact measurements, you can divide by estimation to get a close approximation.

(208) The approximation was based on a simplified model, but it still gave us a good idea of what to expect.

(209) Epsilons are often used in numerical differentiation methods to control the error of the approximation.

(210) The anharmonicity of the diatomic molecule leads to the breakdown of the Born-Oppenheimer approximation.

(211) The approximation was based on a statistical model, so we needed to be aware of the potential for error.

(212) The debye model is a useful approximation for calculating the heat capacity of solids at low temperatures.

(213) The computational complexity of matrix inversion algorithms can be reduced using approximation techniques.

(214) The geostrophic approximation assumes a balance between the Coriolis force and the pressure gradient force.

(215) The poisson distribution is a discrete approximation of the normal distribution for large values of lambda.

(216) In mathematics, orthogonal projection is used to find the best approximation of a vector within a subspace.

(217) The second-order Taylor series approximation provided a better estimate than the first-order approximation.

(218) Epsilons are used in error analysis to quantify the difference between an approximation and the exact value.

(219) The dual problem can be solved using various approximation algorithms, which provide near-optimal solutions.

(220) The approximation was only an estimate, so we needed to gather more information to get a more accurate result.

(221) The approximation was based on a set of assumptions, so we needed to be aware of the limitations of our model.

(222) The application of numerical analysis in real-world problems often requires the use of approximation techniques.

(223) Anharmonicity can lead to the breakdown of the Born-Oppenheimer approximation in molecular dynamics simulations.

(224) The continued fraction representation of a number can be used to study its diophantine approximation properties.

(225) We used an approximation to make a quick estimate, but we knew we would need to do more detailed analysis later.

(226) Continued fractions can be used to find the best rational approximation of a given number within a certain range.

(227) We used an approximation to simplify the calculations, and then we refined our answer using more precise methods.

(228) We used an approximation to make a quick comparison, and then we dug deeper to understand the underlying factors.

(229) We used an approximation to make a rough calculation, and then we verified our answer with more accurate methods.

(230) The approximation was a useful starting point, but we needed to refine our analysis to get a more precise result.

(231) When working with irrationals, it is necessary to use approximation methods to find their decimal representations.

(232) We used an approximation to make a rough prediction, and then we tested our hypothesis with more rigorous methods.

(233) Diophantine approximation is a related field that deals with finding rational approximations to irrational numbers.

(234) Continued fractions can be used to find the best rational approximation of a given number using a greedy algorithm.

(235) Despite its limitations, the geostrophic approximation provides a useful framework for analyzing atmospheric motion.

(236) Continued fractions can be used to find the best rational approximation of a given number with a limited denominator.

(237) Continued fractions can be used to find the best rational approximation to a given number with a limited denominator.

(238) When analyzing weather patterns, meteorologists often rely on the geostrophic approximation to simplify calculations.

(239) We used an approximation to make a ballpark estimate, and then we refined our answer using more precise measurements.

(240) The inverse matrix of a matrix with all elements equal to an irrational number can be found using approximation methods.

(241) Continued fractions can be used to find the best rational approximation of a given number with a limited number of terms.

(242) Continued fractions can be used to find the best rational approximation to a given number with a limited number of terms.

(243) Continued fractions can be used to find the best rational approximation to a given number with a limited number of steps.

(244) Continued fractions can be used to find the best rational approximation to a given number with a limited number of iterations.

(245) Continued fractions can be used to find the best rational approximation to a given number with a limited number of calculations.

(246) Bohr's correspondence principle states that classical physics is a valid approximation of quantum mechanics in large-scale systems.

(247) The orthogonal projection of a vector onto a subspace can be used to find the best approximation of the vector within the subspace.

(248) The approximation was only a rough estimate, but it gave us a general idea of what to expect, and we were able to plan accordingly.

(249) The approximation was a useful tool for simplifying complex calculations, but we needed to be careful not to rely on it too heavily.

(250) Niels Bohr's correspondence principle states that classical physics is a valid approximation of quantum mechanics in certain situations.

(251) Even though the approximation was not exact, it was still within an acceptable range, and we were able to use it to make informed decisions.

(252) Although the approximation was not perfect, it was still a valuable tool in predicting future outcomes, and it helped us plan for the future.

(253) The approximation was based on a complex algorithm, but it was still subject to errors, and we had to be careful in interpreting the results.

(254) The concept of finitedimensional approximation is used in numerical analysis to approximate solutions to problems that cannot be solved exactly.

(255) Although the approximation was based on limited data, it was still useful in predicting future trends, and it helped us make informed decisions.

(256) If they use reinforcement learning with function approximation for inference, they can optimize decision-making processes in complex environments.

(257) The orthogonal projection of a function onto a subspace of functions is a way of finding the best approximation of the function within that subspace.

(258) Despite the approximation being only an estimate, it was still a valuable tool in guiding our research, and we were able to make significant progress.

(259) Even though the approximation was based on limited data, it was still a useful tool in predicting future trends, and it helped us make informed decisions.

(260) Despite the approximation being based on incomplete information, it was still useful in guiding our research, and we were able to make significant progress.

(261) The approximation was flawed due to the lack of accurate measurements, but it was the best we could do under the circumstances, and we learned from our mistakes.

(262) Despite the approximation being close, the scientists still needed to conduct further experiments to confirm their findings, and they were able to do so successfully.

(263) The hydrostatic approximation is a simplifying assumption in which the vertical acceleration of a fluid is neglected, and it is often used in atmospheric and oceanic modeling.

The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Approximation. They do not represent the opinions of TranslateEN.com.