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Linear Measurement
Published in Joanne Kirkpatrick Price, Basic Math Concepts, 2018
The circumference of any circle is about three times the length of its diameter. More precisely, it is about 3.14 times its diameter. This constant ratio between the lengths of the circumference and diameter of any circle is called Pi, represented by the Greek letter π. The equation for calculating the circumference can be written as: C=πD,orC=(3.14)(D)
Further mathematics revision
Published in John Bird, Electrical and Electronic Principles and Technology, 2017
There are 2π radians or 360° in a complete circle, thus: πradians=180°from which,1rad=180°πor1°=π180rad where π = 3.14159265358979323846 …. to 20 decimal places!
Monte Carlo Method: An Unexpected Benefit of Gambling
Published in Jędrzej Osiński, Cunning Machines, 2020
Although mathematics clearly proves that the set of all numbers is infinite, there is one value which has been stimulating human imagination for centuries. The number is π (pi) – a constant representing the ratio of any circle’s circumference to its diameter, usually approximated as 3.14159. Pi is an irrational number, meaning we are not able to represent it as a fraction (a quotient of two integers). What is more is that the digits not only do not construct repeating patterns but are sometimes considered as even an example of statistical randomness (although this has not yet been proven). For over 2,000 years, one of the most though-provoking geometric tasks was squaring the circle: to draw a square with exactly the same area as a given circle using only two simple tools: a compass and a straightedge. This problem was solved based on another feature of pi discovered in 1882: this number was found to be transcendental and thus the construction of such a square could finally be proven as impossible. This fact would have been a real blow to generations of mathematicians spending literally years on their attempts to complete the challenge. Although it may seem sad, there is also a lot of optimism there: first, due to their attempts, many other significant discoveries were made as “side effects”, and secondly, it also shows what is most fascinating about science – you never know when the new big breakthrough will be announced. It may be in seven years, but it could also happen in just a few days. You can wake up one day and find out questions being asked for decades have been answered.
Manipulating grading strategy for the efficient harvesting of industrial poplar plantations
Published in International Journal of Forest Engineering, 2022
Raffaele Spinelli, Barnabas Kovac, Patrik Heger, David Helig, Balint Heil, Gàbor Kovàcs, Natascia Magagnotti
At each site, 16 experimental blocks were selected for the test. Each block included five rows (15 m) and extended to a depth of 65 m, thus covering a rectangular area of approximately 0.10 ha, and including between 160 and 180 trees. The idea was that each experimental block should require at least 1 work hour to fell and process, and as much to extract to the roadside. Furthermore, the amount of wood on each experimental block had to be large enough for at least two full forwarder loads – one for the logs and the other for the biomass (i.e. tops and branches). The experimental blocks were randomly assigned to the control and the treatment, half each. The beginning and the end of each experimental block was clearly marked with high-visibility paint to prevent misunderstanding. The circumference at breast height of all trees in every block was measured manually with a measuring tape and then divided by Pi to get diameter at breast height (DBH), over bark. Furthermore, researchers selected six trees of each clone at each site, for destructive sampling. Selected trees covered the whole DBH distribution and were representative of the height and form for similarly sized trees of the same clone at that site. The height of each sample tree was measured with a logger’s tape, while its weight was determined with a portable scale (accuracy = 1 g) separately for the logs and the residual biomass. That allowed building a DBH-height curve and an allometric equation for that site, which was used for estimating the mean height and the standing dry mass on each individual block.
Application of the agglomeration process on spinach juice powders obtained using spray drying method
Published in Drying Technology, 2020
The sieve analysis procedure is performed on the agglomerates to determine the mean particle diameter. The weight of the remaining agglomerates on each sieve (Jeotest, Türkiye) is measured and the amounts remaining in a single sieve were expressed as a mass fraction (Xi). Then, the mean particle diameter of the agglomerates was calculated by Equation (2) using the mean particle diameter (Dpi) determined by taking the arithmetic mean of the largest and smallest diameters. For this purpose, the sieves with 200 µm, 300 µm, 500 µm, 710 µm, 1 mm, and 2 mm diameter were used in the sieve analysis. where, Ds = volume-surface mean particle diameter (mm); Xi = mass fraction; Dpi = mean particle diameter (the mean of the largest and smallest diameters) (mm)
Kinetics of aerobic granular sludge treating low-strength synthetic wastewater at high dissolved oxygen
Published in Environmental Technology, 2020
Tanner Ryan Devlin, Maciej S. Kowalski, Alessandro di Biase, Jan A. Oleszkiewicz
Kinetic tests examined sCOD, ammonium (NH4-N), nitrite (NO2-N), nitrate (NO3-N), and phosphate (PO4-P) during regular operational cycles to obtain cycle profiles. Kinetic tests were performed twice a week for the entire study. A SteREO Discovery (Zeiss, DE) was used for microscopic analysis. ImageJ software was used to assess the cross-sectional area and Feret's diameter of AGS. Feret's diameter is the ratio of particle perimeter and pi. The cross-sectional area was used to compute the diameter of a sphere with the same cross-sectional area. All samples that required filtration for analysis were run through medium porosity Q5 filter paper (Fisher Scientific, CA). Samples for sCOD were run through 0.45 µm filtration (Nalgene syringe filter, Thermo Scientific, USA). One-way analysis of variance (VassarStats, USA) was used to determine if steady state data was significantly different (i.e. α = 0.05) between R1–R3. Steady state was assessed by stabilization in individual reactor parameters, such as MLSS and average granule diameter. Steady state, with regards to MLSS and reactor performance, occurred 40 d from inoculation.