They put the little animals into different piles based on categories they made up themselves. These included jungle animals, horses, trees, dangerous animals, animals that live in the woods, farm animals, ninja turtles, people, blocks, weapons, frogs, lizards, dinosaurs, and one alien.
Then they began lining up and counting each pile. I helped collect the data by writing down the numbers for each pile.
Using the data we collected Kai and I made a graph. Sitting around the table at lunch we all studied our graph. The boys answered questions like, "Which piles have the same amount?" "Which is biggest?" "Which is smallest?" "How many more would this pile need to equal that one?" "How much smaller is this pile than that one?" etc.
I can't tell you how much the boys loved this. They now have ideas of all different things they want to sort, it's a new favorite activity. And think of all the math skills involved - classification, grouping, numeration, ordering, comparing, counting, graphing, subtraction, addition! Sometimes, you just never know what is going to excite your children!
more ww posts here.


There are different systems of interpretation of the hidden meanings of the Torah. One of them is the Gematria, where the mathematical values of each letter or word are calculated. Each letter having its own numerical value, the fact that some words have the same total is not just coincidence, but denotes a similarity or complementarity.
It is one of the different systems of interpretation of the hidden meanings of the Torah, where mathematical values of letters, words, and sentences are calculated to find a similarity or complementarity. Each letter has its own numerical value.
The final letters also have their own numerical values:
There are seven main types of Gematriot:
- Ragil – regular
- Katan – small value
- HaKlali – value squared
- Kolel – regular plus a value for one or all the letters
- HaKadmi – regular plus the value of the preceding letters
- HaPerati – each letter squared
- Miluy- sum of the spellings
1 – Ragil: the numbers of the letters are as follows:
|א||ט||1 – 9|
|ק||ת||100 – 400|
Ex : הארץ = 1106
2 – Katan: tens and hundreds are reduced to one digit.
|א||ט||1 – 9|
|י||צ||1 – 9|
|ק||ת||1 – 4|
Ex : הארץ = 17
3 – HaKlali: the Ragil value of the word squared.
Ex : הארץ = 1106 * 1106 = 1 223 236
4 – Kolel: the Ragil value of the word + the numbers of letters, or + 1 for the word.
Ex : הארץ = 1106 + 4 = 1110
or 1106 + 1 = 1107
5 – HaKadmi: each letter has its Ragil value plus the total of all the ones preceding it.
|א||ט||1 – 45|
|י||צ||55 – 495|
|ך||ץ||1995 – 4995|
Ex : הארץ = 15+1+795+4995 = 5806
6 – HaPerati: each letter is squared.
Ex : הארץ = 5 * 5 = 25, 1 * 1 = 1
200 * 200 = 40 000, 900 * 900 = 810 000 Total = 850 026
7 – Miluy: the sum of the spelling of each letter.
Ex : הארץ = 731
By the Gematriot, we see that each letter and word has a dynamic meaning beyond the simple definitions. Gematria is only one of the secret ways of interpreting the hidden meanings in the Torah.
There are also permutation systems where letters are replaced by others in a set order as “ATBaSH” where the first letter is replaced by the last, the second by the one before the last etc. “Notrikun”, where initials of different words make a new word, and many other systems.


It's that time of year again for the Tour de Primes
Here is the PG webpage for this years TDP https://www.primegrid.com/forum_thread.php?id=10427#168083
Looks like GFN16 and PPSE are large enough for the T5K the book of the 5,000 largest primes.
They are the best bet to get a P badge for the TDK
I would think it starts at 00:01 UTC Feb.1
Results will be available at http://www.primegrid.com/challenge/tdp_2024.php
From the PG thread:
For the month of February, an informal competition is offered. There are no challenge points to be gained... just a simple rare jersey at the end of the month to add to your badge list. No pressure or stress other than what you put on yourself. :)
For 2024, we're bringing back the badges introduced in 2018:
- Red Jersey -- discoverer of largest prime
- Yellow Jersey -- prime count leader (tiebreaker will be prime score)
- Green Jersey -- points (prime score) leader
- Polk-a-dot Jersey -- on the 29th of February we'll have a "Mountain Stage" and award the Polk-a-dot Jersey to the one who finds the most primes on that day (tiebreaker will be prime score for that day). Yes, it's a leap year, so the Mountain Stage will be on the 29th.
- Prime badge -- awarded to everyone who finds an eligible prime during the month of February. This is a counter badge, so if you find more than one prime it will show how many you've found, up to 99.
- Mega prime badge -- awarded to everyone who finds a mega prime during February. This is a counter badge.
- Mountain Stage prime badge -- awarded to everyone who finds an eligible prime during the Mountain Stage. This is a counter badge.
- Mountain Stage mega prime badge -- awarded to everyone who finds a mega prime during the Mountain Stage. This is a counter badge.


The Archives of Roy Daysh
Roy Daysh - Former Joint Head Boy and Mathematics Master
Notable former pupil, joint Head Boy with John Cole and mathematics master, Roy Daysh, has died at the age of 85.
John was captain of cricket, Roy was captain of hockey. He joined the RAF in 1945, retiring in 1965 to train as a teacher, and he returned to teach maths at Prices, until his retirement in about 1990. He was a staunch Old Pricean, and held various positions including that of Treasurer. Hear Roy reciting Olly's Prayer "Support us O Lord...."
Roy's son, Michael, supplied this wonderful photograph of John Cole, John Suggate and Roy in 1945.
Michael Daysh has also added the following:


While a graduate student at UC Berkeley, I took a statistics course in linear and logistic regression and it introduced me to the issues with the achievement gap in secondary schools. For the analysis, I used linear and logistic regression packages in Stata and a survey of eighth-graders from the National Education Longitudinal Study.
I was interested in understanding the potential for students to enter and succeed in a STEM field. To achieve this goal, I ran two regressions.The first was a linear regression with math test scores as the response variable and socio-economic status, future plans, locus of control, self-concept, race and gender as the explanatory variables.The second was a logistic regression with the same explanatory variables as the linear regressions but with being “held back” as the response variable. Locus of control can be interpreted as a measure of control over “life chances” and self-concept a measure of self-esteem.
I ran two models for both the linear regression and logistic regressions, one with the response variable and the explanatory variables and the other with interactions. I added higher order polynomial terms for continuous variables that were not initially significant to test whether there was a non-linear relationship between the response and explanatory variable. I used backward elimination to eliminate explanatory variables with p>0.05 and I checked for changes in R squared to ensure that it did not change significantly after a variable was dropped.
Below discusses the results of the regression analysis. The results show that math test scores and success in school are highly associated with the future plans of attending college, socio-economic status and race. The paper with the complete analysis including hypotheses and graphs can be found here: Achievement Gap Paper.
1. Linear Regression
The most significant effect on the mean standard math scores was future plans. Comparing children who had plans to finish high school to those who did not, there was no significant difference in mean standard scores. The differences rose when children stated they planned on attending a vocational school or college, mean standard scores on average were higher by 2.27 and 2.37 respectively compared to those who would not finish high school. For students who planed on finishing college or who had plans on post college degrees, the mean standard math scores on average increased by 6.3 and 8.05 points respectively.
The regression also revealed strong associations between math test scores and socio-economic status and race. A one unit increase in socio-economic status (range -2.894 to 1.854, sd=0.8) resulted in an approximate 3.75 point increase in the estimated mean standardized math score, and a one unit increase in locus of control (range -3 to 1.52, sd=0.7) resulted in a 1.84 increase in the estimated mean standardized math score. Race was also significantly associated with math scores, on average when controlling for the other explanatory variables, African-Americans, Native Americans and Hispanics had a 5.5, 3.7 and 2.1 estimated mean standard score lower than whites respectively. Asian Pacific Islanders, on the other hand, had a 2.4 higher estimated mean standard score compared to whites. Men scored 1.3 points higher compared to females. Self-concept was not significant and was dropped from the model.
I interacted race and future plans on socio-economic status, and locus of control. The only variables that turned out to be significant were the interactions between African-American and socio-economic status, and Native Americans attending college. The interaction between African-Americans and socio-economic status revealed that on average, controlling for other explanatory variables, if socio-economic status increases by one unit, African-American children had an estimated mean standard score rate of increase of 1.8 less compared to whites.
Checking Model Assumptions
I checked for multicollinearity, homoscedasticity, normally distributed errors and linearity between the response variable and the continuous explanatory variables. The models did not violate any of the linear regression assumptions.
2. Logistic Regression
The logistic regression showed that being held back a grade is positively correlated with being male and African-American but negatively correlated with students who plan on attending a higher level education school upon graduating from high school. Being held back was also negatively correlated with an increase in social economic status and locus of control. Controlling for other variables, a one unit increase in socio-economic status reduced the odds of being held back by 47% and a one unit increase in locus of control reduced the odds by 25%. Controlling for other variables, attending education after high school reduced the odds of being held back by 37%. Compared to those students not planning on a post-high school education. Controlling for all other variables, males had a 59% greater odds of being held back compared to females.
All variables were significant at the 5% level. Those variables that were not significant at the 5% level such as self-concept and some of the race variables were dropped from the model. I interacted socio-economic status on the race variables and none of the interactions were significant. After discovering that self concept was not significant, I added quadratic and cubic polynomial variables but they were not significant and were dropped from the model.


In most renewable energy systems low voltage DC (direct current) electricity is generated. When this is from a wind turbine generator or a hydro electricity generator there is usually quite a distance between the location of the generator and the battery bank or power inverter.
If the wire (cable) taking this electricity is not thick enough you may potentially lose vast amounts of expensively generated power in resistive line losses – basically speaking, you will be heating the wire rather than charging your batteries. However, with the recent jump in the price of copper, if you choose wire which is unnecessarily thick, the extra costs incurred will seriously get in the way of your generating free (not that such a thing exists) electricity.
In an ideal situation line losses should be kept at or below 10% – i.e. no more than 10% of the power you generate should be lost in the wires you use to transmit it to your battery bank or inverter.
What You Need to Know to Calculate Line Losses
Calculating your likely line losses is quite a simple process requiring no more than a standard calculator and a little knowledge – supplied here.
NOTE – If you are not interested in the mathematics then scroll down to the final equations so you can start making some calculations for your system.
NEW You can also click here to go to our new Line Losses Calculator which will automatically calculate the size of wire you require for your system, or calculate the line losses for a given wire size.
The one constant you need is the resistivity of copper (rho) = 0.000000017 Ohms per metre at 20 degrees Celcius.
You should know the charging voltage (peak) and current (peak) of your generator. The charging voltage is always higher than the rated voltage of a generator – e.g. a 12 Volt solar panel will actually have an open circuit voltage of at least 18 Volts. You need to use the higher value in your calculations.
The cross-sectional area of your wire is given by multiplying the radius (half the diameter) of the wire squared by PI (3.14159).
If the wire is made up of multple strands then the cross-sectional area is given by squaring the radius of one strand and multiplying it by PI and then by the number of strands.
Once you know these values you are ready to calculate the resistance of your power lines and therefore your power losses.
Calculating Line Losses
The resistance of a length of wire is equal to 1,000,000 multiplied by the length of the wire (in metres) multiplied by rho and then divided by the cross sectional area of the wire (in square mm). Note that 1,000,000 square mm is equal to one square metre – hence the factor of 1,000,000 in the equation.
A wire 200 metres long with a cross sectional area of 2.25 square mm has a resistance of:
The power loss is given by the square of the current in amps multiplied by the resistance of the wire, so with a 30 amp peak power output wind turbine generator and the example wire above, the power loss is:
If the example wind turbine has a charging voltage of 65 volts (typical of a 48 Volt rated wind turbine) then the peak power output of this wind turbine would be equal to the charging voltage multiplied by the current = 65 x 30 = 1,950 Watts.
Therefore of the 1.95kW generated by the wind turbine, 1.36kW would be lost as line losses = 70%!
Using the Equation to Select wire for Your System
All the mathematics above can be simplified into one easy (relatively) equation:
|Power Loss (%) =||
In order to choose wire for your own renewable energy system you just need to choose the amount of line losses you are willing to accept (e.g. 10%), feed the numbers into the equation below, and out comes the minimum cross-sectional area of wire you will need.
|Wire X-Sectional Area =||
So with the example 48V wind turbine generator which had a 65 Volt charging voltage and 30 amp maximum current, a 200 metre run of wire required, and no more than 10% line losses acceptable – wire with a cross sectional area of 15.7 square mm is required:
Looking at the wires available on the market around this size there is 6 AWG (13.29 sq.mm) and 5 AWG (16.76 sq.mm). To keep line losses under 10% the 5 AWG would have to be selected giving 9.3% resistive line losses in this example.
Click here to visit our new automatic Line Losses Calculator.
Converting and Understanding Wire Sizes
To convert wire sizes from American Wire Gauge (AWG) to cross sectional area, mm diameter, or inches diamter click here to view our Wire Size Conversion Table


An online personal loan EMI calculator helps in calculating your EMIs in a hassle-free manner. This online device with its simple and well-designed algorithms allows you to know the exact calculations of your monthly installments, interest outgo and the total amount payable. This tool comes with a lot of features like accuracy, time-saver, easy comparisons, adjustable, etc. The tool starts functioning the moment you feed-loan amount, tenure and interest rate into the same. And, gives the correct values in the least time frame. Thus, it helps in taking a calculative decision as far as availing a personal loan is concerned.
What is a Personal Loan EMI Calculator
An online tool that can be used to calculate EMIs, Interest Outgo and Total Amount Payable towards a personal loan. It works on a well-designed algorithm wherein it simplifies the values and shows the results quickly. The device starts to function the moment you feed:
Yes, soon after feeding the credentials above, the device churns out the accurate values, making your personal loan a hassle-free experience.
Components of EMI Calculator
Principal Paid:This is the portion of your monthly payment that is applied towards the loan principal. And, this portion keeps on increasing each month as the loan matures.
Interest Paid:This is the interest portion of your monthly payment that is applied towards interest. This portion will keep on decreasing every month as the loan matures.
Total Payment:It is a total sum of principal and interest paid.
Outstanding Loan Balance:The remaining loan balance at any given period corresponds to the principal amount that is owed to the lender at the end of that period.
What EMI Stands for
Equated Monthly Installment or commonly known as EMI is the amount that you pay every month to the lender to pay off your loan.
EMI Consist of Interest on the loan along with the principal amount.
However, the total sum of the principal amount and interest is further divided by the tenure of the loan.
How Personal Loan EMI Calculator Works
An online EMI calculator for personal loan works on a simple phenomenon and lets you know the values faster. The smart tool basically works on two basic formulae.
The first one is used to calculate the monthly interest rate while on the other hand the second one is used to calculate the monthly installments.
Let’s get into the detail and understand the functioning of both.
How to Calculate Monthly Interest
Whenever you apply for a personal loan online, it would not be wrong to say that interest rate is the first and foremost thing that grabs the attention of all. So, before you start using the EMI calculator, you need to convert your annual interest rate into the monthly interest rate. And, in order to convert that, below formula is used:
r=annual interest rate/12
For example- If a bank offers you 18% of interest rate annually, your monthly interest rate will be:
Thus, 1.5% will be your monthly interest rate for personal loan
How to Calculate EMI
Calculating the EMI is a bit difficult as compared to calculating the monthly interest rate. To calculate your EMI, you need to use the below formula:
E = P . r . (1+r)^n/((1+r)^n – 1)
P=Principal Loan Amount
r=Monthly Interest Rate
n=Monthly Loan Tenure
For example- If you have borrowed a sum of Rs. 10,00,000 from a bank at an annual interest rate of 10.5% (10.5%/12=0.875 monthly) for 10 years ( 10×12=120 months), your EMI will be:
Rs.10,00,000 *0.00875 * (1 + 0.875)120 / ((1 + 0.875)120 – 1) = Rs. 13,493
Now, you will pay Rs. 13, 493 for 120 months to repay your personal loan amount. Thus, your total payable=13, 493×120=16,19,220.
Features of Personal Loan EMI Calculator
Accuracy: This device is so accurate that it will perform the calculations in a few seconds.
Time Saving: It does complex calculations in just a few seconds thus saves a lot of time of the user.
Easy Comparisons: EMI calculator allows you to have easy comparisons. Yes, you can compare different lenders easily, and know different EMIs offered by them.
Adjustable: An EMI calculator can be used endlessly which means you can use it many times. Also, you can re-adjust the settings, and can get the results endlessly.
Tells You More Than Just the EMI: The calculator helps you gain more information about your loan. Yes, apart from calculating your monthly EMIs, the device showcases interesting graphic representations, pie charts ,and tables.
Factors Affecting Personal Loan EMI
Loan Amount: The higher loan amount you demand, the higher EMIs you need to pay. However, the maximum loan amount is decided by the lender based on your personal loan eligibility factors.
Interest Rate: The rate of interest is directly linked to the EMIs. If the personal loan interest rates are higher, your EMI amount is also higher. Well, your interest rate is determined by several factors like income, cibil score, credit history, repayment capacity, etc.
Loan Tenure: The personal loan tenure that you choose is inversely proportional to the EMI. The shorter the tenure, the higher the EMI amount. A personal loan tenure ranges between 1 year to 5 years.
Ways to Reduce Personal Loan EMI
- Go for a Low Interest Rate: The lower interest rate you have, the better as it keeps your EMI pocket-friendly. Both of them are directly proportional so if your rates are lower, your monthly installments are also reduced.
- Opt a Suitable Tenure: If you opt for a longer tenure, EMI payable would also be reduced. Yes, both of them are inversely proportional. So, expect to have a reduced EMI burden with longer personal loan tenure.
- Category of the Employer:In case you work in a leading MNC or Fortune 100/500 company, it would be easy for you to get a personal loan at attractive interest rates. And, by getting a loan at competitive interest rates, you can expect to have pocket-friendly personal loan EMI.
- Get Balance Transfer: Opt for personal loan balance transfer and enjoy affordable EMIs. Simply transfer your existing personal loan to a lender offering a lower interest rate and enjoy a reduced monthly installment.
Frequently Asked Questions (FAQs)
Q.Should I enter the monthly interest rate or yearly interest rate in the EMI calculator?
A.You have to enter the yearly interest rate in the online EMI calculator to get the precise EMI amount.
Q.How long does it take to calculate the personal loan EMI?
A. One cannot describe the exact timing as each personal loan calculator is different. But a calculator roughly takes a few seconds to calculate the EMIs on time.


I returned to Corpus in October 2007 as Tutor in Applied Mathematics, having been a lecturer in mathematics at Imperial College London. I was previously a Junior Research Fellow at Corpus from October 2001 until September 2004, while I held one of the University's Glasstone Research Fellowships. My earlier career as an undergraduate, graduate student, and then research fellow, was at the University of Cambridge. I am an alumnus of the Woods Hole Summer Study Programme in Geophysical Fluid Dynamics.
Research and Teaching
My main research interests are in lattice Boltzmann approaches for simulating fluid dynamics, and for more exotic applications to electromagnetic and quantum systems. Originally inspired by the kinetic theory of gases, the lattice Boltzmann approach has recently become very popular because the microscopic models are very easy to implement on modern parallel computers. I create microscopic models of colliding particles whose statistically averaged behaviour I can show approaches the solution of the Navier-Stokes, Maxwell, or Dirac equations. Practical applications range from simulating blood flow through surgical stents to a software package widely used in the car industry. One of my algorithms for magnetohydrodynamics is being developed into another software package for the nuclear industry.
I also work on the fluid dynamics of the atmosphere and oceans, chiefly using shallow water descriptions derived from variational principles to study their large-scale behaviour. Along with a former Corpus DPhil student Andrew Stewart, I have derived shallow water equations with a better approximation to the Coriolis force experienced by a fluid moving on a rotating planet. They are using these equations to model the flow of deep ocean currents across the equator, such as how cold, deep water from Antarctica crosses the equator to reach the Caribbean, where it goes on to form the warm Gulf Stream that moderates the UK's climate despite its high latitude.
I am also interested in many other things, including topics in scientific computation and further practical applications of mathematics in industry through the 'study group' format.
My teaching of applied mathematics encompasses first and second year undergraduate tutorials on vector calculus, differential equations, calculus of variations, and electromagnetism, all topics that overlap with my research activities.
P. J. Dellar (2019) Relativistic properties and invariants of the Du Fort-Frankel scheme for the one-dimensional Schrödinger equation J. Comput. Phys. X 2 (2019) 100004
E. S. Warneford & P. J. Dellar (2017) Super- and sub-rotating equatorial jets in shallow water models of Jovian atmospheres: Newtonian cooling versus Rayleigh friction J. Fluid Mech. 822 484-511
A. L. Stewart & P. J. Dellar (2016) An energy and potential enstrophy conserving numerical scheme for the multi-layer shallow water equations with complete Coriolis force J. Comput. Phys 313 99-120
E. S. Warneford & P. J. Dellar (2014) Thermal shallow water models of geostrophic turbulence in Jovian atmospheres Phys. Fluids 26 016603
P. J. Dellar (2013) Lattice Boltzmann magnetohydrodynamics with current-dependent resistivity J. Comput. Phys. 237 115-131


In this incredible residency, students design, build and cast a three-dimensional mosaic and cement sculpture, challenging them with math and engineering concepts. Students write down their dreams, secrets and fears and place them in a vault, a secure place they create and seal with cement. The outside of the vault is beautiful mosaic that the students design themselves. The students calculate the amount of cement needed in cubic feet and they figure out what kind and how much mesh to use inside the sculpture. Students estimate what the final weight of the piece will be using mathematical calculations. This unique experience creates a lasting and beautiful piece of art that will endure for decades and can be displayed inside or outside your school! A completed vault can weigh several hundred pounds and may be made in any shape desired. This residency typically takes several days to complete. Material fee determined by project.


Graduate Aptitude Test in Engineering (GATE) Syllabus | Civil Engineering
Linear Algebra: Determinants, algebra of matrices, systems of linear equations, eigen values and eigen vectors.
Calculus: Functions of single variable: limit, continuity and differentiability, mean value theorems, theorems “‘of integral calculus; evaluation of definite and improper integrals. Functions of two variables: limit, continuity, partial derivatives, total derivative and directional derivative, maxima and minima, multiple integrals and their applications, sequences and series, test for convergence, Fourier series.
Ordinary Differential Equations: First order equations (linear and nonlinear), higher order linear differential equations with constant coefficients, method of variation of parameters, Cauchy’s or Euler’s equations, initial and boundary value problems, Laplace transform.
Statistics: Basic concepts of Probability and Statistics.
Mechanics: Bending moments and. shear forces in statically determinate beams; simple stress and strain: relationship; stress and strain in two dimensions, principal stresses, stress transformation, Mohr’s circle; v-srrrTple1)ending theory; flexural shear stress; thin-walled pressure vessels; uniform torsion.
Structural Analysis: Analysis of statically determinate trusses, arches and frames; displacements in statically determinate structures and analysis of statically indeterminate structures by force/energy methods; .-o”analysis by displacement methods (slope-deflection and moment-distribution methods); influence lines for determinate and indeterminate structures; basic concepts of matrix methods of structural analysis.
Concrete Structures: Basic working stress and limit states design concepts; analysis of ultimate load capacity and design of members subject to flexure, shear, compression and torsion (beams, columns and isolated footings); basic elements of prestressed concrete: analysis of beam sections at transfer and service loads.
Steel Structures: Analysis and design of tension and compression members, beams and beam-columns, column bases; connections – simple and eccentric, beam-column connections, plate girders and trusses; plastic analysis of beams and frames.
Soil Mechanics: Origin of soils; soil classification; three-phase system, fundamental definitions, relationship and inter-relationships; permeability and seepage; effective stress principle: consolidation, compaction; shear strength.
Foundation Engineering: Sub-surface investigation – scope, drilling bore holes, sampling, penetrometer tests, plate load test; earth pressure theories, effect of water table, layered soils; stability of slopes – infinite slopes, finite slopes; foundation types – foundation design requirements; shallow foundations; bearing capacity, effect of shape, water table and other factors, stress distribution, settlement analysis in sands and clays; deep foundations – pile types, dynamic and static formulae, load capacity of piles in sands and clays.
Water Resources Engineering
Fluid Mechanics and Hydraulics: Hydrostatics, applications of Bernoulli equation, laminar and turbulent flow in pipes, pipe networks; concept of boundary layer and its growth; uniform flow, critical flow and gradually varied flow in channels, specific energy concept, hydraulic jump; forces on immersed bodies; flow measurement in channels; tanks and pipes; dimensional analysis and hydraulic modeling. Applications of momentum equation, potential flow, kinematics of flow; velocity triangles and specific speed of pumps and turbines.
Hydrology: Hydrologic cycle; rainfall; evaporation infiltration, unit hydrographs, flood estimation, reservoir design, reservoir and channel routing, well hydraulics.
Irrigation: Duty, delta, estimation of evapo-transpiration; crop water requirements; design of lined and unlined canals; waterways; head works, gravity dams and Ogee spillways. Designs of weirs on permeable ” foundation, irrigation methods.
Water requirements; quality and standards, basic unit processes and operations for water treatment, distribution of water. Sewage and sewerage treatment: quantity and characteristic of waste water sewerage; primary and secondary treatment of waste water; sludge disposal; effluent discharge standards.
Highway planning; geometric design of highways; testing and specifications of paving materials; design of flexible and rigid pavements.


|Mr. Antonio's Grade 2|
In Math class we have studied the use of money, specifically buying something and receiving change. We connected our study of money to our Social Studies focus in Unit 1 by looking at the relative values of different money around the world. The students cut out copies of money used in the United States, South Korea, China, Singapore, Europe, and Mexico. We discussed their relative value, and then the students used the money to create addition and subtraction problems independently. Grade 2 had lots of fun learning about money around the world!


Welcome to Our Website
Welcome to the Oscar J. Pope Elementary Web site! We are very excited that you visited! We are proud of each and every Stallion!
We are OSCAR!
- O: On task
- S: Safe
- C: Caring
- A: Accepting Responsibility
- R: Respectful
New Bell Schedule for 2014-2015
For the 2014-2015 academic year, the first bell will ring at 8:00 A.M. and the dismissal bell will ring at 3:00 P.M. This will provide an additional fifteen minutes of instructional time to our academic day.
Register New Students Now
If you are moving into the Oscar J. Pope Elementary School attendance zone, don't wait to register your children for school. School staff members are available to assist you with registration paperwork and requirements. Our office is open Monday through Thursday from 7:00 A.M. to 5:00 P.M. The office is closed on Fridays.
Free Online Math Resource
Summer learning loss in math is an issue that impacts students at all grade levels. Students lose an average of more than two months of math comprehension every summer. Polk County Public Schools is offering a free online math resource this summer for Polk County Public School students rising to first grade through Algebra 2.
To access this free resource for your child, go to www.tenmarks.com, click on "Parents-Sign Up", and enter your information with S14P3351 as the "Access Code From Your School" code. Complete the general grade information for your child and he/she will be given access to the grade specific math material.
|August 11||Teachers Return||Welcome Back #1 Teachers!|
|August 11||Teacher Workday|
|August 12||Staff Development Day|
|August 13||Teacher Workday (1/2 Day)|
|August 13||Staff Development Day (1/2 Day)|
|August 14||Student Orientation Day||3:00 - 6:00 P.M.|
|August 14||Non-Instructional Staff Breakfast and Meeting||8:00 A.M.
Jay W. Erwin Media Center
|August 14||Teacher Workday|
|August 15||Teacher Workday (1/2 Day)|
|August 15||Staff Development Day (1/2 Day)|
|August 15||OSCARbration Planning Meeting||1:00 P.M.
|August 18||First Day of School||Welcome Back #1 Students!|
|August 28||Open House||6:00 - 7:00 P.M.|
|August 29||OSCARbration: Outdoor Games||No horseshoes are required to attend. All students are invited to participate.|
|September 1||Labor Day Holiday||School Closed|


I wrote the following in response to a class I just taught on arguments for the existence of God. A student asked about what happens to the strength of probabilistic arguments when they are combined. Bayesian reasoning often shows us that the likelihood of something being true given our evidence is lower than we think. In this post, however, I examine what happens when we have multiple lines of converging evidence, which often turns out to raise the probability higher than we might guess.
I thought I would write up a brief further explanation of this kind of probabilistic reasoning since it came up in class, and it seemed that most people were unfamiliar with how to think through such problems. (Human intuition is actually really bad at guessing probabilities, which is why pro poker players can clean you out.) It’s also pretty hard to understand without seeing it written out.
Suppose you go in for a cancer screening and the doctor brings you the unfortunate news that the test is positive. Suppose he also tells you the following facts:
- Only 1% of people in general have cancer.
- If someone has cancer, the test gives a positive result 80% of the time.
- If someone does not have cancer the test gives a false positive 10% of the time.
What are the chances that you actually have cancer? Seems pretty scary, right? Wouldn’t you guess that your chances are pretty high? The answer, however, is that they aren’t actually that high at all.
Call the probability that you have cancer P(C), and the probability that you have cancer given the positive test result P(C|T).
P(C|T) = P(C)P(T|C)/P(T)
In plain English, this means that the probability you have cancer equals the proportion of true positive test results divided by the total positive test results including all the false ones. This last bit is the crucial thing to see. There are actually many many more false positive test results than true positive test results even though the false positive rate is only 10% and the true positive rate is 90%.
Why is this? It happens because its so unlikely that you have cancer in the first place. Let’s do the math.
True positives = 1% * 80% = 0.008.
In a population of 10,000 people 1% have cancer, so that’s 100 people. If all of those took the test, 80 of them would test positive.
But how many people would test positive who don’t have cancer?
False positives = 99% * 10% = .099.
In a population of 10,000 people 99% don’t have cancer, so that’s 9,900 people. If all of those took the test, 990 would test positive.
So given that you have a positive test result, what are the chances that you are in the first group rather than the second group?
Well, we take the ratio of the true positives by all the positives, which equals,
80/(80+990) = 0.747663
So you have a roughly 7.5% chance of having cancer given the test result. Surprisingly low right?
Now here’s the real zinger regarding converging lines of evidence that I explained to Micah above in abbreviated fashion. Suppose that you took a second test with similar numbers:
- If a person has cancer, then test 2 gives a true positive 90% of the time.
- If a person does not have cancer, then test 2 gives a false positive 10% of the time.
Unfortunately, this second test also comes back positive. What are the chances that you have cancer now? You might think that it’s just the union of the two probabilities P(C|T1) ∪ P(C|T2), but you would be wrong. That number would actually be way too low, now. (That comes out to 15.18% if you’re curious.)
The trick is to see that given the first test result you have to update the likelihood that you have cancer from 1% likely to 7.5%. (The other, shorter but less intuitive way is just to do an additive version of the Bayes’ Theorem.)
So now we go through the same steps we did above, but instead of multiplying 1% * 80% to get the number of true positives, we have to multiply 7.5% * 90%, which is obviously much higher. We also need to lower the number of false positives. Instead of multiplying 99% * 10% we are now multiplying 92.5% * 10%.
When we run the numbers, we get a result of approximately 42.2% likely that you have cancer given two separate positive results. Interestingly, it is still more likely than not that you don’t have cancer because of how rare cancer actually is, but that second number is way higher than you might think given the low likelihood of either test result independently indicating that you have cancer. This is the power of converging lines of evidence. You can see that if we add a third and fourth test, this likelihood would shoot up pretty fast.
Similarly, lines of argument that on their own only raise the probability of God’s existence slightly can combine to make a very powerful total case, just like multiple pieces of evidence in a trial, provided that they are actually independent pieces of evidence and not just recycling the same evidence in a circular fashion.


An investor buys three shares of XYZ at the beginning of 2002 for $100 apiece. After one year,
the share price has increased to $110 and he receives a dividend per share of $4. Right after
receiving the dividend, he buys two additional shares at $110. After another year, the share price
has dropped to $90, but the investor still receives a dividend per share of $4. Right after
receiving the dividend, he sells one share at $90. After another year, the share price has gone up
to $95, the investor receives a dividend per share of $4 and sells all shares at $95 immediately
after receiving dividends.
1 What are the arithmetic and geometric average time-weighted rates of return and what is the
dollar-weighted rate of return of the investor in the above example (for the dollar-weighted
return assume that (i) the cash flows from dividends received at the end of a given year are based
on the number of shares held at the beginning of that year, and (ii) cash flows from dividends
occur on the same day as the cash flows from buying and selling shares)?
2 Why is the dollar-weighted average rate of return in the above example lower than the
geometric average rate of return?


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From September 2015 the course covers the new 6 areas of Mathematics using the new 9-1 grading system:
- Ratio, proportion and rates of change
- Geometry and Measures
Building on the work completed at Key Stage 3.
There are still two tiers of entry for Mathematics. The Higher tier covers grades 4 to 9 and The Foundation tier covers grades 1 to 5. A student’s Maths set will determine which tier of entry they take. Each tier covers all areas of Mathematics. Students are set across the whole year group based on their ability and their results during Key Stage 3.
There is no coursework for Mathematics as everything is exam based.


This is the most comprehensive collection of IB past papers in the World!
QUESTIONBANKS VERSION 4
PAST PAPERS BY GROUP (2001-2019)
GROUP 1 - Studies in language and literature GROUP 2 - Language acquisition GROUP 3 - Individuals and societies GROUP 4 - The sciences GROUP 5 - Mathematics GROUP 6 - The arts
Download Textbooks (this includes all popular new and legacy textbooks for all major subjects)
TOK TEXTBOOKS GROUP 1 GROUP 2 GROUP 3 GROUP 4 GROUP 5 GROUP 6 DATA BOOKS & FORMULAS EE TEXTBOOKS This site is compiled for teachers and students who maybe don't have the means to buy the papers to practice with. We expect all users of this site to have permission from their teachers to use these examination papers.
This site is no way endorsed by the IBO and we cannot verify the veracity of the files enclosed within.
What is Revision Village?
Voted the #1 IB Mathematics Resources in 2019 & 2020, Revision Village is an award-winning education website that helps IB students learn, practice and revise for IB maths exams. More than 70% of IB Students & Teachers worldwide use Revision Village ~ 350,000+ IB Students from 1,500+ IB Schools.
Who uses Revision Village?
Revision Village is for International Baccalaureate (IB) Diploma Program candidates studying all levels of IB Mathematics.
What IB Subjects does Revision Village cover?
IB Mathematics HL, SL, Studies, Analysis and Approaches SL & HL, Applications and Interpretation SL & HL. We love mathematics and IB students love using Revision Village! Our mission is to create the highest quality IB Math resources available online. We are proud to be voted the #1 IB Mathematics Resource in 2019 & 2020 by IB Students & Teachers worldwide.
What resources are on Revision Village?
Maths Questionbank: The #1 Maths Exam Questionbank for IB Students. IB Maths exam style questions by topic, sub-topic & difficulty. Video solutions & mark schemes for all questions. Learn, practice and master IB mathematics questions.
IB Maths Practice Exams: Test yourself with a wide range of full-length IB Maths Practice Exams. Paper 1 & Paper 2 Practice Exams, Topic Exams, IB Summary Exams, Easy / Medium / Hard Exams and more.
Past IB Exams – Video Solutions: Step-by-step video worked solutions to past IB Maths exams. Short instructional videos taught by experienced teachers.
IB Maths Key Concepts: Short summary videos that teach every topic tested in IB Maths exams. Discover all of the IB Maths exam secrets and practice the most commonly asked questions.
RV Prediction Exams: Carefully created IB Prediction Papers to help you prepare for your finals.
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Will Revision Village be updating all resources for the new IB Maths Curriculum? (exams starting in 2021)
Yes! Revision Village will be releasing all features and resources for IB Mathematics Analysis and Approaches & IB Mathematics Applications and Interpretations in late 2019 and throughout 2020. The Revision Village team is in the final stages of publishing learning videos, 1,200+ exam-style questions filtered by topic with videos, practice exams and more…. stayed tuned!
Current courses (IB Math HL, SL, Studies) will continue to be updated & available until November of 2020 (last exam period).
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Unlike many mathematics websites, Revision Village is 100% focused on IB Mathematics. Students don’t need to spend time searching the internet for IB specific maths videos, tutorials and exam style questions. Revision Village is the perfect place for an IB Student to learn, practice and prepare for their IB Maths Exam stress free.
What are Revision Village Prediction Exams?
The RV Prediction Exams are developed by IB Examiners and Teachers to help students prepare for their upcoming final exams. The RV Prediction Exams are released approximately 1 month prior to May/November IB exams and the questions in the prediction papers are directly aligned to the current trends seen in past IB papers (topics, question style, weighting and difficulty). More than 180,000 IB Students around the world used the 2019 RV Prediction Papers to successfully prepare for their final exams.
Students are encouraged to practice the underlying concepts in the prediction exams, not just simply memorize the questions. As the Revision Village Prediction Exams are ‘Predictions’, Revision Village cannot take responsibility for outcomes due to discrepancies between the prediction and IB papers.
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This is the tenth in a series of blog “snapshots” of how Mercy students benefit from using iPad technology (and other tools) throughout the school day.
In the photos below, students in Geometry Honors are using GeoGebra to investigate the relationship between angles formed by parallel lines and a transversal. They will use the results to develop conjectures about the congruent or supplementary angle pairs. The final component of the activity is to write the formal proof for each conjecture, thus developing the theorems found in geometry textbooks. — Carol Baron
Photos by L. Baker
Patty Perry uses Explain Everything to make tutorials for students to explain difficult concepts. She also uses it to respond to email or message questions.


Predictive modelling leverages statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event, regardless of when it occurred. For example, predictive models are often used to detect crimes and identify suspects, after the crime has taken place. In many cases the model is chosen on the basis of detection theory to try to guess the probability of an outcome given a set amount of input data, for example given an email determining how likely that it is spam. Models can use one or more classifiers in trying to determine the probability of a set of data belonging to another set, say spam or ‘ham’. Depending on definitional boundaries, predictive modelling is synonymous with, or largely overlapping with, the field of machine learning, as it is more commonly referred to in academic or research and development contexts. When deployed commercially, predictive modelling is often referred to as predictive analytics.


- What is the probability of being born on:
a) February 28?
b) February 29?
c) February 28 or February 29?
- A patient newly diagnosed with a serious ailment is told he has a 60% probability of surviving 5 or more years. Let us assume this statement is accurate. Explain the meaning of this statement to someone with no statistical background in terms he or she will understand.
- A lottery offers a grand prize of $10 million. The probability of winning this grand prize is 1 in 55 million (about 1.8×10-8). There are no other prizes, so the probability of winning nothing = 1 – (1.8×10-8) = 0.999999982. The probability model is:
Winnings (X) 0 $10 x 106
P(X = xi) 0.999999982 1.8 x 10-8
a) What is the expected value of a lottery ticket?
b) Fifty-five million lottery tickets will be sold. How much does the proprietor of the lottery need to charge per ticket to make a profit?
- Suppose a population has 26 members identified with the letters A through Z.
a) You select one individual at random from this population. What is the probability of selecting individual A?
b) Assume person A gets selected on an initial draw, you replace person A into the sampling frame, and then take a second random draw. What is the probability of drawing person A on the second draw?
c) Assume person A gets selected on the initial draw and you sample again without replacement. What is the probability of drawing person A on the second draw?
- Let A represent cat ownership and B represent dog ownership. Suppose 35% of households in a population own cats, 30% own dogs, and 15% own both a cat and a dog. Suppose you know that a household owns a cat. What is the probability that it also owns a dog?
- What is the complement of an event?
- Accidents occur along a 5-mile stretch of highway at a uniform rate. The following “curve” depicts the probability density function for accidents along this stretch:
a) What is the probability that an accident occurred in the first mile along this stretch of highway?
b) What is the probability that an accident did not occur in the first mile?
c) What is the probability that an accident occurred between miles 2.5 and 4?
- Suppose there were 4,065,014 births in a given year. Of those births, 2,081,287 were boys and 1,983,727 were girls.
a) If we randomly select two women from the population who then become pregnant, what is the probability both children will be boys?
b) If we randomly select two women from the population who then become pregnant, what is the probability that the first woman’s child will be a boy and the second woman’s child will be a boy?
c) If we randomly select two women from the population who then become pregnant, what is the probability that both children will be boys given that at least one child is a boy?
- Explain the difference between mutually exclusive and independent events.
- Suppose a screening test has a sensitivity of 0.80 and a false-positive rate of 0.02. The test is used on a population that has a disease prevalence of 0.007. Find the probability of having the disease given a positive test result.


In the tapestry of mathematical exploration, problem-solving stands as a masterpiece—a form of art that requires creativity, precision, and a deep understanding of mathematical concepts. This article, “The Art of Math: Problem-Solving Techniques for Success,” delves into the techniques that transform mathematical problem-solving into an artistic endeavor, guiding individuals on a journey to success in the realm of mathematics.
1. Recognizing Mathematics as an Art Form:
Understanding mathematics as an art form sets the stage for appreciating the beauty and creativity inherent in problem-solving. Rather than viewing problems as mere exercises, recognize them as opportunities for artistic expression, where each solution is a brushstroke contributing to the masterpiece of mathematical understanding.
2. Embracing the Creative Mindset:
The creative mindset is the palette from which problem-solving artistry emerges. Embrace a mindset that values innovation, curiosity, and the exploration of multiple solution paths. The creative mindset encourages thinking beyond conventional approaches, fostering a spirit of ingenuity in the face of mathematical challenges.
3. Mastering the Art of Questioning:
The art of questioning is a technique that propels problem-solving into the realm of exploration. Pose insightful questions about the problem at hand—question its assumptions, seek hidden patterns, and inquire about alternative approaches. Mastering the art of questioning elevates problem-solving from a routine task to an engaging and thought-provoking pursuit.
4. Creating Mental Images with Visualization:
Visualization is the brush that paints mental images, bringing mathematical concepts to life. Create mental images, draw diagrams, and visualize abstract ideas to enhance your understanding of the problem. Visualization not only aids comprehension but also adds a layer of artistic expression to your problem-solving process.
5. Crafting Solutions with Elegant Simplicity:
In the art of math, elegance lies in simplicity. Strive to craft solutions that are not only accurate but also elegantly simple. Avoid unnecessary complexities and convoluted approaches, aiming for solutions that embody the beauty of simplicity. The art of crafting elegant solutions showcases a deep mastery of mathematical concepts.
6. Appreciating Patterns as Artistic Elements:
Patterns are the artistic elements that grace the canvas of mathematical problems. Appreciate the beauty of recurring sequences, relationships between numbers, and hidden structures within problems. Recognizing and leveraging patterns not only accelerates problem-solving but also adds an aesthetic dimension to your approach.
7. Blending Logic and Intuition:
The art of math involves a delicate balance between logic and intuition. Blend deductive reasoning with intuitive insights to create a harmonious composition in problem-solving. Logic provides a structured foundation, while intuition allows for creative leaps and innovative solutions. The interplay between logic and intuition enriches the artistic tapestry of mathematical problem-solving.
8. Expressing Individual Style in Approaches:
Just as artists have unique styles, mathematicians can express individuality in their problem-solving approaches. Experiment with various techniques, develop your signature style, and find approaches that resonate with your mathematical intuition. Expressing individual style adds a personal touch to your problem-solving artistry.
9. Iterative Refinement:
Problem-solving, like any art form, benefits from iterative refinement. Approach problems as works in progress, refining your solutions through successive iterations. Embrace the process of continuous improvement, allowing your problem-solving artistry to evolve and mature over time.
10. Learning from Historical Masterpieces:
The art of math has a rich history filled with masterpieces created by legendary mathematicians. Study the works of mathematical pioneers, learn from their problem-solving techniques, and draw inspiration from the timeless masterpieces that have shaped the field. Learning from historical masterpieces provides a sense of continuity and connection with the broader mathematical tradition.
11. Collaborative Artistry:
Problem-solving becomes a collaborative art form when mathematicians come together to share ideas and insights. Engage in collaborative problem-solving sessions, exchange perspectives with peers, and appreciate the collective artistry that emerges from diverse minds working in harmony. Collaborative artistry fosters a sense of community within the world of mathematics.
12. Reflecting on Artistic Growth:
Reflection is the gallery where you showcase your artistic growth as a problem solver. After completing a problem, take a moment to reflect on your approach, the artistic elements incorporated, and the lessons learned. Reflective practice not only enhances your problem-solving skills but also deepens your appreciation for the artistic nuances embedded in mathematical exploration.
“The Art of Math: Problem-Solving Techniques for Success” is an invitation to approach mathematical challenges with the mindset of an artist. By embracing creativity, questioning with depth, and appreciating the beauty of patterns, individuals can elevate problem-solving to an art form. Remember, the art of math is not just about finding solutions; it’s about expressing creativity, fostering individuality, and contributing to the timeless masterpiece of mathematical understanding. As you embark on your journey through the world of mathematics, let the canvas of problems inspire your artistic expression and lead you to new heights of problem-solving mastery.


To refresh your memory, here’s a description of how my model works.
Predictions for the twelfth round are given in the table below. The priors for these distributions are based on the final abilities from last season and the results to round 12.
|Chance of home team winning
|Sunshine Coast Lightning
|West Coast Fever
Score Differential Distributions
The distribution of the predicted score differentials is shown in the figures below. For each game, the chance of the home team winning is calculated and shown in the figure title. Each distribution is coloured by the team’s colours, and the more of a single team’s colour, the higher the chance that team has of winning. Overlaid on each figure are two vertical, dashed dark green lines; these show the score differential that has a 50% predicted chance of happening.
Comparison of Game Results Against Predictions
The following figure shows the results (score difference of the home team) in round 12 (blue vertical line) against the predictions from the model.


AP Calculus BC is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of functions.
Students enrolled in AP Calculus BC will enhance their understanding of topics covered in AP Calculus AB and will also engage in a complete analysis of parametric equations, vectors, series and sequences. Because of the timing of the AP exam, AP Calculus BC students will proceed at an accelerated pace. Throughout the course, students will practice AP type problems and questions in preparation for the AP exam. This course encompasses two full semesters of university-level calculus.
*This course is offered for dual credit through UMSL.
Grade Level(s): 10th-12th
Curricula for Advanced Placement (AP) courses are created by the American College Board, which offers high level coursework and exams to high school students. Colleges and universities may grant placement and course credit to students who obtain high scores on examinations. Curriculum for each subject area is created by a panel of experts and college-level educators in that field of study. The Course & Exam Description (CED) for AP Calculus AB and BC can be found HERE.
Course-Level Scope & Sequence (Units &/or Skills)
- Unit 1: Limits and Continuity
- Unit 2: Differentiation: Definition and Fundamental Properties
- Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
- Unit 4: Contextual Applications of Differentiation
- Unit 5: Analytical Applications of Differentiation
- Unit 6: Integration and Accumulation of Change
- Unit 7: Differential Equations
- Unit 8: Applications of Integration
- Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- Unit 10: Infinite Sequences and Series
Date Last Revised/Approved: 2014


PROBLEM 9. The light-year is the distance traveled by light during one Earth year. To three significant digits, the speed of light is 3.00 x 10^5 km/s. Find the length of the light-year in km and in AU.
Solution:1 Earth year = 365.25 days = 365.25 x 24 x 60 x 60 seconds. In one year, light travels 3.00 x 10^5 x 365.25 x 24 x 60 x 60 km = 9.47 x 10^12 km.
To express this distance in AU,
1 light-year = 9.47 x 1O^I2 km x 1 AU/(1.50 x lO^8km)
= 6.31 x 10^4 AU.
The "parsec" is the astronomical unit of distance that relates to observational measurements. In order to define this unit, we must consider the fact that when we observe the heavens, we have no direct perception of depth or distance. A useful model developed to portray the heavens is the celestial sphere. In this model, Earth is surrounded by an imaginary sphere with infinite radius. A coordinate system, similar to latitude and longitude, is imposed on the celestial sphere by projecting Earth's rotation axis on the sphere to identify the celestial north pole (CNP) and celestial south pole (CSP) as shown in Fig. 2.1. Since the radius of the celestial sphere is infinite, all parallel lines point to the same spot on the sphere, and so every line parallel to Earth's rotation axis also points to the celestial north and south poles.
Every star or celestial object can now have its position identified by the ordered pair of angles in the previous example. Because Earth rotates with respect to the celestial sphere, the time of observation must also be known in order to use the coordinate system. Differences in the positions of two objects on the celestial sphere are expressed in terms of the angle subtended at Earth by the arc joining these points. As Earth revolves around the Sun, very distant stars show no discernible changes in position, but closer stars will show apparent motion with respect to the celestial sphere when viewed from different points in Earth's orbit, as shown in Fig. 2.3. This apparent motion is called "parallactic motion", and the change in position is called the "parallax angle". In this context, 1 parsec is defined as the distance at which the radius of Earth's orbit subtends an angle measuring 1 arc-second (see Fig. 2.4).


The topic on Fibonacci retracements is quite intriguing. To fully understand and appreciate the concept of Fibonacci retracements, one must understand the Fibonacci series. The origins of the Fibonacci series can be traced back to the ancient Indian mathematic scripts, with some claims dating back to 200 BC. However, in the 12th century, Leonardo Pisano Bogollo an Italian mathematician from Pisa, known to his friends as Fibonacci discovered Fibonacci numbers.
The Fibonacci series is a sequence of numbers starting from zero arranged in such a way that the value of any number in the series is the sum of the previous two numbers.
The Fibonacci sequence is as follows:
0 , 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610…
Notice the following: 233 = 144 + 89 144 = 89 + 55 89 = 55 +34
Needless to say the series extends to infinity. There are few interesting properties of the Fibonacci series.
Divide any number in the series by the previous number; the ratio is always approximately 1.618.
For example: 610/377 = 1.618 377/233 = 1.618 233/144 = 1.618
The ratio of 1.618 is considered as the Golden Ratio, also referred to as the Phi. Fibonacci numbers have their connection to nature. The ratio can be found in human face, flower petals, animal bodies, fruits, vegetables, rock formation, galaxial formations etc. Of course let us not get into this discussion as we would be digressing from the main topic. For those interested, I would suggest you search on the internet for golden ratio examples and you will be pleasantly surprised. Further into the ratio properties, one can find remarkable consistency when a number is in the Fibonacci series is divided by its immediate succeeding number.
For example: 89/144 = 0.618 144/233 = 0.618 377/610 = 0.618
At this stage, do bear in mind that 0.618, when expressed in percentage is 61.8%.
Similar consistency can be found when any number in the Fibonacci series is divided by a number two places higher.
For example: 13/34 = 0.382 21/55 = 0.382 34/89 = 0.382
0.382 when expressed in percentage terms is 38.2%
Also, there is consistency when a number in the Fibonacci series is divided by a number 3 place higher.
For example: 13/55 = 0.236 21/89 = 0.236 34/144 = 0.236 55/233 = 0.236
0.236 when expressed in percentage terms is 23.6%.
16.1 – Relevance to stocks markets
It is believed that the Fibonacci ratios i.e 61.8%, 38.2%, and 23.6% finds its application in stock charts. Fibonacci analysis can be applied when there is a noticeable up-move or down-move in prices. Whenever the stock moves either upwards or downwards sharply, it usually tends to retrace back before its next move. For example if the stock has run up from Rs.50 to Rs.100, then it is likely to retrace back to probably Rs.70, before it can move Rs.120.
‘The retracement level forecast’ is a technique using which one can identify upto which level retracement can happen. These retracement levels provide a good opportunity for the traders to enter new positions in the direction of the trend. The Fibonacci ratios i.e 61.8%, 38.2%, and 23.6% helps the trader to identify the possible extent of the retracement. The trader can use these levels to position himself for trade.
Have a look at the chart below:
I’ve encircled two points on the chart, at Rs.380 where the stock started its rally and at Rs.489, where the stock prices peaked.
I would now define the move of 109 (380 – 489) as the Fibonacci upmove. As per the Fibonacci retracement theory, after the upmove one can anticipate a correction in the stock to last up to the Fibonacci ratios. For example, the first level up to which the stock can correct could be 23.6%. If this stock continues to correct further, the trader can watch out for the 38.2% and 61.8% levels.
Notice in the example shown below, the stock has retraced up to 61.8%, which coincides with 421.9, before it resumed the rally.
We can arrive at 421 by using simple math as well –
Total Fibonacci up move = 109
61.8% of Fibonacci up move = 61.8% * 109 = 67.36
Retracement @ 61.8% = 489- 67.36 = 421.6
Likewise, we can calculate for 38.2% and the other ratios. However one need not manually do this as the software will do this for us.
Here is another example where the chart has rallied from Rs.288 to Rs.338. Therefore 50 points move makes up for the Fibonacci upmove. The stock retraced back 38.2% to Rs.319 before resuming its up move.
The Fibonacci retracements can also be applied to stocks that are falling, in order to identify levels upto which the stock can bounce back. In the chart below (DLF Limited), the stock started to decline from Rs.187 to Rs. 120.6 thus making 67 points as the Fibonacci down move.
After the down move, the stock attempted to bounce back retracing back to Rs.162, which is the 61.8% Fibonacci retracement level.


Simplest Form Algebra Calculator Ten Features Of Simplest Form Algebra Calculator That Make Everyone Love It
The protractor and the Bunsen burner. Playing the recorder in music class. Drawing arcs and circles with a ambit in geometry. These accoutrement of the apprenticeship barter become allotment of our lives for a analysis or two and afresh we move on.
Today, NPR Ed begins a new alternation analytical these icons of the classroom. We alpha off with a accessory that already was capital to higher-level math, in academy and in the workplace, but now has all but disappeared:
The accelerate rule.
“Take your batteries out,” Jim Hus says, watching his pre-calculus acceptance abolish the AA batteries that adeptness their calculators. “Let’s do those multiplication problems again.”
For the abutting calculations, Hus’s juniors and seniors at Highland Aerial Academy in Highland, Ind., will use a altered tool: A apparatus that dates aback 400 years.
Before the smartphone, the laptop and the graphing calculator, there was the accelerate rule. It’s a able automated accretion device, generally no beyond than a 12-inch ruler, apparent with numbers — but allotment of it slides in an out to to appearance relationships amid altered sets of numbers.
That acutely simple apparatus has a austere resume. NASA engineers acclimated accelerate rules to body the rockets and plan the mission that landed Apollo 11 on the moon. It’s said that Buzz Aldrin bare his abridged accelerate aphorism for last-minute calculations afore landing.
“The accelerate aphorism is an apparatus that was acclimated to architecture around everything,” says Deborah Douglas, the administrator of collections and babysitter of science and technology at the MIT Building in Cambridge, Mass. The building aloof concluded a three-year display on accelerate rules. “The admeasurement of a avenue pipe, the weight-bearing adeptness of a agenda box, alike rocket ships and cars.”
So, What Is A Accelerate Rule?
Slide rules are about ellipsoidal and about the admeasurement of a ruler. They are disconnected into thirds, the top and basal are anchored in place, but the average area slides aback and forth. Each area has scales — numbers and band marks for calculations.
The aboriginal one was congenital by William Oughtred, a apostolic teaching algebraic in England in the 1600s. It was based on John Napier’s analysis of logarithms.
In its simplest form, the accelerate aphorism adds and subtracts lengths in adjustment to account a absolute distance. But accelerate rules can additionally handle multiplication and division, acquisition aboveboard roots, and do added adult calculations.
For ancestors of engineers, technicians and scientists, the accelerate aphorism was an capital allotment of their circadian lives. Until, all of a sudden, it wasn’t.
In 1972 Hewlett-Packard came out with the aboriginal handheld cyberbanking calculator. Practically overnight, the accelerate aphorism had become obsolete.
“The afterlife of the accelerate aphorism was appealing instantaneous,” says Bob De Cesaris, who oversees dent accomplishment at Intel and has one of the better collections of accelerate rules in the country. De Cesaris estimates his accumulating has about 4,000 accelerate rules.
He is additionally the admiral of the Oughtred Society — a accumulation of 400 accelerate aphorism collectors and enthusiasts gluttonous to bottle the device’s history (and area you can acquisition out all sorts of advice about them).
And yet, admitting the artful adeptness these canicule in alike your handheld phone, the accelerate aphorism isn’t absolutely dead.
Here and there, agents like Jim Hus still use them in the classroom. Sister Paula Irving, a nun at the Community of Jesus in Orleans, Mass., teaches a computer programming advance to homeschooled aerial academy students. And aback she covers the history of the computer, she teaches acceptance how to use a apparatus she remembers watching her ancestor use as he affected their family’s finances.
More than a thousand afar west, Laurie Emery, a algebraic abecedary at South Winneshiek Aerial Academy in Calmar, Iowa, will advise her inferior pre-calculus chic how to do intricate calculations after a calculator.
There’s alike a apprentice academy about the accelerate aphorism at the University of California, San Diego, that Professor Joe Pasquale has been teaching aback 2003.
“We alive in this age aback accretion is accepting exponentially added able but we generally don’t alike anticipate about the calculations actuality made,” says Pasquale. “We aloof let our computer do all the work.”
In the seminar, Pasquale says his acceptance are generally afraid that the accelerate rule’s answers accomplish sense.
Thinking About The Math
“The nice affair about a calculator is you don’t accept to anticipate – but it’s additionally a bad thing,” he adds. “When you’re application a accelerate aphorism you accept to be engaged. You accept to be cerebration about math.”
And that’s one of the capital affidavit some agents still adhere on to the old “slipsticks.”
MIT’s Debbie Douglas says that alike admitting the accelerate aphorism isn’t as absolute as a calculator, acceptance can accept the abstraction of what it’s doing. “It absolutely makes one affianced with the process.”
Jim Hus still remembers chief to advance $400 in a calculator and abandoning his accelerate aphorism during his apprentice year at Purdue, aback in 1974.
But it’s a accessory he’ll never balloon and he hopes his acceptance at Highland Aerial Academy in Indiana won’t either. He’s planning to accept his acceptance body a classroom accelerate rule.
“I antic it will be the better accelerate aphorism in the world,” he says, laughing. “But this way, I’m not aloof handing the acceptance a tool, we’re acquirements how it operates so we can admission college algebraic concepts.”
Copyright NPR 2019.
Simplest Form Algebra Calculator Ten Features Of Simplest Form Algebra Calculator That Make Everyone Love It – simplest form algebra calculator
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Dr. Montessori demonstrated that if children have access to concrete mathematical equipment in the early years, they can easily and joyfully assimilate many number facts and skills.
Specially designed concrete materials are used, these represent all types of quantities and allow children to become interested in counting by touching or moving the items around as they enumerate them. By combining this equipment, separating it, sharing it, counting it, and comparing it, they can demonstrate to themselves the basic operations of mathematics.
At Little Einstein children never sit down to memorize addition and subtraction facts; they never simply memorize multiplication tables. They learn these facts by actually performing the operations with concrete materials. The concrete experiences allow greater concentration and ensure the children gain a real understanding of what each operation means. Our classroom is full of materials in multiple quantities which can be used for numeration, adding, subtracting, multiplying, dividing and working with fractions, that each child has an individual access to them and as early as 6 years old, children can learn numbers up to 9,999 along with a solid understanding of the Decimal system.


You have been using the = character to name variables and set them to numbers or strings. We're now going to blow your mind again by showing you how to use = and a new Python word return to set variables to be a value from a function. There will be one thing to pay close attention to, but first type this in:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
def add(a, b): print "ADDING %d + %d" % (a, b) return a + b def subtract(a, b): print "SUBTRACTING %d - %d" % (a, b) return a - b def multiply(a, b): print "MULTIPLYING %d * %d" % (a, b) return a * b def divide(a, b): print "DIVIDING %d / %d" % (a, b) return a / b print "Let's do some math with just functions!" age = add(30, 5) height = subtract(78, 4) weight = multiply(90, 2) iq = divide(100, 2) print "Age: %d, Height: %d, Weight: %d, IQ: %d" % (age, height, weight, iq) # A puzzle for the extra credit, type it in anyway. print "Here is a puzzle." what = add(age, subtract(height, multiply(weight, divide(iq, 2)))) print "That becomes: ", what, "Can you do it by hand?"
We are now doing our own math functions for add, subtract, multiply, and divide. The important thing to notice is the last line where we say return a + b (in add). What this does is the following:
As with many other things in this book, you should take this real slow, break it down, and try to trace what's going on. To help there's extra credit to get you to solve a puzzle and learn something cool.
$ python ex21.py Let's do some math with just functions! ADDING 30 + 5 SUBTRACTING 78 - 4 MULTIPLYING 90 * 2 DIVIDING 100 / 2 Age: 35, Height: 74, Weight: 180, IQ: 50 Here is a puzzle. DIVIDING 50 / 2 MULTIPLYING 180 * 25 SUBTRACTING 74 - 4500 ADDING 35 + -4426 That becomes: -4391 Can you do it by hand?
This exercise might really whack your brain out, but take it slow and easy and treat it like a little game. Figuring out puzzles like this is what makes programming fun, so I'll be giving you more little problems like this as we go.


Nous accueillons Antoine Deza qui est depuis peu professeur à Orsay.
On the polynomial Hirsch conjecture and its continuous analogue
The simplex and primal-dual interior point methods are the most computationally successful algorithms for linear optimization. While simplex methods follow an edge path, interior point methods follow the central path. Within this framework, the curvature of a polytope, defined as the largest possible total curvature of the associated central path, can be regarded as the continuous analogue of its diameter. In this talk, we highlight links between the edge and central paths, and between the diameter and the curvature of a polytope. We recall continuous results of Dedieu, Malajovich, and Shub, and discrete results of Holt and Klee and of Klee and Walkup, as well as related conjectures such as the Hirsch conjecture that was disproved by Santos. We also present analogous results dealing with average and worst-case behaviour of the curvature and diameter of polytopes, including a result of Allamigeon, Benchimol, Gaubert, and Joswig who constructed a counterexample to the continuous analogue of the polynomial Hirsch conjecture. Based on joint work with Tam ́as Terlaky (Lehigh), Feng Xie(Microsoft), and Yuriy Zinchenko (Calgary).


The concept of Degrees of Freedom is a mathematical idea that suggests there is one degree of freedom for every independant mode of motion.
For example the ERS210?'s Degrees of Freedom can be calculated as follows.
|Mouth||1 Degree of Freedom|
|Head||3 Degrees of Freedom|
|Legs||3 Degrees of Freedom (x4 Legs)|
|Ears||1 Degree of Freedom (x2 Ears)|
|Tail||2 Degrees of Freedom|
| || |
|Total||20 Degrees of Freedom|


Custodian of Policy: Registrar
Relevant Minnesota State System Policy: Minnesota State System Policy 3.3Relevant Procedures: Minnesota State System Procedure 3.3.1Effective Date: Spring 2020Last Review: Fall 2016Next Review: Fall 2022
English Placement Policy
In order to be considered valid for placement purposes, ACT/SAT scores and ACCUPLACER scores must have been earned within five years from the start of the class. High school GPA must be within the last ten years. The English Placement policy will be reviewed every two years.
English Placement for International Students who do not have English as their first language.
Math Placement Policy
Two sets of Accuplacer placement scores are available:
ACT Math and SAT Math Scores Comparison: ACT 19 = SAT 510; ACT 22 = SAT 540; ACT 23 = SAT 560; ACT 24 = SAT 580.
ACT, MCA and SAT scores are valid for 5 years. Accuplacer scores are valid for 2 years.
*MCA, Minnesota Comprehensive Assessment, Mathematics score will be used for only MATH105, MATH134, and MATH127 placement.
The purpose of this policy is to improve student success in college and university courses through student assessment and course placement that addresses reading comprehension, written English, and mathematics knowledge and skills.


Pihl Hatch posted an update 3 weeks, 4 days ago
Do you understand how to calculate the chances of winning the lottery, like the Florida Lottery? It is possible to calculate each group of odds for every different lottery game you play. With the help of a small handheld calculator or with the free calculator on your pc, you merely multiply the numbers together and add one division process when "the order" of one’s chosen numbers is not required for a particular lottery game.
What you "have to know" is the number of total balls that the winning numbers are drawn from…..could it be 59, 56, 42, 49, or 39? When there is a second drawing for the single extra ball, like the "red ball" with Powerball or the Mega Millions’ "gold ball" you have to know how many balls are in this group as well. Is there 49 or 39?
It doesn’t matter if it’s the Florida, Ohio, Texas, PA or NJ Lottery. This strategy or formula gives you the true odds. Florida Lottery is 6/53. New York Lottery is 6/59. The Ohio Lottery, Massachusetts Lottery, Wisconsin Lottery, and the State of Washington Lottery carry a 6/49 lottery numbers ratio. Illinois Lottery posesses 6/52.
Once you have this information correctly before you and your calculator at hand, you can start working the formulas.
Hongkong Lottery You should choose five regular balls and one extra ball correctly matched to the winning drawn numbers to win the multi-million dollar jackpot that most of us dream of winning someday.
In the first example you can find 56 balls in the initial group and 46 balls in the secondary group. So that you can win the Jackpot you should match each one of these balls (5 + 1) exactly, but not necessarily in order. The California Lottery’s Super Lotto Plus is 47/27. The big drum is spinning with the initial part of the drawing. You have a 1/56 chance to match your number to this first ball.
With one ball removed following the first number has been drawn, at this point you have a 1/55 potential for matching another one of your numbers to the next ball drawn. With each drawn number a ball is removed lowering the number of remaining balls by way of a total of one.
The odds of you correctly matching the quantity on the 3rd ball to be drawn is now 1/54 from the total number of balls remaining in the drum. With the third ball removed from the drum and sitting with the other two winning numbers, your odds of correctly matching the fourth ball is reduced to 1/53.
As you can see whenever a ball is released from the drum the odds are reduced by one. You started with a 1/56 chance, then with each new winning number it really is reduced to 1/55, 1/54, 1/53, sufficient reason for the fifth ball you have the odds of 1/52 correctly matching this fifth winning number. It is the first the main formula of how exactly to calculate your probability of winning the lottery, including the Florida Lottery.
Now take these five odds representing the five winning numbers (1/56, 1/55, 1/54, 1/53, and 1/52). The "1" along with the fraction represents your only possiblity to correctly match the drawn number.
Now you take your calculator and multiply all top numbers (1x1x1x1x1) equal one (1). After that you multiply all the bottom numbers (56x55x54x53x52). Correctly entered and multiplied you discover the total is 458,377,920. The brand new fraction becomes 1/458,377,920. It is a 458 million to one possiblity to win. If you were necessary to pick the numbers in order just like they are drawn, then these would be the odds against you to win this Pick 5/56 ball lottery game.
Fortunately or unfortunately, you are not required to pick the numbers in the precise order they are drawn. The next step of the formula will certainly reduce the odds, which allows you to match these five winning numbers in any order. In this step you’ll multiply the quantity of balls drawn — five (1x2x3x4x5). With calculator at hand you see that the full total equals 120.
To give you the proper to choose your five matching numbers in any order, you create these odds by dividing 120/417,451,320. You certainly need a calculator because of this one. 120/458,377,920 minimises your odds of winning this lottery to 1/3,819,816. They are over 3.5 million to 1 odds against you of winning this Pick 5/56 ball lottery game.
If this were the Mega Millions Lottery, you need to add the "gold ball" to these five winning drawn balls in order to win the Multi-Million Dollar Jackpot. The single gold ball is calculated as a 1/46 potential for matching it correctly, and since you are drawing just one number it has to be an exact match. Again, you merely have that "1" chance to do it right. Now you need to multiply 3,819,816 by 46.
Grab your calculator and do the multiplication. Your final odds against you winning the Mega Millions Jackpot are calculated to be 175,711,536 or clearly stated 175 million, 711 thousand, 500 36 thirty-six to one (175,711,536 to at least one 1). Now you learn how to calculate the chances of winning the Mega Millions Lottery.
The Powerball Lottery calculations are based on a 1/59 for the first five white balls and 1/39 for the "red" power ball. The first set of multipliers is 59x58x57x56x55. This group totals 600,766,320. Now divide 600,766,360 by 120 (1x2x3x4x5). Your brand-new total is 5,006,386. You will find a 1/39 chance to catch the "red" ball. 39 x 5,006,386 gives you the real probability of winning the Powerball Jackpot, namely 195,249,054 to at least one 1.
Another 5 +1 Lottery that is apparently everywhere in the United States is the "Hot Lotto" that includes a 39/19 count. It really is played in 15 different States. DC Lottery, Delaware Lottery, Idaho Lottery, Iowa Lottery, Kansas Lottery, Maine Lottery, Minnesota Lottery, Montana Lottery, New Hampshire Lottery, New Mexico Lottery, North Dakota Lottery, Oklahoma Lottery, South Dakota Lottery, Vermont Lottery, and the West Virginia Lottery. The ultimate probability of winning the minimum $1 Million Jackpot is 10,939,383 to at least one 1.
A Pick 6/52 ball Lottery game formula looks like this: (1/52, 1/51, 1/50, 1/49, 1/48, 1/47) for a total of 14,658,134,400 divided by 720 (1x2x3x4x5x6) for the odds of 1/20,358,520. Your possiblity to win the 6/52 Lottery has ended 14.5 million to 1 to win, like the Illinois Lotto.
The Hoosier Lottery that uses Indiana State’s nickname, posesses 6/48. Michigan Lottery is 6/47, Arizona Lottery and Missouri Lottery are 6/44, Maryland Lottery is 6/43, and Colorado Lottery is 6/42. Compare this to the Florida Lottery.
A Pick 5/39 ball Lottery game formula looks like this: (1/39, 1/38, 1/37, 1/36, 1/35) for a complete of 69,090,840 divided by 120 (1x2x3x4x5) for the chances of 1/575,757 of winning the Jackpot like the Illinois Little Lotto. Other States with the same 5/39 lottery numbers are the NC Lottery, Georgia and Florida Lottery Fantasy 5, and Tennessee Lottery’s Pick 5. Virginia Lottery’s Cash 5 carries a 5/34 range.


In Maths we have been delving deeper into the concept of subtraction. We have been using a range of concrete and pictorial examples in our lessons to help us build our understanding of this operation. We have applied our skills of subtracting both one and two digit numbers from a two digit number in a variety of ways. We have also been using our previous learning on addition to help us understand that subtraction is the inverse of addition and vice versa. We have practiced applying this knowledge to help us double check our answers and ensure that we have used careful counting skills.
In English, we have been exploring a range of villains. We have been generating powerful adjectives to describe these nasty, hostile characters on the inside and outside. Building on our previous learning within our Rainbow Fish topic, we have explored the work of other authors and analysed how they use characterisation to control villains in their work in order to make sure that they are disliked by their reader. We have been using our learning to build up a bank of ideas and words that will support us to write a character description about George’s vile grandma. In SPaG, we have been exploring proper nouns and a range of co-ordinating conjunctions.
In our Religion lessons, we have begun our learning about the Liturgical season of Advent. During an extra special collective worship we worked together to prepare our prayer table for the season. We changed the prayer cloth from green, which represents ordinary time, to purple which represents a time for preparation. We also worked together to create an Advent Wreath for our classroom. We will use this to help us countdown to Christmas and prepare for the birth of Baby Jesus.


Seung Eun "Rina" Park conducts quantitative research on the impact of financial aid program to college enrollment and labor market outcomes.
Park is a doctoral student in the economics and education program at Teachers College, Columbia University. She holds an MA in statistics from Stanford University and a BA with double majors in applied mathematics and economics from the University of California, Berkeley.
Prior to joining CCRC, Park worked as a research assistant for the Center for Education Policy Analysis (CEPA) at Stanford University. Her research interests include higher education finance, fiscal federalism, and correctional education.


RSJ is one of the world’s largest algorithmic traders currently trading in London (NYSE Liffe), Chicago (CME), and Frankfurt (Eurex). RSJ is the largest algo trader at NYSE Liffe, and one of the largest algo traders at Chicago Mercantile Exchange and Eurex.
All volume is conducted fully automatically by a state of the art technology. The monthly traded volumes exceeds 20 million lots. In 2011 we traded 238 million contracts. The trading algorithms used by RSJ are based on sophisticated mathematical models. The models are an outcome of applying the results of deep theoretical mathematics on financial markets.
RSJ is a Prague based company employing top mathematicians, statisticians, developers and traders.
We are convinced that the success of our civilization depends on the quality of education and the ability to bolster logical thinking. Therefore we provide grants for higher education, science and research.


Keeping the “A” in STE(A)M
Please join us at Plains Art Museum’s next gathering in the Art & Business Breakfast series. This innovative program brings Fargo-Moorhead-West Fargo artists together with business and cultural leaders. Through presentations, conversations, and activities, we explore the connections art and business share.
STEM appears in 2005 when two US House members “set up the Science, Technology, Engineering, and Math, or STEM, caucus” in Congress. A few more mentions of STEM appear in 2006. And by 2008, STEM is making headlines. STEAM—the addition of ART—arrived around 2010-2011. But why has it been so difficult for the “A” to stay in STEM? What will it take keep it there? Join us as Lisa Parrish tells us why and how.
Parrish is founder of Musical Bridges, a Fargo-Moorhead based organization that connects cultures through music, uses STEAM concepts by relating Science, Technology, Engineering, Art, and Math to one another, demonstrating that the whole is stronger than its parts.
Registration required for this FREE event, generously sponsored by Heartland Trust Company.


The central segment of the measurement model uses a series of cross-correlation calculations as shown in the equation below. This function essentially measures the similarity of two signals.
- where x and y are the two signals whose correlation is to be measured
- t1 and t2 are the period over which the correlation is measured
- and τ is an offset between the two signals under measurement
- (adapted from [Ifeachor and Jervis 1993])
This equation may be applied to any two signals, though for the purpose of our measurement model it is employed to analyse a pair of binaural signals (the signals that reach the ears of a listener or a head and torso simulator as discussed previously
). In this case, τ is usually measured over a range that is large enough to encompass the maximum interaural time difference that is caused by the physical separation of human ears, typically ±1 ms, though this can be specified in the measurement model.
The final output value is then commonly taken to be the maximum absolute value across the range of τ. However, we tend to use the maximum value, not the maximum absolute value for two reasons. Firstly, we believe that positive and negative output values relate to different perceived attributes and using the absolute value causes this difference to be lost. Secondly, the use of half-wave rectification as described previously
causes the range of results from the measurement to be between 0 and 1, meaning that the absolute and raw value maxima will be identical.
Also useful is the fact that the value of τ of the maxima relates to the interaural time difference of the sound. This can be used to predict the perceived location of the sound, though is not a full model of the perceptual process of localisation.
Both the maximum value of the calculation and the related value of τ are passed on for further processing in the measurement model.


this is how you actually reform education. Not corporatizing or privatizing.
Children are intrinsically eager and able to learn. If we step back from our limiting preconceptions about education, we discover learning flourishes when we facilitate it rather than try to advance it through force, intimidation, and coercion.
Over 85 years ago a pioneering educator proved that delaying formal instruction, in this case of mathematics, benefits children in wonderfully unexpected ways. Louis P. Benezet, superintendent of the Manchester, New Hampshire schools, advocated the postponement of systematic instruction in math until after sixth grade. Benezet wrote,
I feel that it is all nonsense to take eight years to get children thru the ordinary arithmetic assignment of the elementary schools. What possible needs has a ten-year-old child for knowledge of long division? The whole subject of arithmetic could be postponed until the seventh year of school, and it could be mastered in two years’ study by any normal child.
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f(n+2) = f(n+1) + f(n)
where n begins with 1, f(1) = 1, and f(2) =1
The series is named for Leonardo Fibonacci, an Italian mathematician who first posed a mathematical problem (based on reproduction patterns in rabbits) the answer to which is the sequence that would later bear his name. (See, generally, wikipedia.org/wiki/Fibonacci.) Fibonacci lived from around 1170 to 1250, and he is widely considered to be the greatest western mathematician of the Middle Ages. He haled from Pisa -- hence his nickname: Leonardo of Pisa.
Well, the Fibonacci Sequence is absolutely everywhere. It proves, definitively, that if God is not a lawyer, s/he is a mathematician. I need one quick detour to back up that conclusion. It concerns the "Golden Ratio."
If you take two consecutive Fibonacci numbers and divide the later one by the earlier one, a pattern quickly emerges:
1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.666666....
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615384...
What you see is that the ratios approach a special number called the Golden Ratio, which is approximately 1.618. (The actual number is 1 plus the square root of 5 where the entire sum is divided by 2.) A rectangle where the ratio of length to width is 1.618 is considered to be most pleasing to the eye and is called a "golden rectangle." The Greeks knew this, so the Parthenon is a "golden" rectangle. Da Vinci knew this, so he used golden rectangles everywhere including in the Mona Lisa. The same goes for other famous works of art that are too numerous to mention here.
We find the golden ratio and Fibonacci numbers in music too, most famously in the work of Bela Bartok.
And nature. The spiral of the chambered nautilus spins out in a path that tracks the golden ratio and the Fibonacci Sequence. (See, e.g., 2muchfun.info/nautilusshell.html.) Likewise for the spirals on pine cones and on the faces of sunflowers. (See, e.g., io9.com/5985588/15-uncanny-examples-of-the-golden-ratio-in-nature.) Reproductive patterns in some species -- like bees -- follow the Fibonacci Sequence. (Id.) Even the patterns of spots on Dalmatians are organized according to Fibonacci numbers. (OK, I totally made that last one up; just wanted to see if anyone was still reading.)
But, seriously, other examples from the arts, nature, aesthetics, sex, computer science, physics, and other branches of mathematics abound. I could go on and on. And I did -- this was a project for three straight years in high school, and even in one class during college.
So, the point here is that Pisa remains proud of its greatest mathematical son. In the Camposanto, which is one of the 4 buildings that constitute the Campo dei Miracoli, stands a statue of Fibonacci. Seeing it live was a thrill for me and I'm sure it would be the same for you. The crowd around the statue of Fib was not quite as huge as the line for the Leaning Tower. But it was close.
There is actually more. According to a website I read on the train ride up to Pisa, as well as the map on my iPhone, there is a street in Pisa named after Fibonacci. It's a little bit out of the way and completely on the other side of town from the Leaning Tower. But we trekked over there. I mean, how many times will you get to see the intersection of 2 streets where one is named after Galileo and one is named after Fibonacci?!?!? The only problem is that the street sign for Rue de Fibonacci was missing. It was cute to see Galileo Avenue though.
|This is where the street sign for Leonardo Fibonacci is supposed to go.|