Once you have solved them (or gotten tired of trying to solve them and want to give up), highlight the white space under the question. I've written the answers there, but made the text white, so it won't show up until you highlight it. :)
1. Prove that seven is half of twelve.
Write twelve in Roman numerals - XII. Halve the number by drawing a line horizontally across its center. The upper half is VII.
2. Place three sixes together so as to make seven.
The answer to this is a fraction - I would write it as a fraction but Blogger won't let me! It's 6 6/6
4. Express 100 by repetition of the same figure six times over.
Another fraction one. 99 99/99 = 100.
5. What is the surest way of keeping water from entering your house?
Don't pay your water bill.
6. Five herrings were divided among five persons. Each had a herring and yet one remained in the dish. How was this managed?
The last of the five received his herring in the dish.
7. What gets bigger the more you contract it?
8. Prove that two sixes make eleven.
This is dependent on the use of Roman numerals. One six (VI) is placed above another six, but the latter in an inverted position, the combination making XI.
9. What speaks all languages?
10. You undertake to show another person something which you never saw before, which he never saw before, and which, after you both have seen it, no one else will ever see again. How is it to be done?
The puzzle is solved by cracking a nut, showing your interlocutor the kernel, then eating it.
11. How many times can you subtract 5 from 135?
Only once. After that it isn't 135 anymore.
12. You undertake to put something into a person's left hand which he cannot possibly take in his right. How is it to be done?
You place in the person's left hand his own right elbow, which, obviously, he cannot take in his right hand.
13. Take one from nineteen and leave twenty.
Write nineteen in Roman numerals - XIX. Remove the I and you have XX, which is twenty.
Did you get any of them wrong?
Do you have any puzzles for me? Leave them in the comments. :)
Happy May everyone!
I leave my front door, run on a level road for some distance, then run to the top of a hill and return home by the same route. I run 8 mph on level ground, 6 mph uphill, and 12 mph downhill. If my total trip took 2 hours, how far did I run?ReplyDelete
Over 600 other puzzles:
That's a great one. Thanks for sharing!Delete
We play a similar game to #2 in the car: Look for a number-plate with four numerals and try turn them into 10, for example 5363 would be 5+6-(3/3)ReplyDelete
#4 9999÷99=101 not 100
#5 Turning of the main valve is surer
#11 Answer is infinitely either you continue subtracting into negative infinity or get a new 135 each time
:) Thanks for commenting!ReplyDelete
#4 The answer is 99 99/99 (99, not 9999) lol :)
You mean 99+(99÷99)?Delete
Yup, that's exactly right.Delete
Another answer would be 5x(5+5)+5x(5+5)Delete
That is actually a very good point.Delete
I actually got those puzzles out of a book I found in the library. You'd probably really enjoy it.


Name: Yohannes Dagne
Assignment: Lab #10
You will write a simple calculator that can determine if a number is even or odd. Use the more blocks function within scratch to create a block that calculates the distance between two points. Note, you should access values from a list. One option is to have a list of x-values and another list that stores the y-values. Using your code block from the above question, create a program that allows a user to determine if a polygon is a regular polygon (all sides equal length) by entering the coordinates of the polygon.
I completed the required tasks that each problem asked me to do.


Calculations: 10 Mistakes that Most People Make
Advantages of finding the Best Online Calculators Search Website
The purpose of a calculator is to make it easy to find answers to different math equations. Through internet to can make use of an online calculator. You will need to see the website that will aid you to get the online calculator that has functions for your math problem. Thus, you will avoid having a calculator with complicated functions that you do not need. Below are reasons why you should consider switching to using online calculators from the best site.
The best platform will ease your search for the online calculator suitable to your needs. For example, you may be searching fraction to decimal calculator. It is vital you know where you can get this online calculator to carry out these math functions. The top website will categories the online calculators depending on the equations they solve. Hence, you will easily get the online calculator that suits your field of study. The goal is to eliminate getting a calculator with formulas that do not fit the equations you are solving. Therefore, the website will make it easy for you to get the online calculator you need.
The other benefit of using the best online calculators search platform is finding calculators that are fast and accurate. The result of your math equation will depend on your expertise and the calculator you are using. You should strive to get the best online calculator that will calculate the equation accurate to give you the correct figure. For instance, when searching for fractions to decimals calculator. Therefore, you can rely on the platform to help you choose the best online calculator for your math problem. Therefore, you will visit the website to get the ideal online calculator to use. You should strive to find the top online calculator search website that will aid you to get right answers to your math problem.
The other benefit of using the best platform is getting the latest online calculator. Currently you can find an online calculator that has updated functions that your manual calculator lacks. You should strive to see the site that has all the latest online calculators. Thus, you can utilize the platform to solve complex math equations. Thus, you will find an online calculator that can help you quickly find solutions to a complicated math problem. Therefore, to enjoy this benefit you will need to check the best online calculator search website. The online calculator will have all advanced formulas to simplify doing a hard math problem.
Using the best online calculator will help you save the money of buying a manual gadget.
Comments are closed.


Supercharging customer touchpoints with uplift modeling
Technical post, 33 minute read
An introduction to a powerful way of predicting individual treatment effects, with synthetic data in Python using pandas and XGBoost.
Designing an energy arbitrage strategy with linear programming
Technical post, 30 minute read
How to use a classic mathematical optimization technique to guide the operation of a grid-connected battery and maximize profit.
Visualizing a balance history from transaction data using pandas and Plotly
Technical post, 18 minute read
A practical post on data wrangling and visualization that could be applied in a professional setting, or to your personal finances.
Why decision trees are more flexible than linear models
Conceptual post, 7 minute read
This blog post will examine a hypothetical dataset of website visits and customer conversion, to illustrate how decision trees are a more flexible mathematical model than linear models such as logistic regression.
Overfitting, underfitting, and the bias-variance tradeoff
Technical post, 25 minute read
Explore these foundational machine learning concepts and learn how to use regularization to leverage the bias-variance tradeoff to improve model performance, through an illustrative example of polynomial fitting in Python and scikit-learn.
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We first raised that question nearly a year ago, when we asked financial products comparisons site Ratehub.ca to calculate the minimum income. a 2.99 per cent five-year fixed rate mortgage and a 25.
Free amortization calculator returns monthly payment as well as displaying a schedule, graph, and pie chart breakdown of an amortized loan. Or, simply learn more about loan amortization. Experiment with other loan calculators, or explore hundreds of other calculators addressing topics such as math, fitness, health, and many more.
PMI Calculator with Amortization. This unique mortgage calculator will not only generate an amortization schedule, but will also show the private mortgage insurance payment that may be required in addition to the monthly PITI payment, and when it will automatically cancel.. Want to learn more about PMI?
Canadian mortgage calculator with amortization schedule. Mortgage calculator with amortization schedule . Principal Amortization months Help . Interest Rate : Payment Info : Or Input Payment . and . The above is for illustrative purposes only. Canadian Rates are compounded semi-annually.
compare fha and conventional loans A 15-year FHA loan with 22% down payment gets you out of paying PMI, which can actually make the FHA loan cheaper than a conventional. When we bought our house in 2012, the best FHA loan was a 2.75% 15-year fixed (no PMI with 22% down), but the best conventional was over 3% for a 15-year fixed.Compare Mortgage Options But there’s more to getting a good mortgage rate than just looking at the rate. Read on to learn how to compare lenders and rates to find the mortgage you need. Or you can start comparing loans in.
what is the fha interest rate right now FHA 203k interest rates. It is because of this concern that a fha 203k loan carries an interest rate premium over the standard fha 203b loan. Since the lender holding a the FHA 203k loan during the renovation process won’t know the value of the loan for upwards to seven months, when the renovation project is complete,
Amortization Schedule generated by the www.amortization-schedule.info website.. How to use our amortization calculator? To calculate the amount of the regular periodic loan payments and to generate automatically a loan schedule, the following values are required: loan amount, interest rate, loan length and payment frequency.
Further, "an amortization schedule is a table detailing each periodic payment on an amortizing loan (typically a mortgage), as generated by an amortization calculator." (To be technical here, I take issue with the use of the word "regular" as used in the definition. I prefer "periodic" or "recurring" instead. Perhaps I should edit the entry?)
Mortgage calculator – calculate payments, see amortization and compare loans. In just 4 simple steps, this free mortgage calculator will show you your monthly mortgage payment and produce a complete payment-by-payment mortgage amortization schedule. You can also see the savings from prepaying your mortgage using 3 different methods!
Pmi Cost Mortgage How to Calculate Mortgage Insurance (PMI). Private mortgage insurance (PMI) is insurance that protects a lender in the event that a borrower defaults on a conventional home loan. mortgage insurance is usually required when the down payment.


Let’s use the formula (price ÷ # of yards = $/yard) in a practical application.
One popular luxury line of yarn offers 60 yrd/50 g skeins for $12.10. This seems like a great deal, right? The skeins are reasonably priced. But let’s go on. One pattern to support this yarn is for a simple scarf. The pattern calls for 7 skeins of yarn. So here we go with our calculations:
$12.10 ÷ 60 yds = .20/yard
We need 7 skeins, or a total of 420 yards (60 yds x 7 skeins):
$12.10 x 7 = $84.70
Let’s compare this to a yarn of similar fiber content that we carry. The yarn for this example comes in 235 yard skeins for $38.00. At first glance, you may think that this is way too much money to spend on your project. Let’s do the math.
$38.00 ÷ 235 yds = .16/yard
We only need 2 skeins of this yarn to get 420 yards of yarn. 235 yds x 2 = 470 yds
$38.00 x 2 = $76.00
Although you can see that the second yarn is a better value just by the price per yard, it is sometimes useful to continue the calculations all the way through.
Pricing can be deceiving, but with this information, you can now make more informed decisions about the yarn you purchase.


Please note that students will use the TI-Nspire CX handhelds developed by Texas Instruments in all of their math classes during the school year. If you want to buy a calculator for home use, the Crowley ISD Curriculum and Instruction Department recommends that you purchase the one used in your classroom. The TI-Nspire CX can be used on the eighth grade STAAR, Algebra 1 EOC, ACT, PSAT, SAT and AP tests.
If you purchase a TI-Nspire CX from a store or online, please have your students give the back of the box with the barcodes to their teacher. The school will have an opportunity to use these to receive free items from Texas Instruments for their classrooms.


Curriculum Area Overview
Developing young peoples confidence and ability. Students learn through interesting stimulating interactive activities that develop real life maths knowledge.
The broad aims at all levels are to promote mathematical thinking and transferable skills rather than rote learning. Students will also cover:
- Maths that is useful in everyday situations and the world of work
- Clear routines and procedures for specific situations
- Contextual material which is familiar and accessible to the student.
Examination Courses Offered
Functional Skills at Entry 1, 2 & 3
New GCSE Maths (AQA)
Level 1 Money Management
Units towards Asdan Personal Progress.
Skills and Knowledge Learned
Money, Time, Real life problems, Key skills


The Welsh Government has made raising standards of literacy and numeracy in schools a priority and from September 2013, the National Literacy and Numeracy Framework (LNF) became a statutory curriculum requirement. Children aged 7-14 now have annual reading and numeracy tests.
The LNF is designed to embed literacy and numeracy across the curriculum not just in English, Welsh and Maths. The LNF is a curriculum planning tool to help teachers of all subjects, think about how they can plan and provide opportunities for pupils to develop literacy and numeracy skills in practical ways.
What’s in the Framework?
The LNF describes the skills that children and young people aged 3-16 are expected to develop and sets out outcome statements for each year.
An artist working with a school will probably find it helpful to discuss with the teacher(s) which literacy and numeracy skills can naturally be teased out of the project. (These may be skills involved in the project done with the school or skills that the artist uses in his/her wider work.) Another approach could be to ask the teacher to explain the literacy and numeracy aspects they are currently working on – and consider any natural links with the planned art project. The teacher may want to use the outcomes of the project as a way of assessing how pupils are making progress in developing certain skills in the LNF.
Literacy and numeracy, are divided into the following strands:
• oracy across the curriculum
• reading across the curriculum
• writing across the curriculum.
• developing numerical reasoning
• using number skills
• using measuring skills
• using data skills.
It may help to download / print out the quick reference overview guide to the LNF and use it as a prompt to think about how you use these skills in your own practice and/or your work with young people. In particular, it’s worth bearing in mind that numeracy is NOT exactly the same as Maths. (The emphasis in Numeracy is on using ‘numerical reasoning’ skills (number, measurement and data) to solve real world problems – and on being able to plan, carry out and explain the procedures involved in finding the answer).
The table simply gives the headings used by the Framework, rather than the detail. To find out more about the kinds of skills and levels, go to the Learner Friendly versions of the LNF which describe the literacy and numeracy outcomes that teachers work towards, by key stage and year but be aware that the class may be working at several different years in the LNF depending on each individual pupil’s level.
How do teachers use the LNF?
Teachers use the Framework to:
Training in how to support the LNF
Teachers are supported by the Regional Educational Consortia to improve literacy and numeracy.
Guidance for artists in working with the LNF is beginning to emerge to support their unique role in developing these essential skills. For more information contact the Regional Arts & Education Networks.
All the case studies show how projects have helped develop skills identified in the LNF Framework.


Arithmetic Lesson PowerPoint Template
Arithmetic Lesson Presentation
Free PowerPoint template and Google Slides theme
Arithmetic is very useful in our lives. Teach your students the core arithmetic skills! Now use this creative template, which contains illustrations of books, cups, and science-related items. Use its maps, charts, timetables and tables to add your information.
With this template, you can add and subtract and multiply and divide easily in your classroom.
Features of this template
- 100% editable and easy to modify
- 27 different slides to impress your audience
- Contains easy-to-edit graphics such as tables, charts, diagrams and maps
- Includes 500+ icons for customizing your slides
- Designed to be used in Google Slides and Microsoft PowerPoint
- 16:9 widescreen format suitable for all types of screens
- Includes information about fonts, colors, and credits of the free resources used


Name: Guo Xi（郭希）
Business Address: Hubei University, Wuhan, 430062,People’s Republic of China
09, 2008–07, 2013 Tsinghua University
Department of Mathematical Science (For Ph.D degree)
Research Focus: Differential geometry
09, 2004–07, 2008 Dalian University of technology
Department of Mathematical Science, Undergraduate student
07, 2013– Lecturer, Faculty of mathematics and statistics, Hubei University, Wuhan
1. Xi Guo, Haizhong Li, Submanifolds with constant scalar curvature in a unit sphere, Tohoku Math.J., 65(2013), 331-339.
2. Xi Guo, Haizhong Li, Guoxin Wei, On variational formulas of a conformally invariant functional, Results. Math., 67(2015), 49-70.
3. Xi Guo, Haizhong Li, The stability of Fubini-Study metric on CPn, submitted
4. Xi Guo, Lan Wu, On variational formulas of Gauss-Bonnet curvatures, submitted
5. Xi Guo, Ni Xiang, Gradient estimates for Neumann boundary value problem of Monge-Amp`ere type equations on Riemannian manifolds, submitted


Dimensional weight has been used by air freight for a long time, and about 5 years ago, large shipping companies like FedEx and UPS started calculating dimensional weight and applying the results to packages shipped by ground service. The old way dimensional weight was calculated was by multiplying length, width and height. There are new policy changes that are going into effect at the end of December for FedEx and UPS that change the way dimensional weight is calculated. It is now calculated by multiplying the length, width and height of a package and dividing by 166 cubic inches per pound.
Dimensional Weight- The Specifics
Dimensional weight is more specifically calculated by measuring the height, length and width of a package in inches, using the longest point on each side and taking into consideration any misshaped edges or bulges. To get the cubic size of the package, multiply those dimensions. For example, if your package is 20” x 13” x 13”, the dimensional weight would be 3,380 cubic inches. When calculating dimensional weight, most shipping carriers have customers round to the nearest whole number. So, for example, if the length of your package is 10.50 inches or higher, you would round up to 11” but if it is 10.49” or below, you would round down to 10 inches, and so on.
The major carriers, UPS and FedEx, currently calculate dimensional weight the same way, which is the package’s cubic size divided by 166 for domestic shipments and 139 for international shipments. Dimensional weight is used to determine a package’s billable weight, which is the cost of shipping the package. If air service is being utilized for your package’s delivery, dimensional weight will always factor into the cost. If ground service is the shipping method used, usually it’s only subject to dimensional weight if the package is 3 cubic feet or larger (5,184 cubic inches). If the cubic size is less than 3 cubic feet, dimensional weight isn’t used and billable weight is determined by actual weight. However, now, any package shipped by FedEx or UPS will be rated by dimensional weight. J.M. Field Fulfillment is here for you to explain the changes and give you the best rates when shipping with us.


A system of linear equation is a collections of linear equation with the same set of variables.
A way to solve a system of equations is with Cramer’s rule.
To solve the 2×2 matrix:
First find the determinant:
If the determinant is not zero:
> V = (X, Y)
If the determinant is zero (a/a’=b/b’):
> If a/a’ = c/c’: V = ((c-b*µ)/a, µ)
> else: V = ∅
Try it yourself:X + Y =
X + Y =


Gender inequality is a fact around the globe. According to the U.S. Department of Commerce, women occupy nearly half of all U.S. jobs, yet represent less than 25% of those in science, technology, engineering and math (STEM). The White House has framed the need for women in STEM careers as critical to the continuing success of the U.S. economy. According to the Department of Education, 31% of the degrees and certificates in STEM fields were earned by women in 2008-2009. While this represents an increase of approximately 6% since 2000, this is still troubling given that women represent over 50% of enrollment in bachelor’s (57.4%) and master’s (62.6%) degree-granting institutions.
To better understand the factors that could contribute to such imbalances, Gijsbert Stoet of the University of Leeds and David C. Geary of the University of Missouri looked at sex differences in math and reading achievement levels and their relationship with gender equality indicators. The resulting study, “Sex Differences in Mathematics and Reading Achievement Are Inversely Related: Within- and Across-Nation Assessment of 10 Years of PISA Data,” was published in PloS One in 2013. The researchers used data collected by the Programme for International Student Assessment (PISA), which included math and reading achievement data for nearly 1.5 million 15-year-olds in 75 countries.
The study’s findings include:
- Sex differences in math are inversely correlated with sex differences in reading, meaning that countries with smaller sex differences in math have larger sex differences in reading, and vice versa.
- The sex difference in math was negligible among the students at the bottom of the math achievement continuum, but the difference increased as performance levels rose. This difference ranged from 1.9 points favoring girls to 2.4 points favoring boys among boys and girls at the bottom 5% of achievers. At the high end of performance scores, the performance difference ranged from 19.3 points to 21.7 points, both favoring boys. The authors note that this large difference between boys’ and girls’ achievement in math has implications for the under-representation of women in STEM fields.
- Conversely, sex difference in reading is smaller at the high end of the performance continuum. The average sex difference in reading was three times larger than the sex difference in math. The average difference increased from 32 points in 2000 to 38.8 points in 2009. In 2009, the bottom 5% of boys scored 50 points lower than the bottom 5% of girls.
- Countries with higher living standards showed larger differences in math.
- Among all countries, as math and reading scores for both boys and girls go up, living standards and gender equality measures are more likely to be higher.
In considering possible approaches to closing the gender gap in STEM employment, the authors argue that increasing national prosperity is not enough. “The implication is that if policy makers decide that changes in these sex differences are desired, different approaches will be needed to achieve this for reading and mathematics,” they state. “Interventions that focus on high-achieving girls in mathematics and on low-achieving boys in reading are likely to yield the strongest educational benefits.”
Tags: youth, higher education, technology


How to Calculate Future Value of a Investment
Do The Math!
The very last couple of weeks have been insane with the sum of Math and Calculation in Finance I am learning and devouring. Sharpening your Finance knowledge is critical business enterprise and why learning this would make you a Professional as Financial investment Advisor. Here is a Finance Calculation that can compute the Long term Value of a Financial commitment as long as you know A. The Present Value. B. The Charge of Return and C. The time involved for the return.
Video – How to Determine Future Value of a Financial investment with a primary calculator.
(Effortless NASAA/FINRA Check HOW TO) – Not Semi Yearly Calculation
Right here is the Calculation to follow to Find the Potential Value of a Investment
The current price of $87,500 with receipt of the cash remaining taken 3 decades (t) from these days. The sought after desire charge of return (r) for these money is 9%.
To work out this we will comply with this order of operations.
Current Value (PV) = Long term Value (FV)
PV = FV (1+interest price or return)-n
Use Math Get of Functions
PV 87,500 / (1+ .09)3rd energy
PV 87,500 / (1.09)3rd ability
PV 87,500 / 1.295029
Equals = $67,566.55 Long term Price
If you come across your self getting problems? Watch the online video on my youtube channel.
I hope you identified this Mathematical Method beneficial on your way as a Wealth Management, Financial investment Advisor, or if your just assessing a Financial commitment to spend in as a Day-to-day Joe! Im good this formulation will be handy to a lot of.
Godspeed – JS


Objectives: This workshop introduces participants to statistical methods for meta-analysis of the accuracy of a specific prediction model and of the added value of a specific predictor to an existing model. We discuss opportunities/challenges of the statistical methods and of common software packages.
Description: Prediction models are commonly developed and validated for predicting the presence (diagnostic) or future occurrence (prognostic) of a particular outcome. Prediction models have become abundant in the literature. Many models have been validated in numerous different studies/publications. Also, numerous studies investigate the added value of a certain predictor/biomarker to a specific existing prediction model. In both situations, aggregating such evidence is important for making inferences on the (added) predictive performance of a specific model or predictor/marker. Meta-analytical approaches for both situations have recently been developed.
In this workshop we illustrate these statistical approaches and how to combine - quantitatively - results from published studies on the predictive accuracy of a specific model or added predictive accuracy of a specific predictor. We illustrate this with various empirical examples.


tony's Dad, Steve, Tells our first success story
More Success Stories*
High school girl--Math concepts and equation solving strategies
Kay was a high school student struggling in algebra. Our in-depth assessment and analysis of Kay’s results indicated challenges in fundamental mathematical concepts and equation solving strategies. Kay enjoyed working with her learning specialist and she grew in confidence as her scores in algebra improved. Improving in math meant Kay would achieve her career goal of working in the medical field.
First grade bilingual boy--Word attack and comprehension in English and Spanish
Pedro was a quiet, hard-working 1st grader in a bilingual program. He was below grade level in all subjects; however, math was his best subject. Our in-depth diagnostic assessment and analysis of Pedro’s results indicated challenges in word attack and comprehension in English and Spanish. Within months, Pedro was reading on grade level in both languages. He developed a strong rapport with his bilingual learning specialist.
Fourth grade girl -- Phonological dyslexia
Lydia was a bright, curious, and funny 4th grader. She excelled in math, but struggled in reading, writing, and spelling. Our in-depth diagnostic assessment and analysis of Lydia’s results indicated phonological dyslexia. Within a few months, Lydia’s spelling and reading scores improved significantly. Her writing is more successful. At school, Lydia is now a member of the academic and leadership club. Lydia invites her learning specialist to attend her school activities.
Fourth grade boy--Double deficit dyslexia
Ray is a ten-year-old boy with a contagious sense of humor. In first grade, he was diagnosed with ADHD. Our recent in-depth assessment and analysis of Ray's results also identified dyslexia as a learning disability. Ray is engaged with a reading and a math learning specialist. He "loves" working with both of them! He has made significant gains in reading and math continues to be his academic strength. The learning specialists work with his teachers and mentor Ray's mother and grandmother by demonstrating learning methods to utilize with Ray that support his reading and math growth.


Leonardo Bonacci (c. 1170 – c. 1250), popularly known as Fibonacci or Leonardo of Pisa, was the first great Western mathematician after the decline of Greek science.
His well-known moniker “Fibonacci” is derived from the Latin words “filius Bonacci”, literally translated to “son of Bonacci”. Fi'-Bonacci could be considered the equivalent of the English William-son or John-son.
Fibonacci was born in Pisa, Italy, to Guglielmo Bonacci, a wealthy merchant who directed a trading post at a major port located in present day Algeria. As a boy, Fibonacci accompanied his father on his commercial trips to the Orient. It was during his travels along the Mediterranean coast that the budding mathematician became acquainted with the Hindu-Arabic number system and discovered its enormous practical advantages compared to the Roman numerals, which were still current in Western Europe.
Fibonacci ended his travels around the year 1200 and returned to Pisa. Upon his return, inspired by his interactions with the foreign merchants he met while under the tutelage of his father, Leonardo wrote a number of influential texts that played an important role in reviving ancient mathematical skills. His works garnered him recognition among his contemporaries and high esteem from the reigning Holy Roman Emperor, Frederick II.
His most well-known published book is Liber Abaci (1202), literally translated as “Book of Calculations” or “Book of the Abacus”. The book, which went on to be widely copied and imitated, was based on the arithmetic and algebra that Fibonacci had accumulated during his travels. In it, Fibonacci introduced the so-called modus Indorum (method of the Indians), today known as Arabic numerals and the Hindu-Arabic place-valued decimal system. The book showed the practical importance of the new numeral system by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interest, money-changing, and other applications. Furthermore, Abaci contains a large collection of problems aimed at merchants. They relate to the price of goods, how to calculate profit on transactions, how to convert between the various currencies in use in Mediterranean countries, and problems which had originated in China. The book was well received throughout educated Europe and had a profound impact on European thought.


About Plato & Nous
It all started in 360 BC.....
Timaeus is a work by the Greek philosopher Plato, written in 360 BC. .
"…….. Plato presents an elaborately wrought account of the formation of the universe and an explanation of its impressive order and beauty. The universe, he proposes, is the product of rational, purposive, and beneficent agency. It is the handiwork of a divine Craftsman (“Demiurge,” dêmiourgos) who ………… imposes mathematical order on a preexistent chaos to generate the ordered universe (kosmos). ………. For Plato this arrangement is ……….. the outcome of the deliberate intent of Intellect (nous)…"
First published Tue Oct 25, 2005 in the Stanford Encyclopedia of Philosopy; substantive revision Mon Dec 18, 2017
Then in 1623 …….
And in 2010 …………
A book by John Frederick Carden Michell (1933-2009) called Sacred Geometry was published.
Mitchell believed in the spiritual significance of numbers and geometry. His book has many elegant water colours reminiscent of M.C. Escher's mathematically inspired art.
There was also a drawing of a cat called Nous going through a cat flap in the front door of Plato's Academy.
So now we have explained the origins of Plato's Nous. We have included an image of a descendant of Naus. Meet my niece's cat Maude, with her geometrically elegant and lovely face. Maude hopes you will enjoy our presentations.


In sales, it’s important to understand how much effort you need to put in to achieve your income goals.
One way to do this is by understanding the conversion rates for each step in your sales process.
For example, if you know how many emails it takes to get an interview, how many interviews it takes to close a sale, and how much revenue each sale generates, you can start to predict your future income based on the amount of activity you put in.
Let's take a look at some hypothetical sales numbers to illustrate this concept:
- 20 emails convert to 1 interview, or 13 phone calls convert to 1 interview
- 5 interviews convert to 1 close
- 1 close generates $350 in revenue
Using these numbers, we can calculate how many emails, phone calls, interviews, and closes are needed to generate a specific amount of revenue. Here are some examples:
- For example, to earn $55,000 in revenue in a year, you would need to close 157 sales. To close 157 sales, you would need to conduct 785 interviews (157 x 5), which means you would need to have 15,700 emails sent out (785 x 20), or 10,201 phone calls (785 x 13).
- If you want to focus on increasing the number of phone calls you make, you could aim to make 30 calls a day. This would result in 2.3 interviews per day (30/13), and if you close 20% of those interviews, you would close 1 sale every 12 days (5 interviews / 20% = 1 sale, 12 days per sale). To earn $55,000 in revenue, you would need to close approximately 140 sales per year (55,000 / 350), which means you would need to make 690 phone calls per sale (140 sales x 5 interviews x 13 phone calls).
By understanding the conversion rates for each step in your sales process, you can start to set realistic goals for yourself and adjust your activity levels accordingly.
Whether you choose to focus on increasing the number of emails you send, the number of phone calls you make, or the number of interviews you conduct, it’s important to have a clear understanding of how each step contributes to your overall revenue goals.
Automate and simplify the whole calculation process with salesquotasetter.com
So you can measure your conversion rates and production. Know you averages easily with SQS. Set realistic targets that will earn you your commission you want!
Sign up now for a free trial and exceed your targets!


Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. How to convert meters to feet and inches step-by-step One meter is a length measurement and equals approximately 3. Hey, I bet that's around, my height. This is the number of 16th's of an inch and also the numerator of the fraction which may be still reduced.
More examples of heights converted from cm to feet and inches:
Harm to minors, violence or threats, harassment or privacy invasion, impersonation or misrepresentation, fraud or phishing, show more. How tall is cm in feet? Like 5 foot 6 or something? I am confused, none of the conversion websites make sense to me, and i can't find a tape measure. Are you sure you want to delete this answer? For the best answers, search on this site https: Have a nice day: Hi,pretty much spot on 5 foot 5 inches sweet.
Use this page to learn how to convert between centimetres and feet. Type in your own numbers in the form to convert the units! You can do the reverse unit conversion from ft to cm , or enter any two units below:. A centimetre American spelling centimeter, symbol cm is a unit of length that is equal to one hundreth of a metre, the current SI base unit of length. A centimetre is part of a metric system. It is the base unit in the centimetre-gram-second system of units.
A corresponding unit of area is the square centimetre. A corresponding unit of volume is the cubic centimetre. Obviously, this is equivalent to 1. The previous step gave you the answer in decimal inches 4. See below a procedure, which can also be made using a calculator, to convert the decimal inches to the nearest usable fraction:. This is the number of 16th's of an inch and also the numerator of the fraction which may be still reduced. You can use this table to find any value in feet, in inches or in feet plus inches when you know the value in centimeters.
It is an alternative to the converter above. Here is another version of this Centimeter to feet and inches table. See also this equivalent fractions chart version and also our cm to feet and inches calculator with steps. Download the Excel version of this chart. Download the Word version of this chart. Download the printable pdf version of this chart. While every effort is made to ensure the accuracy of the information provided on this website, we offer no warranties in relation to these informations.
Quickly convert centimetres into feet ( cm to ft) using the online calculator for metric conversions and more. rows · About Cm to Feet and Inches Converter. The online cm to feet and inches conversion . Convert cm to feet and inches Meter (m) or centimeters (cm) to feet (ft ′) and inches (in ″). Here is the answer to questions like: what is cm in feet and inches. cm equals feet.


The work has not been graded but I like the output that was submitted to me. Is it possible for the same prof to do the next assignment I will be submitting? If possible, I will greatly appreciate it.
Question 1: 5 marks
Preliminary plans are under way for the construction of a new stadium for a football team in Italy. Officials have questioned the number and profitability of the luxury corporate boxes planned for the upper deck of the stadium. Corporations and selected individuals may buy the boxes for € 100000 each. The fixed construction cost for the upper-deck area is estimated to be €1500000, with a variable cost of €500000 for each box constructed.
a. Develop a model for the total cost. Let x represent the number of boxes. (1 mark)
b. What is the breakeven point for the number of luxury boxed in the new stadium? (2 marks)
c. Develop a model for the total profit if x participants enroll in the workshop. (1 mark)
d. Preliminary drawings for the stadium show that space is available for the construction of up to 50 luxury boxes. Promoters indicate that buyers are available and that all 50 could be sold if constructed. What is your recommendation concerning the construction of luxury boxes? What profit is anticipated? (1 mark)
Question 2: 18 marks
GulfGolf makes two different types of golfing gloves: a regular model and a professional model. The firm has 900 hours of production time available in tis cutting and sewing department, 300 hours available in its finishing department and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table.
Assuming that the company is interested in maximizing the total profit contribution, answer the following: (Solve using 4 decimal places)
a. What is the linear programming model for this problem? (4 marks)
b. What is the standard form of the linear programming model? (1.25 marks)
c. Solve graphically and find the extreme points. (6 marks)
d. What is the optimal number of gloves that must be manufactured graphically (round off the optimal number to an integer). ( 3.25 marks)
e. What is the total profit contribution the company can earn with the listed production quantities? (0.5 mark)
f. How many hours of production time will be scheduled in each department? (2.25 marks)
g. What is the slack time in each department? (0.75 mark)
Question 3: 13 marks
Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of United Oil and H shares of Huber Steel. The annual return for United Oil is €3 per share and the annual return for Huber Steel is €5 per share. United Oil sells for €25 per share and Huber Steel sells for €50 per share. The portfolio has €300,000 to be invested. The portfolio risk index (0.25 per share of United Oil and 0.05 per share of Huber Steel) has a maximum of 700. In addition, the portfolio is limited to a maximum of 5000 shares of United Oil. The linear programming formation that will maximize the total annual return of the portfolio is as follows:
Max 3U + 5H Maximize total annual return
25U + 50H ≤ 300, 000 Funds available
0.25U + 0.05H ≤ 700 Risk maximum
1U ≤ 5,000 United Oil maximum
U, H ≥ 0
a. Solve this problem using the graphical solution procedure. (4.25 marks)
b. Find the feasible solution region and optimal solution (round off the optimal solution to the nearest tens integer). (2.75 marks)
c. Calculate the range of optimality for the objective function coefficient of U. (2 marks)
d. Calculate the range of optimality for the objective function coefficient of H. (2 marks)
e. Suppose the objective function coefficient of ‘U’ is decreased from 3 to 1.5 and ‘H’ is increased from 5 to 9. What is the new optimal solution? (2 marks)
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Tom Torlakson is impressed with River Islands Technology Academy. So impressed that the man who oversees 10,000 public schools and the education of 6 million students as California’s State Superintendent of Public Instruction made his second visit in three years to the Lathrop charter school. The infusion of cutting edge technology to advance science, technology, engineering, and math education first lured Torlakson to visit in 2013.
Last spring, California held a statewide Assessment of School Performance and Progress testing for grades 3 -8 to ascertain students’ progress “in a more rigorous education regimen associated with the Common Core standards that were adopted in 2010”.
Performance was measured by the percentage of students who exceeded state standards, met state standards, nearly met state standards and did not meet state standards in English and mathematics.


Although geometry and algebra are the most commonly taught subjects in mathematics, there are still many groups in mathematics that are taught differently
Some areas of mathematics are taught with drawings or photographs and others require text and a diagrammatic representation.
Geometry and algebra will be the custom writing two varieties of math that are educated in both primary and secondary educational institutions. They are instructed at the same fashion at both degrees. There are still other sorts of mathematics which can be taught at either basic and secondary levels.
Geometry is educated in different grade levels in school than it is in secondary school. A student begins with carrying algebra and geometry.
Geometry is the second most used subject in mathematics. This group of subjects involves geometrical figures, numbers, lines and curves. Geometry is used in everything from scientific instruments to babies home toys.
Geometry is difficult to show in grades 1 through 8. By now a student http://www.liberty.edu/online/masters/communication/ enters the eleventh level, they should have mastered the use website samedayessay.com of gear like the linear and design construction algebra. At the same way as algebra, geometry is educated in secondary and elementary faculty and was part of levels of mathematics for centuries.
Algebra is probably the hardest type of mathematics to teach because the student does not understand what algebra is before taking it in grade school. Algebra begins with addition, subtraction, multiplication and division and continues on to calculus. Calculus is a subject that is used by all students of mathematics, including those who wish to go on to higher levels of study.
Geometry is taught in the same way as algebra. Geometry takes place only when problems in geometry require shapes or figures. Students of geometry study a set of symbols that describe different shapes and use these symbols to solve problems. Geometry is taught to students of elementary school before they start the main five types of subjects such as algebra, trigonometry, calculus and statistics.
Geometry is taught in elementary school with writing tests, chalk boards and basic geometrical equations. These are taught in grades six but the development of basic shapes and figures that can be solved using algebra and geometry is taught earlier. All of the subjects that have been learned using geometric tools are taught to all students of mathematics during elementary school.
Students of geometry have been educated the easy difference between volume and area. The easiest type of all geometry is quadratic geometry which is used in resolving simple equations that are cubic. College students of geometry can also be educated how to fix quadratic equations.
Differentiation is taught to students of geometry before they learn the difference between area and volume. Areas and volumes are necessary to solve cubic equations. The differential equation requires students to compute the change of a quantity or concept and then solve for a new value using addition, subtraction and multiplication.
R is educated in various kinds in various settings. The types of instruction themes have been used to show methods of mastering math. The results could be disastrous If a student learns mathematics in an instruction style that is educated otherwise than the way in she or he sees math.
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A reader has requested that we give an explanation of cash on hand and profit. There seems to be some confusion about how the numbers work.
Cash on Hand is exactly what it sounds like – how much cash money is in the bank, right now?
If you’re looking at the balance in your checking account and add that to your savings account, that is “cash on hand.” Let’s assume that amount is $7500.
“Days cash on hand” = Cash on Hand / Daily Operating Expenses
Daily Operating Expenses = Annual Operating Expenses / 365
Let’s assume that it costs you $36,500 each year to run your household (Annual Operating Expense). If you divide that by the number of days in the year (365) you will get your “daily operating expense.”
$36,500 / 365 = $100 $100 is your daily operating expense.
Earlier, we said that you had $7,500 in your bank account (your “Cash on Hand”).
$7,500 / $100 = 75 You have 75 Days Cash on Hand. That means you have enough money to pay your bills for 75.
Profit is a different formula: Profit = Revenue – Expenses
Let’s assume you earn $42,000 each year (Revenue).
Your annual expenses are $36,5000 (Expenses).
$42,000 – $36,500 = $5,500 You had a “profit” of $5,500.
Notice that your profit of $5,500 is not equal to your cash on hand of $7,500.
Cash on Hand answers the question “how much cash do we have, right now?” That could on Jan. 1, Mar. 4, July 31, etc.
Profit answers the question “how much did we get to keep after we paid all the bills, during a certain time?”
The certain time could be a month, a quarter, or a year, “How much did we get to keep this year?”
For most people, the year starts on January 1 and ends December 31.
For Singing River, the year starts on October 1 and ends September 30.
When Singing River has a profit of $600,000 that answers the question “How much did SRHS keep after they paid the bills, from Oct 1, 2014 – Sept 30, 2015?”
According to the audit, as of Sept. 30, 2015, Singing River had $45 million cash on hand, which is approximately 51 days cash on hand.


Saturday, February 5, 2011
Math Munchers Math Game on TpT!
While making the cute little googly-eye pointers in my last post, I was inspired to create "Math Munchers". Just like their gator counterparts, they like to devour large numbers. In this case, furry-monster-pom-pom counters or "arrays". My third grade peanuts still struggle with multiplication fact fluency a bit and rely a little on arrays to solve problems. This game allows students to create an array to solve a problem and then compare their product with their partner's practice comparing numbers too! It is a double duty game, and it's cute! I have created a game that has two versions: one for multiplication and one for addition. Instead of building an array, students could use the pom poms as counters for the addition game. Both sets of directions are included. You can check this 9-pager out HERE! If anyone picks up a copy, please let me know what you think. :)


Two projects aimed at boosting female representation in STEM have won the second Nature Research Awards for Inspiring Science and Innovating Science, in partnership with The Estée Lauder Companies.
Jean Fan spent a year volunteering at a science club for high school students during her Ph.D. program at Harvard University and was struck by how many of them dismissed the idea of becoming scientists themselves.
“A lot of my students would make remarks like ‘I’m not quite a maths person,’ or would not see themselves as future scientists,” she tells Julie Gould.
“I really wanted to leave them with some type of gift to encourage them to continue developing their interest in science.”
As a result, Fan, who was the sole female graduate student in her Ph.D. bioinformatics program, launched customized, a non-profit that uses personalized educational storybooks (which she writes and illustrates) to inspire girls about scientific careers.
This week, at a ceremony in London, she won the 2019 Inspiring Science Award, one of two offered by Nature Research and the Estée Lauder Companies.
The second award, Innovation in Science, goes to Doreen Anene, a Ph.D. student at the University of Nottingham, UK.
In 2017 Anene launched The STEM Belle, a non-profiled based in Nigeria, her home country. The STEM Belle also works in Ghana and Pakistan. As its website says, The STEM Belle is “focused on leveling up the female representation in Science Technology Engineering and Mathematics fields by attracting, retaining and advancing more girls and young women to STEM subjects and fields.”


In this how to use the Quartile Function in Google Sheets tutorial article, first I’ll talk about the benefit of the Quartile Function, the syntax of the function. After that I’ll explain with example and show you how to use it. And I’ll finish with some FAQs on the Quartile Function.
So read on.
If you need to calculate the quartile for your Google Sheet dataset and you want to find the quartiles manually, the data must be ordered from lowest to highest.
But if you use the quartile function, you will be able to calculate the quartile for the Google Sheet dataset without having to order data from lowest to highest.
Quartiles are actually dictated three points in an array or a dataset. They are:
- In the first quartiles select the middle data point.
- The second quartiles are divided into min and middle data points.
- The third quartile is split into a middle and max data point.
Inside the quartile function, there are 5 quartile numbers, that number (minimum, maximum, median, and two quartile points) is 0, 1,2,3,4.
Of the five quartile number 0 return the minimum value and there also use the Min function. 4 return the maximum value there also use the Max function.
The Google Sheets Quartile function uses the lowest (Min value) and highest (Max value) numbers in the dataset.
Syntax of the Quartile Function for Google Sheets:
The function will return the value closest to a certain quartile in your dataset.
The syntax used QUARTILE function is:
Data: It is an array or range that contains the dataset for the calculation and is used to find the quartile.
quartile_number: this formula tells which quartile value (0 to 4) returns.
- 0 return minimum value in the array or dataset (similar to the MIN function). (“0th percentile”)
- 1 return the value nearest the first quartile number in the array. (“25th percentile”)
- 2 return median value in the array. (“50th percentile”)
- 3 return the value nearest the third quartile number in the array. (“75th percentile”)
- 4 return maximum value in the array or dataset (similar to the Max function). (“100th percentile”)
Examples of uses of Quartile function in Google Sheets
Now you know the basic syntax of the quartile function, so let’s see an example using Quartile Function in a spreadsheet.
In this example, you can see I have used some dataset value A2:A7 and applied quartile function formula =Quartile(data, quartile_number) that has been presented quartile number 0 to 4 and each result in a different quartile number.
How to use the QUARTILE function in Google Sheets
- First, I put some datasets in any cell. For example, I have put some datasets in column B from B2 to B7.
- Click the cell where you want the result for example the cell is C2.
- Type on the keyboard =qu and you can see the quartile function.
- Click quartile and manually type(=QUARTILE(B2:B7,0)) or drag over the intended dataset in the array.
- What does result in you want type quartile number (0 to 4) and press quartile number and do bound by the first bracket.
- Then press enter.
In the above example, you can see the quartile function is very easy to use.
- If data is blank, QUARTILE returns the #NUM!. That’s a means error value.
- If quart is not an integer, it is reduced.
- If quart less than or if quart greater than 4, QUARTILE returns the #NUM!
- When quart is equal to 0 (zero), 2, and 4, respectively then MIN, MEDIAN, and MAX return the same value as QUARTILE.
How to Find Quartiles Manually in Google Sheets
Sometimes you find data manually so I have an easy way. You need to follow the steps below:
- Suppose you have following the data or array: 4,2,3,6,8,5,9,7,1
- First data must be shorted and you find the median/middle value.
- So, eliminate the lowest and the height value.
- In the same process now the first quartile is between 1 to 5.
- And the second quartile is between 5 to 9.
Quartile Function FAQs
How is quartile used in real life?
Some companies use the quartiles to benchmark other companies.
For example, the median company pay for a given position is set at the first quartile of the top 20 companies in that region. The quartiles and IQR information are typically used when you create a box-plot of your data set.
What are the differences between QUARTILE.INC and QUARTILE.EXC in Google sheets?
The syntax of Quartile.inc and quartile function is the same. Here 0 to 4 has a total of 5 values. 0 return minimum value and 4 return maximum value.
Quartile.exc function’s syntax is the same here 1 to 3 has a total of 3 values. There is no minimum and maximum value here.
Quartile function is a very easy and simple way to do, so quartile calculations can be done very easily.
I think if you use the function, it will be easier to do quartile calculations faster than manually. Because to manually, data must be sorted, but if you use a function, you can do calculations in both data sorted or unsorted situations.
I hope that after you go through this article properly, you will understand how to find quartiles manually and through the quartile function in Google sheets.
More Related Google Sheets Tutorials on:


- N. Kudasov, E. Riehl, and J. Weinberger, Formalizing the ∞-categorical Yoneda lemma, to appear in 13th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2024), 1–13, arXiv:2309.08340
- P. Hackney, V. Ozornova, E. Riehl, and M. Rovelli, Pushouts of Dwyer maps are (∞,1)-categorical, to appear in Algebr. Geom. Topol. (2022), 1–29, arXiv:2205.02353
- P. Hackney, V. Ozornova, E. Riehl, M. Rovelli, An (∞, 2)-categorical pasting theorem, Trans. Amer. Math. Soc. 376 (2023), 555–597, arXiv:2106.03660
- E. Riehl and M. Wattal, On ∞-cosmoi of bicategories, La Matematica 1, (2022), 740–764, arXiv:2108.11786
- E. Riehl and D. Verity, On the construction of limits and colimits in ∞-categories, Theory Appl. Categ. 35 (2020), no. 30, 1101–1158, arXiv:1808.09835
- E. Riehl and D. Verity, Recognizing quasi-categorical limits and colimits in homotopy coherent nerves, Appl. Categ. Struct., 28(4), (2020), 669–716, arXiv:1808.09834
- E. Riehl and D. Verity, ∞-category theory from scratch, Higher Structures 4(1):115–167, 2020, arXiv:1608.05314
- R. Garner, M. Kędziorek, and E. Riehl, Lifting accessible model structures, J. Topology, 13 (2020), no. 1, 59–76, arXiv:1802.09889
- E. Riehl and D. Verity, The comprehension construction, Higher Structures 2 (2018), no. 1, 116-190, arXiv:1706.10023
- K. Bauer, B. Johnson, C. Osborne, E. Riehl, and A. Tebbe, Directional derivatives and higher order chain rules for abelian functor calculus, Topology Appl. Women in Topology II: Further collaborations in homotopy theory 253 (2018), 375–427, arXiv:1610.01930
- E. Riehl and M. Shulman, A type theory for synthetic ∞-categories, Higher Structures 1 (2017), no. 1, 116–193, arXiv:1705.07442
- K. Hess, M. Kędziorek, E. Riehl, and B. Shipley, A necessary and sufficient condition for induced model structures, J. Topology 10 (2017), no. 2, 324–367, arXiv:1509.08154
- E. Riehl and D. Verity, Kan extensions and the calculus of modules for ∞-categories, Algebr. Geom. Topol. 17 (2017), no. 1, 189–271, arXiv:1507.01460
- E. Riehl and D. Verity, Fibrations and Yoneda’s lemma in an ∞-cosmos, J. Pure Appl. Algebra 221 (2017), no. 3, 499–564, arXiv:1506.05500
- M. Ching and E. Riehl, Coalgebraic models for combinatorial model categories, Homol. Homotopy Appl. 16 (2014), no. 2, 171–184, arXiv:1403.5303
- E. Riehl and D. Verity, Completeness results for quasi-categories of algebras, homotopy limits, and related general constructions, Homol. Homotopy Appl. 17 (2015), no. 1, 1–33, arXiv:1401.6247
- M. Bayeh, K. Hess, V. Karpova, M. Kędziorek, E. Riehl, and B. Shipley, Left-induced model structures and diagram categories, Contemp. Math. 641 (2015), 49–81. arXiv:1401.3651
- E. Riehl and D. Verity, Homotopy coherent adjunctions and the formal theory of monads, Adv. Math 286 (2016), 802–888, arXiv:1310.8279
- T. Barthel, J.P. May, and E. Riehl, Six model structures for DG-modules over DGAs: model category theory in homological action, New York J. Math 20 (2014), 1077-1159, arXiv:1310.1159
- E. Riehl and D. Verity, The 2-category theory of quasi-categories, Adv. Math. 280 (2015), 549–642, arXiv:1306.5144
- E. Riehl and D. Verity, The theory and practice of Reedy categories, Theory Appl. Categ. 29 (2014), no. 9, 256–301, arXiv:1304.6871
- E. Cheng, N. Gurski, and E. Riehl, Cyclic multicategories, multivariable adjunctions and mates, J. K-theory 13 (2014), no. 2, 337–396, arXiv:1208.4520
- A.J. Blumberg and E. Riehl, Homotopical resolutions associated to deformable adjunctions, Algebr. Geom. Topol. 14 (2014), no. 5, 3021–3048, arXiv:1208.2844
- T. Barthel and E. Riehl, On the construction of functorial factorizations for model categories, Algebr. Geom. Topol. 13 (2013), no. 2, 1089–1124, arXiv:1204.5427
- E. Riehl, Monoidal algebraic model structures, J. Pure Appl. Algebra 217 (2013), no. 6, 1069–1104, arXiv:1109.2883
- C. Kennett, E. Riehl, M. Roy, M. Zaks, Levels in the toposes of simplicial sets and cubical sets, J. Pure and Appl. Algebra 215 (2011), no. 5, 949–961, arXiv:1003.5944
- E. Riehl, On the structure of simplicial categories associated to quasi-categories, Math. Proc. Camb. Phil. Soc. 150 (2011), no.3., 489–504, arXiv:0912.4809
- E. Riehl, Algebraic model structures, New York J. Math. 17 (2011), 173–231, arXiv:0910.2733
- J. D’Angelo, S. Kos, E. Riehl, A Sharp Bound for the Degree of Proper Monomial Mappings Between Balls, J. Geom. Anal. 13 (2003), no. 4, 581–593.
- E. Graham Evans, Jr. and E. Riehl, On the intersections of polynomials and the Cayley-Bacharach theorem, J. Pure and Appl. Algebra 183 (2003), no. 1–3, 293–298.
- E. Riehl, Could ∞-category theory be taught to undergraduates?, Notices of the AMS 70(5). May 2023, 727–736.
- E. Riehl, Homotopy coherent structures, Expositions in Theory and Applications of Categories 1 (2023), 1-31, arXiv:1801.07404, also available via AMS Open Math Notes OMN:201901.110786.
- E. Riehl, Homotopical categories: from model categories to (∞, 1)-categories, to appear in a forthcoming volume on spectra to appear in the MSRI Publications Series with Cambridge University Press, (2019), 1–67, arXiv:1904.00886
- F. Loregian and E. Riehl, Categorical notions of fibration, Expositiones Mathematicae 38 (2020), no. 4, 496–514, arXiv:1806.06129
- E. Riehl, Made-to-Order Weak Factorization Systems, Extended Abstracts Fall 2013, Research Perspectives CRM Barcelona, 2015.
- E. Riehl, Complicial sets, an overture, 2016 MATRIX Annals, (2017), 49–76, arXiv:1610.06801
- E. Riehl, The Kan Extension Seminar: An Experimental Online Graduate Reading Course, Notices Amer. Math. Soc. 61 (2014), no. 11, 1357–1358.
- A.M. Bohmann, A comparison of norm maps, with an appendix by A.M. Bohmann and E. Riehl, Proc. Amer. Math. Soc. 142 (2014), no. 4, 1413–1423, arXiv:1201.6277
- E. Riehl, On the ∞-topos semantics of homotopy type theory, (2022), 1–37, arXiv:2212.06937
- S. Hazratpour and E. Riehl, A 2-categorical proof of Frobenius for fibrations defined from a generic point, (2022), 1–15, arXiv:2210.00078
- E. Riehl and D. Verity, Cartesian exponentiation and monadicity, (2021), 1–71, arXiv:2101.09853
- E. Riehl, Inductive Presentations of Generalized Reedy Categories


SIGMA is an academic open-access journal which has been established for the dissemination of state-of-the-art knowledge in the field of mathematics and mathematics education. This journal published in Mathematics Education Department at Bondowoso University. It is published twice in a year (February and August). The SIGMA welcomes manuscripts resulted by researchers, scholars, teachers, and professionals from a research project in the scope of Pure Mathematics, Computing Mathematics, Statistics, Mathematics Learning, Evaluation and Assessment in Mathematics Learning, STEAM, Ethnomathematics, ICT in Mathematics Education, Design / Development Research in Mathematics Education and sciences. All submitted manuscripts will be initially reviewed by editors to ensure the quality of the published manuscripts in the journal. The manuscripts should be original, unpublished, and not in consideration for publication elsewhere at the time of submission to the SIGMA.


History of Mathematics
By Utkrista Mulmi
We have been taking notes on various concepts such as The human being, The human systems and The history of Mathematics.
Mathematics is a very old subject and we could not have survived without it. It is used a lot in our everyday life.
On this subject, we have taken notes about uses of numbers, about mathematics, history of mathematics and number prefixes. They can be explained as below:
Uses of numbers: We use numbers in everyday life to count, measure, make codes, compare, figure location. People use these methods of mathematics constantly.
About mathematics: Mathematics has six main subjects, them being: Arithmetic, Geometry, Trigonometry, Algebra, Calculus, Data Probability and statistics.
Arithmetic consists of addition, subtraction, multiplication, division, fractions and other simpler forms of mathematics. This form of mathematics is used most often.
Geometry is the study of shapes, position, space, and star mapping. Trigonometry deals with measuring angles, sides, and their relationships. This also applies to waves, sounds light waves and angles.
Algebra is the use of variables representing numbers that can be used to solve complex problems, equations, structures, groups, constructions and concepts.
Calculus is the most difficult form of math. It uses limits, functions, derivatives, infinite series and study of change.
Number prefixes: These are shortened words relating to numbers. They are:
People use prefixes in words like unicycle or octopus.
Some interesting historical facts of mathematics1. 30000 years ago, Seasons were counted
2. 6000 years ago, Sumerians used shapes to count 1, 10 and 100
3. 5300 years ago, Babylonians used other shapes like triangles and circles.
4. Romans used I II III IV V and so on for 12345.
5. Zulus used fingers and toes as did others.
6. Nigerians used shells based on 205.
7. Persians used knots
8. Incas used Kibu, Strong.
9. Arabic numbers were invented 5000 ago
10. Egyptians used fractions
11. Sumerians and Babylonians used number 60 system.
12. Chinese used 10s and decimals and started using Abacus.
13. Egyptians used multiplication.
14. Abacus was the calculator.
15. Arabic Mathematician AI Quaresuna introduced 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.