by Bob Romero —
Bob Romero has been a diligent student of esoteric spiritual subjects and metaphysics for many years, with a life-long quest for answers. He has submitted new and original articles that focus on life lessons and experiences he wishes to share with our readers and the world.
There are many different manifestation techniques that are available. Some are shown and demonstrated on YouTube. Jake Ducey has several of these tools on his YouTube channel. He cites them as examples to his success as an author and as a prolific Internet star and personality. One of the methods that he touts as one of the most powerful is Nikola Tesla’s 3-6-9 Method. But there several other videos that also describe the same method and after watching a few of them, it seems as if they are all reading the same script. They all start off with the quote by Galileo, “The book of nature is written in the language of mathematics” and that Nikola Tesla said that the sequence of 3-6-9 holds the keys to the universe. They also point out that Tesla would walk around a building 3 times before entering the building. He would wash his dishes with 18 napkins because 18 is divisible by 3,6, and 9, and only stay in hotel rooms where the room number was divisible by 3. While he appeared to be eccentric, they point out his inventions and his concepts that laid the groundwork for other inventions.
The videos continue to follow the same script as to why Tesla felt that 3-6-9 was the key to the universe. Vortex Math is a major reason, but they don’t go into the detail. I will explain some of it later. They continue with the fact that atoms are 99.999% empty space but are manifested as physical. So, the 99.999% of an atom is represented as energy which is in the quantum field. Our DNA is composed of 3 chemical subunits sequenced 3 at a time. And each time you add 3 chemical subunits of DNA, you subsequently get 6 and 9. Scientist Marco Rodin believes that 3-6-9 represents an energy field from the third dimension to the fourth dimension. Tesla said that to find the secrets of the universe think in terms of energy, frequency, and vibration. So, the technique is to use this trinity of energy, frequency, and vibration to create a magnetic field that will attract what you want.
The 3-6-9 method is very easy to do. You think of three specific affirmations that you want to manifest in your life. Some of the same examples are used in the videos like “I’m so happy and grateful that I’m making $10,000 a month”, or “I’m so happy and grateful that I healed my health and I’m in perfect health”. The trick is to start off with “I’m so happy and grateful that …” and then state what you want and say it out loud and be excited about it, so that it’s out there in the universe. After you come up with your three affirmations, you review it for 9 seconds. I found out that by saying it twice, it will take about 9 seconds. Then you do this 6 times a day for 9 days.
A video by a group called “Engineering Made Easy” explains the vortex math and elaborates on the reasons why Tesla believed in the 3-6-9 method. This was really fascinating to me especially because I’m a math junkie. They talk about how all living things are made up of cells and multicellular organisms are formed by the division of a singe cell. So, a cell divides into two cells and those two cells divide into four cells and so on until a living organism is formed. So, this is where the vortex math comes in. You start doubling and then take the digit root of each number. The digital root is the single digit number that is obtained by adding the digits that comprise the original number and resolving the sum and any following sums to a single digit. For example, 797 is 7+9+7 = 23 and 2+3 = 5. So, the digital root of 797 is 5. Hence, doubling the numbers starting with 1 will resolve as follows:
1 = 1
2 = 2
4 = 4
8 = 8
16 =1+6 = 7
32 = 3+2 = 5
64 = 6+4 = 10, 1+0 = 1
128 = 1+2+8 = 11, 1+1 = 2
256 = 2+5+6 = 13, 1+3 = 4
512 = 5+1+2 = 8
1024 = 1+0+2+4 = 7
2048 = 2+0+4+8 = 14, 1+4 = 5
and so on.
You can see that the sequence of 1,2,4,8,7,5 will continue to repeat infinitely and the numbers of 3,6 and 9 are missing. When you halve the numbers starting with 1, the sequence is 1,5,7,8,4,2 and 3,6, and 9 are still missing. If you start with the number 3 and keep doubling, the digital root of each number will be 3 or 6 and halving the numbers from 3 will always produce 3 or 6 as a digital root. If you start with the number 9 and keep doubling, the digital root will always be 9 and halving the numbers from 9 will always produce 9 as a digital root. Unfortunately, vortex math was never covered in any of my math classes, and we never talked about digital roots, as there are a lot of cases in time and space where 9 is the digital root and a few of them are discussed here.
A circle is 360 degrees and 3+6+0 =9. If you divide the circle in two, you get 180 degrees and 1+8+0 = 9. Half of that is 90 degrees, and 9+0 = 9. Half of that is 45 degrees and 4+5 = 9. Continuing on to infinity, the result will always resolve to 9. The same applies to polygons. The sum of the angles in a triangle is 180 degrees and 1+8+0 = 9. The sum of the angles in a rectangle is 360 degrees and 3+6+0 = 9. The sum of the angles of a pentagon is 540 degrees and 5+4+0 = 9. The sum of the angles in a hexagon is 720 degrees and 7+2+0 = 9. Continuing to add a side to each polygon will result in adding 180 degrees to the sum of the angles and thus will always resolve to a digital root of 9. As the number of sides approach infinity, the polygon will become a circle.
Engineering Made Easy also gives examples of number 9 being found in the universe as the digital root, like the speed of light in miles per second, the diameter of the sun, the diameter of the earth, and the diameter of the moon, in miles. Time also relates very much with the trinity of 3, 6 and 9, and especially 9. On a clock, which is a circle, you have 3, 6, 9 and 12 in rotation at 90-degree angles. 12 is 1+2 = 3. There are 60 seconds in a minute, 6+0 = 6, and 60 minutes in an hour, 6+0 = 6. Also, there are:
3,600 seconds in an hour, 3+6+0+0 = 9,
86,400 seconds in a day, 8+6+4+0+0 = 18 and 1+8 = 9,
604,800 seconds in a week, 6+0+4+8+0+0 = 18, and 1+8 = 9
1440 minutes in a day, 1+4+4+0 = 9
10,080 minutes in a week, 1+0+0+8+0 = 9.
And so on …
Another interesting fact is that if you replace 9 with 0 or 0 with 9 in a number that has two digits or more, the digital root is the same. So, in the example I gave of 797 with a digital root of 5, and replacing the 9 with a 0, the number is 707, and 7+0+7 = 14 and 1+4 = 5. They also state that our universe vibrates at a frequency of 432 hz, and when Om (Aum) is chanted correctly, it produces a frequency of 432 hz and 4+3+2 = 9. That’s why Om is considered the primordial sound of the universe. 108 is sacred in Hinduism and there are 108 beads in a mala which reduces to 9. Note that the interior of a rosary has 54 beads which reduces to 9.
It was always apparent to me that multiples of 9 resolved to 9, like 18, 27, 36, 45, and so on. And multiples of 3 and 6 resolve to 3, 6 and 9. Of course anything times 0, will be 0, and so in that case, 0 and 9 are similar. Adding the single digits up to 9 will resolve to 9, 0+1+2+3+4+5+6+7+8 = 36 and 3+6 = 9. Thus 9 contains all of the other numbers and represents both nothing and everything and is found throughout space and time. Now you can see why Tesla regarded 3, 6, and 9 as sacred and are the keys to the universe because of the mathematics and the appearance of 9 throughout the universe. To me, this beautiful symmetry and order demonstrate the presence of God everywhere. So perhaps then, this method will indeed work for manifestation.
Unfortunately, none of the videos mentioned Chaldean Numerology where numbers are assigned to alphabetical letters and so that names can be resolved to a digital root. Maybe because it’s more mystical as there are characteristics and traits assigned to each digit. The Chaldean Numerology chart has the following alignments:
1 – A I J Q Y
2 – B K R
3 – C G L S
4 – D M T
5 – E H N X
6 – U V W
7 – O Z
8 – F P
Notice that 9 is missing. That’s because the Chaldeans also regarded 9 as holy and sacred. However, 9 could still be resolved as a digital root. The class that I took on Chaldean Numerology was a lot of fun as we looked at what names resolved to what numbers and then what the traits each name has according to the digital root. Take “Bob” for example, Bob is 2+7+2 = 11 and 1+1 = 2. According to Chaldean Numerology, a couple of positive traits of 2 are kindness and creativity. (I won’t mention the negative traits). 11 is considered a master number because of the two 1’s and it bestows on the digital root of 2 imagination and vision. I looked at “Jesus” and it is 1+5+3+6+3 = 18 and 1+8 = 9. “Christ” is 3+5+2+1+3+4 = 18 and 1+8 = 9. Then using the full name of “Jesus Christ” I got (1+5+3+6+3) + (3+5+2+1+3+4) = 36 and 3 + 6 = 9. I was amazed at this and thought that if we use the trinity of energy, frequency, and vibration with the trinity of love, compassion, and gratitude, we will manifest something far greater than material gain or physical wellbeing.


Petroleum Risk and Decision Analysis - PRD
About the Course
Good technical and business decisions are based on competent analysis of project costs, benefits and risks. Participants learn the decision analysis process and foundation concepts so they can actively participate in multi-discipline evaluation teams. The focus is on designing and solving decision models. About half the problems relate to exploration. The methods apply to R&D, risk management, and all capital investment decisions. Probability distributions express professional judgments about risks and uncertainties and are carried through the calculations. Decision tree and influence diagrams provide clear communications and the basis for valuing each alternative. Monte Carlo simulation is experienced in detail in a hand-calculation exercise. Project modeling fundamentals and basic probability concepts provide the foundation for the calculations. The mathematics is straightforward and mostly involves only common algebra. The emphasis is on practical techniques for immediate application.
This is a fast-paced course and recommended for those with strong English listening skills. This course is intended as the prerequisite for the Advanced Decision Analysis with Portfolio and Project Modeling course.
Target AudienceGeologists, engineers, geophysicists, managers, team leaders, economists, and planners.
You Will Learn
Participants will learn how to:
- Describe the elements of the decision analysis process and the respective roles of management and the analysis team
- Express and interpret judgments about risks and uncertainties as probability distributions and popular statistics
- Represent discrete risk events in Venn diagrams, probability trees, and joint probability tables
- Solve for expected values with decision trees, payoff tables, and Monte Carlo simulation (hand calculations)
- Craft and solve decision models
- Evaluate investment and design alternatives with decision tree analysis
- Develop and solve decision trees for value of information (VOI) problems
- Decision Tree Analysis: decision models, value of information (a key problem type emphasized in the course), flexibility and control, project threats and opportunities
- Monte Carlo Simulation: Latin hypercube sampling, portfolio problems, optimization, advantages and limitations
- Decision Criteria and Policy: value measures, multiple objectives, HSE, capital constraint, risk aversion
- Modeling the Decision: influence diagrams, sensitivity analysis, modeling correlations
- Basic Probability and Statistics: four fundamental rules including Bayes' rule (the easy way), calibration and eliciting judgments, choosing distribution types, common misconceptions about probability
- Expected Value Concept: foundation for decision policy, features, pitfalls to avoid
- Implementing Decision Analysis: problem framing, guidelines for good analysis practice, team analyses, computer tools (discussion and demonstrations), mitigating risks
- Evaluating a multi-pay prospect (team exercise)


In our district, we have been pushing Number Talks as a strategy to get students (and teachers) thinking mathematically. The beauty of Number Talks is that the focus is on how the student is thinking, not on the answer. Being a math mentor teacher for special education teachers, this is one strategy that I can model fairly quickly for teachers. Here is what I have noticed doing them:
- No matter what, I cannot predict all of the strategies. I have tried to plan by predicting their strategies how I am going to record their thinking – especially trying to bring in visual models. But there are always students that surprise me with how they are thinking. These students have improved my ability to ask questions.
- Start with a problem that you think might be too easy for students. I was in a sixth grade class and we did an addition problem that I thought was fairly straightforward. The number of strategies that students were able provide was amazing – and the principal was in the room to hear all of it! The next week, we did a multiplication problem. The students grasped on to the traditional algorithm and did not provide the same variety of strategies.
- Listen and learn from your students. My favorite Number Talk to do is a dot number talk that I saw in Jo Boaler’s “How to Learn Math” course. I love this dot number talk because it brings out how people see things, and possibly how people see numbers. It also surprises everyone how complex dots can be. My favorite explanation of the dots is from Matt, a student who was in a low math class. Here’s his thinking:Matt saw the dots as two lines that cross and then three separate distinct dots on the outside. He also realized that where the two lines intersected, he had counted that dot twice so he needed to subtract one dot. Pretty complex thinking from a “low level” math student!
Matt made me realize two things. 1) I need to listen to how students see the world of math to help me choose the next steps I need to take with them. 2) Just because a student has been labeled as low in math does not mean that they see the world of math as any less complex.
I could go on and on about Number Talks and all the learning that is going on around them – for students and for teachers – but I’ll save that for a later post where I look at how teachers view them.


This happens year in and year out. The BCS has all SEC teams strength that much higher than that of the Pac12 or any other conference. I wondered about this several years ago and then looked deeper into what constitutes the BCS.
To figure out who gets to play, a complex, mathematical formula is used to rank the top 25 teams throughout the season. Each Monday, the BCS ratings are updated based on the teams' performances during the previous week. At the end of the regular season, the top two teams in the ratings play each other for the national championship. The calculations performed by a small number of mathematicians and statisticians off the field are more important to a team's chances of being in the final game than their efforts on the field. The computer rankings percentage is calculated by dropping the highest and lowest ranking for each team and then dividing the remaining total by 100, the maximum possible points. (Example: the 6 rankers have Team A ranked 2, 3, 3, 3, 3, and 4. Take away the 2 and 4 which leaves an average of 3rd place. The BCS quotient of this component would be 0.92. (23 / 25 = 0.92).
So then how can 66% (coaches poll, Harris poll) override a computer poll at only 33%? Great question. This system should have been dismantled years ago to a playoff situation.


Doctorate of Philosophy in Mathematics (PhD Mathematics) is a research-based doctoral program. This program includes the extensive study of the quantity, space, numeric, structure and changes. The major concepts that include in PhD in Mathematics are algebra, literal equations, vectors, trigonometry, algebraic fractions etc.
Postgraduates in Science subjects or Mathematics can apply for this program. Doctorates have various career options in various field. They can work in wide areas like Complexity and networks, numerical analysis, Mathematical physics, Biomathematics group and so on. The admission procedures will be different for various universities and colleges.
Skills Required for the PhD in Physics
- For analysing the research data, its findings and also to derive results, the scholar should possess the analytics skills.
- Mathematical and logical ability is important for those who are pursuing a PhD in Mathematics. Because the scholars may face some problem where they have to create mathematical modelling, finding solutions to scientific problems etc.
- Communication skill is also important for scholars for interpreting and explaining the research results and problem with others.
Highlights of the Course
|Full-Form||Doctorate of Philosophy in Mathematics|
|Eligibility||Master’s in science or Mathematics|
|Employment Areas||Investment Firms, Commerce Industry, Business Industry|
|Job Type||Mathematician, Statistician, Cryptographer|
Doctorate Of philosophy in Physics is research-based Doctoral Program in Physics. This course can only pursue on a full-time basis.
Duration of the Course
The period of the program depends on the research topics and its feasibility. In a normal scenario, the minimum period for this program is three and the maximum is five years.
Eligibility of the Course
- The postgraduates in Mathematics or Science subjects with a minimum mark of 50% are the basic requirement for a PhD in Mathematics. The B.Tech graduates from any stream can also apply for this course.
- The M.Phil graduates in mathematics can also apply for the same. The Advantage of the M.Phil graduate is that he/she need not attend the entrance examinations and interview rounds for the selection procedures.
- In addition to that, they can start their PhD program without attending the course work.
Admission Criteria for the Course
- As already mentioned, the universities have their discretion to set the selection procedures. Some may admit the students who have qualified National Eligibility Test (NET) or Junior Research Fellowship (JRF)
- Some universities may conduct entrance examinations and interview sections even for the NET or JRF holders. While attending the entrance examinations, the students should prepare from the areas like
- Abstract Algebra
- Complex Analysis
- Elements of Numerical Analysis
- Linear Algebra
- Ordinary Differential Equations
- Partial Differential Equations
- Real Analysis
- The research scholars have to prepare their research proposal at the time of the interview.
- Some private institutions may admit student based on their marks in postgraduation and graduation.
Syllabus of the Course
The first six months of PhD program comprises of course-works that help the research scholar to understand the research concepts and the procedures that have to be followed in the research works. This course involves the study of statistical concepts related to quality assurance, designs, and inspections.
The major concepts that include in PhD in Mathematics are algebra, literal equations, vectors, trigonometry, algebraic fractions, word problems and so on. It also involves the research of various theories like asymptotic analysis, stochastic process, ordinary & differential equations, Scientific computations, probability and statistics etc.
Some of the subjects that are included in the PhD in Mathematics are as follows:
- Differential Equation
- Mathematical Finance
- Differential Geometry
- Discrete Mathematics
- Metric Space
- Computational Techniques
- English Literature
- Number Theory
- Computer Science
- Linear Programming
- Probability Theory
Career Prospects of Doctorates in Mathematics
Through this doctoral program, the aspirants will gain knowledge in accordance with the present economic and social scenario. It helps the researcher to improve their presentation skill which can empower them to find their career in various fields like:
- Educational Institutes
- Banking Sector
- Maths Research Centres
- Trade & Transportation Centres
- Military Schools
- Defence Services
- Stock Exchanges
- Ernst & Young
- Investment Firms
- Tiger Analytics
- TCS Innovation Lab
- Weizmann Institute
Professor/Assistant Professor: the doctorates can teach and deliver the lecturing notes to students for assisting them for gaining knowledge in this field of study.
Finance Manager: the duty of a financial manager is to review the financial reports, monitor and prepare the account reports, forecasts financial matters for business matters.
Cashier: they perform the cashier duties, select the right products, set up the store displays etc. the employers will provide effective training for performing these duties.
Loan Counsellor: loan counsellors work for a financial institution for processing the client’s applications, verify their information and also to come with an effective financial plan.
Subject Matter Expert (SME): doctorates will be an expert in their respective fields so they can work as an SME in mathematics.


Your opponent has executed a safety, placing the cue ball behind a cluster and you have to kick out and make a good hit.
Do you walk up to the table and think:
“Now what do I do!” Or do you think, “I know how to kick this!’
Place the cue ball in front of Diamond Point 0, from four inches to three diamonds out from the rail. Place an object ball on the rail at Diamond Points 1, 2, & 3, as shown. Shoot, with 1-Tip of English, Right of Center on the cue ball, into Diamond Point 0 to hit the 1 ball. Shoot, with 2-Tips of English, Right of Center on the cue ball, into Diamond Point 0 to hit the 2 ball. Shoot, with 3-Tips of English, Right of Center on the cue ball, into Diamond Point 0 to hit the 3 ball.
Starting Explanation: The diamonds numbered 1-10 at the bottom of the photo, going right and up the bottom rail, are referred to as DP, meaning: Diamond Points. The diamonds numbered 1-11 at the top of the photo are referred to as the DCP, meaning: Diamond Contact Points. The 1 ball in this diagram is located at the TDP, meaning: Target Diamond Point.
The cue balls have a number on them. This means the number of cue stick tips to use from the center out (also see the suggested striking point diagram below). Place the cue ball in front of (DP) 0, about four inches or more off the rail as shown above (the added cue balls on the ball path in the diagram indicate optional points to shoot the cue ball from).
Next, place the 1 ball on the rail at TDP number 4, as shown above. Hit 3-Tips Right of Center, into DCP 1, to hit the 1 ball at TDP 4, or Hit 2-Tips Right of Center, into DCP 2, to hit the 1 ball on TDP 4, or Hit 1-Tip Right of Center, into DCP 3 to hit the 1 ball on TDP 4, or Hit 0-Tips Right of Center, into DCP 4 to hit the 1 ball on TDP 4.
Do the math! At DP 0 using 3 Tips + DCP 1 (the Cue Ball Path) = TDP 4 (the Target object ball)
The Secret Formula:
A. B. C. Whatever diamond the cue ball is on, that DP and the DCP directly across become the new 0 points to begin adding the TIPS plus DCP spaces to hit the TDP. Start by counting the number of DP’s from DP-0 to the TDP (the object ball to kick at). Next, add 0, 1, 2, or 3 (Cue TIPS of English) plus a DCP number until it equals A, the TDP spaces to hit total (see the diagram below: The TDP diamond number value is 4). Note: The TIP number, plus the DCP number must equal the TDP spaces number. Count how 3+1, 2+2, 1+3 or 0+4 all equal reaching the TDP space number 4).
Editor: Dana Gornall


Weekends at any time
EducationHarvard University - BA, Math , Oxford - PhD, Statistics
ExperienceI received a B.A. in Mathematics from Harvard University and a Ph.D. in Statistics at Oxford. Since then, I have been working many years in Los Angeles as a tutor. Nothing gives me more pleasure than teaching and helping children and university students. The ability to give students confidence and help them have a greater understanding is something that is very important to me.I believe helping a student academically is empowering that student to such an extent that it will make a positive impact on his or her life. Helping students navigate academia is not only rewarding to them, but it is to me as well. I am passionate about teaching, and within the realm of education, tutoring is where I feel the most comfortable. When I tutor, I am able to teach a vast array of subjects on a one-on-one level. Teaching privately allows me to understand my student's strengths, weaknesses, and study habits. I also enjoy tutoring because it allows me to have more flexibility with my schedule, which is something that is not as common in a formal educational setting.I truly believe that my background in academia, combined with my strong mathematical skills and drive to teach, are my personal strengths as a tutor.
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I’m hoping I can get some ideas from math teacher types (and others) around an idea I’ve been kicking around for my son Tucker, who, as you might guess by the title of this post, loves basketball. (He loves math, too.) Not that he needs it or has asked for it, but I keep wondering what a “Basketball Math” curriculum might look like for Tucker, one that would combine his serious interest in the sport with his growing interest in math, and one that would also give him opportunities to connect with other basketball and math lovers outside of the classroom. A few basic things seem obvious, even to my English teacher brain, in terms of learning percentages, ordering numbers, reading some blogs on using statistics in basketball, etc. But I’m thinking there’s a lot of other stuff about geometry, physics and more that he might find hidden in the game as well.
So if you have a second, I’m hoping you might post your ideas here. Assuming we could (and would want to) build a K-? math curriculum around the game of basketball that, if possible, takes advantage of these social learning spaces online, what might that look like?
Field goals of the top 40 NBA players!
Bivariate data to understand writing equations of lines and interpreting slope. Plot field goals attempted as the independent variable and field goals made as the dependent variable.
How would the top 20 WNBA players data look in comparison?
How does your team’s data compare to these elite players? What is their practice standard for honing and keeping their skills?
Oh, you might have to explain to your students what a field goal is in basketball; I did!
Also works with free throws.
I have data, graphics, etc. to share if wanted.
Player heights…single variable data. How does the WNBA and your team’s stats compare to the NBA?
Is the ability to dunk dependent on height? gender?
Will Richardson says
This last is a really great question, and he’s rattling off all the characteristics that are required to dunk.
George Woodbury says
There are some probability applications. If a free throw shooter has a 75% chance of making a free throw, what are the chances that he or she makes 2 free throws? 1 of 2? 0 of 2?
You could use a spinner to simulate the probability, or even a deck of cards (heart/spade/club = made free throw, diamond = missed free throw).
It is interesting (mathematically) to ask what is the most likely outcome in a 1-1 free-throw situation.
There is the straightforward version: Player X makes P percent of their free-throws. In a 1-1 situation, what is the most likely outcome? The least likely outcome.
There also the backwards version. For which values of P is 2 points the mostly outcome of a 1-1 situation? For which values of P is 1 point the most likely outcome? For which values of P is 0 points the most likely outcome?
Angie B says
Dan Meyer’s dy/dan blog had this on it:
I don’t have a huge math background and am trying to stretch myself into that field because I know it’s important, and I really like this post and find his math so interesting. I would think this could be expanded on in many aspects.
Greg McVerry says
Why not set up a fantasy team with a salary cap? Involves almost every type of mathematical equation.
Will Richardson says
He has fantasy teams on ESPN…is there a place that adds in the $$$ piece?
Anna Watkins says
Check out the bball article in the Encyclopedia of Sports Science (1997, MacMillan/Simon & Schuster). It’s got discussions of arc, force, angles, trajectories, spin, direction, friction, ratios, center of gravity, balance, etc. You could get a LOT of math out of that!
My initial thoughts are just to expound on the things you named. For example, one of my favorite players was Allen Iverson, who could score 30 points on any given night, but did it while shooting about .300 from the field which probably hurt his team in the long run. You can probably set up different metrics – basically giving different weights to things like free throw percentage, scoring, rebounds, steals, etc. – and compare players and be able to claim “I can prove that Kobe is better than Lebron” or whoever else you want to compare. This would also extend to comparing teams and stuff.
Will Richardson says
We’re liking comparisons like these. Tucker’s talking about how Lebron may not score as much this year since he’s a part of the “Big 3” so that’s why he may not be “better” than Kobe this year even though he may be a better player. (I’m liking his analysis.)
Terry Kaminski says
Could study linear inequalities and look at profits and losses when running managing a basketball team.
Could study quadratic functions and look at the path of the basketball. Force required to obtain correct arc to make basket.
I think you are getting at how we should redesign ALL of our math instruction. Instead of teaching specific curricular outcomes we should take a real world situation and study all parts of it indepth and the math outcomes WILL be covered.
Some other mathematical / physical connections are: Volume of air in ball, volume of the air if it were out of the ball, mass of air in ball, density of air. Design an experiment to determine these. Volume of skin making up ball assuming skin is 1/16 th thick. Mass of skin. Density of skin. Design an experiment to determine skin density. Now recalculate the volume of air in ball taking into account the thickness of skin. What is definition of mass and weight. Does ball have water vapor or liquid water or both? What would this depend on?
Lyn Hilt says
Incorporate geography…calculating traveling distances/methods to visit arenas and attend games. Ticket prices. NBA Tour 2010-2011.
Will Richardson says
I’m liking this one. Tucker’s a little overwhelmed by the idea of using the calendar to make sure the teams are actually playing on the nights we visit. ;0)
There’s gotta be an app for that.
How about studying the lines and shapes on the court? A little bit of geometry there.
Of course you could study force, mass, and acceleration which is applied math.
You could throw in something about advertising that is done inside the arenas and money made through selling clothing etc at the souvenir stores (not to mention the cost of drinks and snacks.)
matt montagne says
To build off WM’s idea…
using the vernier physics application for iPhone/iPod touch, he could do some data collection, analysis, etc. I wrote a post about this not too long ago: http://middleschoolblog.blogspot.com/2010/09/video-analysison-my-phone.html
matt montagne says
one other comment.
Motion Math is a math game targeted to elementary aged students…it was actually developed by a graduate of the stanford learning, design and technology program who interned with, Gabriel Adauto. Not sure where the connection here is, but if he has any interested in coding, this is at least something to consider.
More on motion math at: http://motionmathgames.com/
Ryan Maksymchuk says
As a former three-point killer myself back in the 80’s, I can relate to such a curriculum with profound respect.
My favourites would tend to be around a perfect arced three-pointer/jumper/free throw, where the parabolic trajectory of the ball is definitely ‘find-out-able’ through quadratic functions, or possibly cubics. Huge potential to teach regression analysis, curve-fitting, and possibly even 3-D vectors. (Your son may be a bit too young, but I commented because many of the previous commenters were discussing stats, and this is a different path)…
As always, your blog inspires. Thank you for what you write.
Swan River, Manitoba, Canada
Ted Henning says
I would suggest incorporating a video game like EA’s NBA Live 10 into the curriculum and using it both as a data generator and motivational tool. It could be used for lower level math skills for the younger grades to complex statistical analysis for older grades. It can be played in groups to promote collaborative and team-building skills. Off-line exercizes can be created to utilize the data that comes from the game and help define the next set of data the students need to generate (ie, play the game). I teach a course about using entertainment console video games in standards-based curriculum and many math teachers have used sports games in this way.
Will Richardson says
Tucker likes this idea. Imagine that! 😉
I recently started coaching a girl’s soccer team in an area where math and english scores are consistently low. I would love to find a way to incorporate both into everyday practice. Does anyone have any ideas about this?
Jason Kornoely says
Estimation, Rates, and Perimeter:
Discover many high-knees it take to go across one side of the goalie box, then apply that knowledge to how many high-knees it would go around the perimeter of the entire goalie box.
If it takes one player an average of 15 seconds to dribble across the field, how much time would it take for a team of x to finish?
Jason Kornoely says
Area, perimeter of the floor. Determine the hypotenuse using the distance from the free throw line to the center of the hoop and the height of the hoop. Compare the diameter and circumference of the hoop and different sized balls.
Create a scale model of a court and engineer a shooting mechanism to launch a ping-pong ball toward the hoop.
Jane St. Pierre says
Put “basketball math” into NCTM’s search box and you will come up with many other ideas and articles. One NCTM link for math basketball ideas:
Alex Rosenwald says
Basketball is great for physics, and I use it quite a bit when talking about not only the obvious things (projectile motion, parabolic trajectory, freefall, vectors) but also things like energy (potential & kinetic), collisions (dribbling, bank shots), as well as relative vectors (passing lanes, dribbling) and rotational dynamics (why you put backspin on your jump shots).
It’s a really great base for a good physics curriculum.
I have created a Physics Performance Task with this scenario (based on an event that happened in 2006):
“You are the National Basketball Association scientific advisor and you have to evaluate whether or not a new type of ball should be used in the upcoming basketball season.”
The students receive seven different documents (included a biased article) that will help them in validating their decision. The physics concepts are related to friction, conservation of energy, absorbency, bouncing, etc.
The task culminates when the students have to design and conduct their own experiments.
Our athletic department has been very generous donating old basketballs and swatches of different types of balls: leather, synthetic, etc.
Will Richardson says
Thanks Alex and Dolores…when Tucker gets to the physics stage, I’ll link him back here. 😉
Haven’t had a chance to see any of the comments above, but I’ll throw mine out there just in case.
More Algebra I/II topics…
How many times will a ball bounce before it stops (exponential decay)
How long will a ball bounce before it stops (sequences and series)
After observing a ball bounce 5 times, determine how high you would have to throw it from half court for it to bounce and make it in the basket (that one might be made more clear with a diagram, but it’s math [quadratics] and physics)
I see some great ideas from the physics people out there! I home-schooled a “b-baller” as well. I’ve been in your shoes! It sounds like some of those ideas are for the future. (?) Not sure how old your son is now.
I remember early on having my son count shots from this angle and that, keep stats, etc. Also, the league we joined kept stats posted on their web site – he would scour through that site (reading!) and compare everyone’s stats.
But I do have a little “warning” – Eventually backyard b-ball became his dreamy alone time (I think probably pretending to be M. Jordan though he won’t admit it.) So, I’m sure you’ve thought of this, but you don’t want him to reject you, math, and b-ball if he gets in a tizzy at some point!
Our son is in high school advanced math now. It is by far his favorite subject.
So, the main thing I can tell you from my past experience is don’t panic and enjoy this precious time!
Cooking (recipe manipulation), yahtzee, “Math 24” all helped along the way – esp. the latter as both our sons loved beating their parents at a math game.
I think their confidence is helped if they feel like they are “discovering” a concept vs. being taught – so in a way (err), maybe a little acting from Mom and Dad comes in handy at times too. And chatting casually about shopping, politics, etc. and being as “nerdy” as possible demonstrates how life can be viewed quantitatively. It calms me to think of all the prior math that humans have done throughout time and place – so we must be wired for it. And, not to be too gender-bender, but I’m in an all male clan now (‘cept me) and competition, numbers, and systemization just ooze about in every corner.
Anyway, do you know how to you make classic literature a blast? 🙂
Oops! I think I thought I was in a different forum! Sorry if I offended!
To summarize a little better: we believe that math (well, school actually) is a game, and learning to teach yourself is the match point.
We’ve had our kids in and out of public school – private not really a financial option – but when they go back to public school, they are given the option.
Everything that helps put them in the driver’s seat seems to help.
My father in law – a med school proff – told me that in some classes in med school in Canada, they had to throw out grades or nobody could learn it. And little guys are supposed to be more mature than that?
Larry Rosbach says
Play fantasy basketball. Means, standard deviation, and z-scores become extremely important in comparing the relative strengths of players in the various statistical categories. Later in the season the player makes judgments about how many opponents are still within striking distance in each statistical category. The team owner also needs a system to evaluate players when offering or making trades.
Diana Day says
Will, my brother-in-law is a huge Strat-o-matic baseball player. I just checked their website, and it looks like there is a Strat-o-matic basketball, too: http://www.strat-o-matic.com/products/basketball.
I have no idea if this is what you’re thinking of, but I do know that the game involves heavy stats.
Will Richardson says
Too funny…I used to play Strat o Matic baseball as a kid! Thanks, Diana.
Punya Mishra says
Karen Bruce, math teacher, over at Sine of Times has a great post about seeing math everywhere with an example of basketball. May be worth a peek. Check out the post: I see math
At Tutor.com, we had a series of blog posts about math in sports. I hope this helps!
How Math Can Lead to a Career in Basketball
Using Math to Calculate Baseball Statistics
Pat Hamblett says
Thought I’d weigh in on this one — if I’m not too late. In the spirit of thinking ‘globally’, consider expanding to other sports as well. I participated in a wonderful training this summer (at Patriot’s Place in Foxborough, MA) where teachers learned about ‘sports materials’. The training was given by CASE (Center for the Advancement of STEM Education) trainers who used the Materials World Module — Sports Materials, (http://materialsworldmodules.org/modules/sports.shtml)
Middle and high school teachers explored a large vaiety of sports materials (basketballs, golf balls, soccer balls, tennis balls — you get the picture). The training comes with a kit of sports materials (balls) cut in half so one experience is seeing what’s inside and thinking about how the inside impacts the performance of the sports ball. It was an engaging inquiry experience that really looked at the practical connections between math and science.
This leads me to my established belief that ALL ideas should be presented outside the vacuum of single content/concept teaching. We are such isolationists when we present new material. We force students to think that everything stands by itself — yet in truth everything (and I DO mean EVERYTHING!) has a relationship to something (usually many things) else. No wonder our students cannot grasp the essence of an idea — there are no references that allow them to appreciate some or all the connections.
Brain research has acknowledged that long term memory needs those connections. So if we MUST teach to the test we need to help student recall by creating obvious connections for our students. Let’s provide them with ‘memorable’ experiences that make sense (using real world experiences).
Kent Chesnut says
I’ve enjoyed all of the creative ideas. They do seem like they could be incorporated into a basketball math “curriculum”.
I wonder, however, if it might not be better to let the student(s) brainstorm and come up with ideas for projects that they may want to pursue. The ideas in the replies could be used as a brainstorming aid if necessary.
Keep up the great great posts!
Jason Dyer says
There’s someone in one of the districts near here working on a sports statistics book, with questions like ‘Is it possible to go on a shooting “hot streak”?’ and ‘Did LeBron James choke during the NBA Finals?’
I’m not sure how close the book is to publication, though.
Plot the relationship between ball pressure and bounce height.
Find which shoe allows the quickest pivot.
After you do the path of the ball through flight. Use http://www.addictinggames.com/gimmefrictionbaby.html to explore how the ball bounces off the backboard. That leads to the reason for the square on the backboard. Why a square and not a rectangle, and even why the basket is set away from the backboard.
Then there’s also why the big backboard if most shots off the backboard won’t go in? What’s the proportion of the area of the square to the backboard? Proportion of lengths. There’s probably some human perception issue there that leads to an ideal size.
From an 8th grade math class I taught once a week:
Start with who’s the better team: Celtics or Lakers? Justify. Eventually, it gets down to Kobe versus the trio of Pierce, Allen and Garnett.
Alright, so what makes a good team a good team? Star players or the strength of the whole team? Check out the stats (PPG), what’s the distance between Kobe and the second best player on the Lakers? How about between each member of the Celtics top trio? Or even the lowest of the Celtics three to the fourth best player on their team? OR even the distance between the first and last ranked players on both teams. Let your son figure out all the ways to compare the two teams using the Points Per Game stats. We’re hitting decimal subtraction, comparison, and range. We could even check out average PPG of the entire team for both sides(hitting decimal addition and division) and you could intro different measures of central tendency by comparing the average PG with the median PPG for each team.
Heck, we could illustrate it for people who don’t want to get bogged into the details and would rather see a visual. Graph the distribution of PPG for each team’s players. Do a bar graph, a line graph, even a box and whisker…you can still see the distribution of PPG among all the players really clearly with any of those. Maybe do ’em all and have him choose which is clearest and have him explain why.
And finally, it all comes back to the original question: which team is “better”? He’ll be able to speak his mind with authority and back it up with data. As often as you can, make sure you always bring the context of basketball scores to the data analysis, so he has a stable link to the reality of the points on the graph or the whisker of the box and whisker; that way they won’t get lost in the theoretical.
I have the lesson plan somewhere on my other computer, if you want me to fire it up for further info. Sorry for any confusion in this transcript of my memory.
Will Richardson says
Yeah…these are the types of questions that he’s most interested in right now. And I’m thinking there is a lot of useful math he could learn in the context of defending his choice of the Lakers over the Heat. (Even though he’s wrong, of course.)
I’m going to suggest this type of an exercise to his math teacher. We’ll see.
Not sure what grade level you’re thinking about, but here are some basketball lessons that you might find helpful:
Basketball IQ (shooting distance vs. percent, or Is a 3-pointer ever a good idea)
Mad Hops & Super Strength (do NBA players really jump that high?)
I’ve created a 3 variable system of equations problem by printing out a Celtics box score and then blacking out a few of the statistics. Say you block out all of Ray Allen’s shooting statistics, and Paul Pierce’s point totals, and the 3-pt statistics for everyone but Pierce. Maybe the question is how many 3-pointers did Ray Allen make…In order to find it you have to find Pierce’s point total by adding up his made 2’s and 3’s, and then from that and the team total points, you’ve got Allen’s point total, and, well, you can take it from there.
Bill Genereux says
I would suggest downloading a free copy of Alice, the 3-D virtual world simulator from http://www.alice.org. It includes 3-d basketball models that can be manipulated through a simple drag & drop programming interface. He could actually create a fairly complex basketball game using Alice.
I have posted a brief introduction to Alice on my blog and it includes resources such as a basic Alice programming PDF. To make a successful simulation, you’ll have to get into some physics math, which I haven’t written about yet, but I do know you can do a pretty good model of projectile motion in Alice. Maybe I should write something up on that topic? I do have an Alice project (but not basketball) I did a while ago that uses projectile physics. Let me know if you would like a copy you could play with and modify if you decide to try this idea out.
Figuring out the math needed to model the physical world is a great way to connect these ideas together, and using Alice software would be a good way to do it.
Sports provides teachers will a tremendous opportunity to bring statistics to life for students. This is an area of mathematics that is sorely lacking in our schools. Whether students are picking their own all-star lineup and using stats to justify their decisions or engaged in a fantasy sports league, sports and stats are a natural route to engage students in math who would otherwise be disengaged. In general, we need to move statistical mathematics up the hierarchy of math topics, as data and data-based decision-making become more common in the workplace.
There are some really interesting possibilities here. If you are targetting algebra students, you could have problems or lessons concerning the parabolic path of the ball. If you could measure the initial upward velocity of the ball when shot you could determine the vertex of the shot (the max height) which could be interesting if you were Spud Webb trying to shoot over Manute Bol…I know that I am dating myself.
You could also do something with the magic number when the end of the season is drawing close. The magic number is the number of wins by the 1st place team or losses by the second place team or combination of both that the 1st place team needs to clinch the division. For example, if the magic number was 5, then any combination of wins by the 1st place team and losses by the second place team that totals five ensures that the first place team will win the division.
One other thought is to have the students explore what happens to the score when the other team steals the ball and scores…is it a 2 pt difference or a 4 pt difference (your team didnt get the 2 pts they were trying to and the other team did). Might make for interesting discussions.
Bill Genereux says
Download a copy of Alice and build a simulation of the physics. I built a projectile simulation a few years ago. It uses an outlaw and a revolver, but the same ideas should work. You can download the simulation here, and see how the math programming works. Please let me know if you try this idea. I’d like to see what you come up with.
For a short overview & resources on getting started with Alice, visit this page</a?.
Sandy Fivecoat says
Excellent request, and, as always — Teachers respond with some terrific ideas! I just did a search on the WeAreTeachers “IDEAS” tab for Basketball and found lots of great ideas here as well. http://www.weareteachers.com/ideas
Full disclosure- – I am a former teacher, and the CEO of WeAreTeachers — Wanted to let you know we have about 10,000 teaching ideas on our site, and we find corporate sponsors to award grants to support many of them — THanks for great blog post, and for getting such great teacher response. I’m always amazed — Teachers are always so willing to share their best ideas and strategies with one another.
Jeff Powers says
Have you considered how the max. cross-sectional area of a BB compares to the area inside the rim? How would a ball of smaller/larger cross-sectional area affect shot percentages. Isn’t the WNBA ball smaller than the men’s? Consider a do-it-yourself experiment with different basketballs. Shoot 25 free-throws with each and compare results with conjecture.
You’re the basketball coach. Your team is down by 1 point, there are 5 seconds left, and you have to decide who you’re going to throw the ball into. That person will either have to make the shot or get fouled and make free his free throws. How would you pick the first and second targets for the throw in.
You’re the coach. Your team is up by 1 point, there are 5 seconds left, and the other team took a time out and is going to throw the ball in. Will you double team any of the players? Will you foul the player who gets the ball? How are you going to decide?
For both parts, assume you can have access to the numbers of shots that each player has made, the number of attempts, the number of free throws made, and the number of attempts (this year and in this game). The class can use the Internet to look these up for a real team if you are teaching this live.
I have read some articles purporting to prove (or disprove) the notion that baseball and basketball players get “hot” or “in a zone”.
Is there such a phenomenon?
Try the Basketball Math curriculum. It is fantasy basketball and I have used it with 3-8 graders and they have all loved it. Also baseball, football, soccer, hockey books available. They come with a free code to the fantasy scoreboard site.
You could have him listen to/watch games and evaluate the comments as fact or opinion.
He could also research to find out if questionable statements could be supported factually.
Julie S says
Here are a couple of fun bball simulations:
Just let your son play and see what conclusions he draws from the games.
Sean Sweeney says
You should look at the approach on my colleague Brian Mark’s website, Yummy Math, and particularly his recent post on Fantasy Football:
Brittany Schneider says
I think this is a great conceptual idea. So many educators seem to get wrapped up in the idea of curriculum being rigid and only about the subject at hand. So many other lessons can be taught by allowing children to do what they enjoy. This provides inspiration for future teachers to dig deeper than the surface lesson to allow students to have fun while learning the stated curriculum.


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Can summation go on infinitely why or why not
How do you know that this equation has infinitely many solutions can anyone find a number that is not a solution why or why not how can you tell if an equation has infinitely many solutions go back. 256 chapter 11 sequences and series and then lim i 1 1 2i = 1 0 = 1 there is one place that you have long accepted this notion of in nite sum without really. Section 15 : summation notation + work with sequences read section 15 (pages 65 - 69) overview summation, but did not add how do we go about this task in a very organized way. Here is why zeno said that to go from the start to the finish line augustine wrote that the reason god can understand the infinite is that every infinity is the cauchy-weierstrass idea is that instead of overtly saying the infinite sum s 1 + s 2 + s 3. Sum of series involving natural log jul 30, 2009 #1 icosane 1 the as n goes to infinity how does the natural log of a number infinitesimally larger than 1 not go to 0 but when looking at it like an infinite sum of ln(n. Teaching the mathematics of infinity by patrick just be careful these debates can go on forever cardinality of number sets the cardinality of a set is and in his piece take it to the limit, mr strogatz uses an infinite sum to derive the formula for the area.
Addition is also commutative, so permuting the terms of a finite sequence does not change its sum for infinite summations this property may fail the summation can be interpreted as a riemann sum occurring in the definition of the corresponding definite integral. How can adding an infinite number of rationals yield an irrational number but can still be expressed as an infinitely long non-repeating sequence digits can one force a linear regression fit to go through an arbitrary point. It is often difficult to compute the sum of an infinite series exactly however, you can often tell that a series converges without knowing what it converges to go back to the inequality above i have. By varying , we get infinitely many parallels theorem 2 in hyperbolic geometry, all triangles have angle sum an amazing consequence of this theorem is that in hyperbolic geometry a segment can be determined with the aid of an angle. What people want if we were to take hinduism as a but this is different from condemning enjoyment to the person who wants pleasure, india says in effect: go after it -- there is nothing wrong but if this is true and we really are infinite in our being, why is this not apparent.
Why does commutativity of addition fail for infinite sums but here we go: q: why the commutative property would allegedly not apply to infinite series such as the one i mentioned above a: an infinite sum is a limit of a sequence of finite sums. Really equal -1/12 you put in two numbers, and you get out one number but you can extend it to more numbers if you have roughly speaking, we say that the sum of an infinite series is a number l if, as we add more and more terms. (more technically known as elements) since the fibonacci numbers go on and on forever, they're what's the sum of all the numbers in the series must be infinite so the sum of an infinitely long sequence of numbers an infinite can an infinite number of things have a. Is the universe finite or infinite i find this question slightly nonsensical, as the universe is a four dimensional spacetime get out of grade school stardust magician not rated yet mar 31, 2015 of course it's finite the big bang stopped, so much came out and no more. Answerscom wikianswers categories science biology human anatomy and physiology muscular system can summation go on infinitely what would you like to do flag can summation go on infinitely save cancel already exists what does summation of infinite series. I have heard that python can do infinite sums for instance if i want to evaluate the infinite sum: 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + how should i go about i am a newbie to python so i would.
Can summation go on infinitely why or why not
When i first heard of an infinite sum at school i was just taught to plug the numbers into the formula, without fully understanding why or how it works in this video i go over some examples of geometric series and how we can get some insight on why it works by using visuals. A series a n is said to converge or to be convergent when the sequence (s k) of partial sums has a finite limit if the limit of s k is infinite or does not exist, the series is said to diverge when the limit of partial sums exists, it is called the value (or sum) of the series. Infinite series keith conrad 1 introduction the two basic concepts of calculus not a paradoxical idea sum of the rst nterms, called a partial sum, and see what happens in the limit as n1.
Individually the stimuli cannot evoke a response, but collectively they can generate a response successive stimuli on one nerve are or temporal, in which successive signals are received from the same synapse spatial and temporal summation can occur simultaneously you can go to edit. First of all, the infinite sum of all the natural number is not equal to -1/12 you can easily convince yourself of this by tapping into your calculator the partial sums diverges to infinity or, to put it more loosely, that the sum is equal to infinity. Summation notation [practice problems ] if you know exactly which file you'd like to download or you want a file different from any listed below you can go directly to the download let's now take a look at a couple more examples of infinite limits that can cause some problems on. Yesterday, i posted an article about a math video that showed how you can sum up an infinite series of numbers to get a result of, weirdly enough, -1. Can summation go on infinitely why or why not if the stimulation continues and muscle never reaches its relaxation period, tension will rise to a peak muscle twitch response and recruitment, summation and tetanus exercise 1.
Converting a bicimal to a fraction (series method) by rick regan august is just a concise way to represent an infinite sum we can compute that sum and use it in place of the summation by using a variation on a well-known let's go back to our example this is where we left.


Don’t play roulette without me,
otherwise, you will lose your money!
Many years ago, one of my friends, an experienced roulette player, asked me to go to a casino with him to see if I could develop any game method that would make win relatively safely. He knew, that I was writing a book about the slot machines. I studied deeply some permanent number of a casino and experimented with a roulette wheel. The result of my Weeks long and relative expensive study and experiments is as an ebook to buy. I would like to invite you to give your attention to the following information before you play roulette!
What is roulette?What do you think how high your winning probability at roulette is if you set for example on zero? Is your answer one to thirty-seven 1/37?
Then I have to tell you that your answer is wrong! If you look more closely at the physical/ mechanical conditions of the roulette wheel then you will find that roulette is not a real random number generator! – The probability calculation is not the right way to calculate win chances for the roulette conditions because of the following reasons: First, we have to know what coincidence is! Coincidence is an event where the results are: -Unpredictable -Not repeatable -Not controllable. Lotto and Bingo, for example, are pure and fair gambling. If for the raffle, a physical random generator is used consisting of a rotatable container in which there are numerous physically identical balls (number representatives), which are thrown back and forth in the “three-dimensional” space during the draw, then the drawn number is a pure coincidence!
A precise calculation of the position and movement of a ball during the event is absolutely impossible!The probability that a ball with the number 49 falls out of the container is just as likely as that of any other ball, i.e. one to 49 (lotto numbers). Here we can only estimate the probability: 1 to 49 or 1/49 by Lotto – 1 to 100 or 1/100 by Bingo.
Why the roulette wheel is not a real random number generator!1- The numbers have a fixed distance from each other 2- They move in a certain direction 3- The rotation speed of the roulette wheel is measurable. – Therefore, the position of each number in the time unit of a game is quite predictable! 4- The ball moves along a two-dimensional path. 5- The direction of the ball is unambiguous and the speed is measurable. -Therefore, the landing point of the ball is predictable!
This means the roulette wheel is not a real random number generator and the roulette is not a coincidence!
Roulette would be fair gambling if, instead of the Roulette wheel, a real random number generator like in Lotto and Bingo were used!Then the probability for all thirty-seven numbers: 1/37 would be one to thirty-seven!
Roulette has a “cheating” appearance!The misguided idea of roulette leads to a false and easy-going gameplay, which is one of two main reasons why many multi-millionaires become “dishwashers” every day! The second possible reason is the croupier! Croupiers are selected among certain people. They have to be very skilled. They are not only able to calculate the table quickly, but they can also let the ball land on a selected number or keep it from landing on a certain number or pocket! The correct winning probability calculation at a roulette game: Probable and unlikely numbers: The probability calculation for a certain number is only relevant when the ball is running! This means that as soon as the ball is thrown into the wheel, one should be able to calculate the end position of the ball within a few seconds. (Only at this moment can one speak of a win calculation!) The numbers in the range of the end position of the ball have a much higher profit chance than 1:37 and depending on the distance to the calculated end position of the ball, the other numbers belong to the less probable or to the unlikely numbers! The calculated end position numbers belong to the “winning numbers“! To calculate the final position of the ball correctly, and, consequently, to estimate the winning numbers, is not exactly easy. Besides, in most cases, the final position of the ball is predetermined by the Croupier! A short demonstration:
The ball is in the landing position.The correct assessment in this example would be: The unlikely numbers 7, 31, 12, … in the clockwise direction to 24. The probable numbers from 11 in the direction counterclockwise to 16. The winning numbers could be one of these: 24, 33, 16 and 1. So we should have bet on these numbers shortly (very few seconds) after the release of the ball. Now you know why you should, under no circumstances, “play the game” before the ball has been thrown in the wheel! Conclusion: You have no chance to win if you rely on coincidence by playing roulette, even if you are a billionaire! You can experiment yourself and use different methods to find out which game strategy you can use to successfully play roulette. But that can cost you several thousand dollars. I strongly recommend you either avoid this games or read my ebooks first. Protect your money and avoid losing roulette forever with Losses back-Team-Strategy! You will be enthusiastic and also convinced!


Maximum likelihood estimation (MLE) is a probability-based approach to determining the values of model parameters. Parameters could be defined as blueprints for the model because, based on this, the algorithm works. MLE is a widely used technique in machine learning, time series, panel data, and discrete data. The motive of MLE is to maximize the probability that the values of the parameter achieve the desired results. Here are the topics to discuss.
- What is the probability?
- How maximum likelihood estimation works
- Maximum Likelihood Estimation in Machine Learning
To understand the concept of Maximum Likelihood Estimation (MLE), you must first understand the concept of likelihood and how it relates to probability.
What is the probability?
The likelihood function measures how well the data provides support for different values of the parameter. It indicates the probability that a particular population will produce a sample. For example, if we compare the likelihood function to two-parameter points and find that for the first parameter the likelihood is greater than the other, this could be interpreted as the first parameter being a more plausible value for the learner as the second parameter. More likely, one could say that he uses a hypothesis to conclude the result. Frequentist and Bayesian analyzes take into account the likelihood function. The likelihood function is different from the probability density function.
Difference Between Probability and Probability Density Function
Probability describes how to find the best data distribution for a feature or situation in data given a certain value of a characteristic or situation while probability describes how to find the chance of something given a distribution sample data. Let us understand the difference between probability and probability density function with the help of an example.
Consider a data set containing the weight of customers. Let’s say the mean of the data is 70 and the standard deviation is 2.5.
When the probability is to be calculated for any situation using this dataset, the mean and standard deviation of the dataset will be constant. Suppose the probability of weight >70 kg is to be calculated for a random record in the data set, then the equation will contain weight, mean and standard deviation. Considering the same data set, now if we need to calculate the probability of weight > 100 kg, then only the height part of the equation will be changed and the rest would be unchanged.
But in the case of probability, the equation of probability reversals conditional on the equation in the probability calculation, i.e. the mean and standard deviation of the data set, will be modified to obtain the maximum probability for a weight > 70 kg.
Are you looking for a comprehensive repository of Python libraries used in data science, check here.
How maximum likelihood estimation works
Maximizing the likelihood estimate is the main goal of MLE. Let’s understand this with an example. Consider that there is a binary classification problem in which we need to classify data into two categories 0 or 1 based on a characteristic called “salary”.
So MLE will calculate the possibility for each data point in the salary, then using that possibility it will calculate the probability of those data points to rank them as 0 or 1. It will repeat this probability process until the learner’s line is the best. team. This process is known as likelihood maximization.
The above explains the scenario, as we can see that there is a threshold of 0.5, so if the possibility turns out to be higher, it is labeled 1 else 0. Let’s see how MLE could be used for classification.
Maximum Likelihood Estimation in Machine Learning
MLE is the basis of many supervised learning models, one of which is logistic regression. Logistic regression maximum likelihood technique for classifying data. Let’s see how logistic regression uses MLE. Specific MLE procedures have the advantage of being able to exploit the properties of the estimation problem to provide better efficiency and numerical stability. These methods can often calculate explicit confidence intervals. The “solver” parameter of logistic regression is used to select different solving strategies for classification for better MLE formulation.
import numpy as np import pandas as pd import seaborn as sns from sklearn.linear_model import LogisticRegression from sklearn.model_selection import train_test_split from sklearn import preprocessing
The data is linked to advertisements on social networks that indicate the gender, age and estimated salary of users of this social network. Gender is a categorical column that needs to be labeled encoded before passing the data to the learner.
le = preprocessing.LabelEncoder() df['gender']=le.fit_transform(df['Gender'])
The encoded results are stored in a new feature called “genre” so that the original remains unchanged. Now divide the data into training and testing to train and validate the learner.
X=df.drop(['Purchased','Gender'],axis=1) y=df['Purchased'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.30, random_state=42)
This is divided into a ratio of 70:30 according to standard rules.
Adjusting data in the learner:
lr=LogisticRegression(max_iter=100,solver="lbfgs") lr.fit(X_train,y_train) lr_pred=lr.predict(X_test) df_pred=pd.merge(X_test,pd.DataFrame(lr_pred,columns=['predicted']),left_index=True,right_index=True)
The predicted results are added to the test dataset under the “predicted” feature.
Draw the learner line:
sns.regplot(x="Age", y='predicted',data=df_pred ,logistic=True, ci=None)
In the graph above which is between the age of the feature and the prediction, the learner line is formed using the principle of maximum likelihood estimation which helped the logistic regression model to classify the results. So, behind the scenes, the algorithm chooses an age-scaled probability of observing “1” and uses that to calculate the probability of observing “0”. This will suffice for all data points and finally it will multiply all data probabilities given in the row. This multiplication process will continue until the maximum likelihood is not found or the line of best fit is not found.
The maximum likelihood approach provides a persistent approach to parameter estimation as well as mathematical and optimizable properties. With a practical implementation of this concept in this article, we could understand how maximum likelihood estimation works and how it is used as the backbone of logistic regression for classification.


Brace, Seth Collins
||Materials entirely in
||The Seth C. Brace collection comprises eight original pencil sketches and one modern reproduction of an original watercolor
depicting churches and landscapes surrounding Newark, Delaware, drawn by Delaware College mathematics professor Seth C. Brace
between 1842 and 1844.
- 8 drawings (7 sheets) : pencil sketches ; images 17 x 20 cm or smaller and 1 photomechanical print (color reproduction of an original watercolor) ; image 15 x 17 cm
||Gift of Miriam Hill, 1926.
||Processed by Iris Snyder, 1997. Revised and encoded by Lora J. Davis, August 2009. Finding aid prepared using Describing Archives: A Content Standard


If you have never read the glorious webcomic Hark! A Vagrant by Kate Beaton, then by all means start now. Her comics are always informative, hilarious, and more often than not, downright silly. This week she has created a comic about one of my new-found heroes, Ada Lovelace, who I heard about last year through one of Beaton’s older comics. The older one also features the famous Charles Babbage:
Anyway, after reading Beaton’s first comic on Ada, I did a little Wikipedia search, immediately became obsessed with Mrs. Lovelace, and wrote an enthusiastic blog entry. I decided to do a little copy-paste action from my old blog to share the Ada-love.
It turns out that Ada Lovelace (1815-1852) was Lord Byron’s only legitimate daughter, and was a mathematical genius. Her mother wanted to weed out the supposed insanity in the family (which she perceived in Lord Byron; why ever would she think that??), so she had Lovelace schooled pretty much exclusively in math and science. Lovelace married well and became the “The Right Honourable Countess of Lovelace,” and was known for her incredible mathematical intellect. She was fascinated with Charles Babbage’s “Analytical Engine” (an early computer design), and in a set of extensive notes she wrote on the machine, she included “what is recognized as the first algorithm intended to be processed by a machine” (“a method for calculating a sequence of Bernoulli numbers with the Engine, which would have run correctly had the Analytical Engine ever been built.”) Because of these notes, she is widely considered the world’s first computer programmer, and the method in the notes is considered the first computer program. How awesome is that!?
I am especially impressed by the success of a woman fathered by the infamously rakish, notoriously flighty, and essentially unfit-for-fatherhood, Lord Byron. She could have been a mess, but turned out a genius with a relatively balanced and successful life. Here’s to you Ada Lovelace!
In sum, Ada Lovelace was a total badass bluestocking and certainly overcame the ol’ Byronic “madness” (which, if you check out Byron’s Wikipedia page, you will learn is quite a feat). And now with the context above, I hope you enjoy Kate Beaton’s most recent Ada Lovelace comic, the inspiration for the entire digression above:
KEEP THOSE NASTY POETS AWAY!!!
Pip pip cheerio!


Do you have a child who is fascinated by outer space? This week we are continuing the space theme! Last week I shared our Hands-on Solar System for Preschoolers. Today, I am sharing a FREE printable Moon Math Game to teach counting, one-to-one correspondence, and number recognition to preschoolers.
Moon Math Game Board
I wanted to make a space themed grid game that was a little different than a square grid, so I drew this one up, scanned it into the computer, added some color and made it a FREE printable to share with everyone! (You’re welcome! And please make sure you share this link with your friends and not just the download file. Thank you!)
To make a Moon Math Game for your preschooler first download and print two copies of the Moon Math Game Board found HERE. Then I laminated them for durability and re-usability. There are a few different ways you can play with this game board so it helps to have it laminated. All the games use these large glass gems.
The first game we played with this game board is just like the math grid games. We take turns rolling the die and placing however many gems on our game boards. The first player to fill their game board wins. This is a great game for teaching counting and one-to-one correspondence.
The second way you can use this game board is to practice number recognition. Use a wet erase marker write the numbers your child needs more practice to recognize in the circles on the game board. Then write those same numbers on some glass gem stones. Your preschooler can then practice number recognition by matching up the numbers on the game board with the numbers on the glass gems.
Using the same concept you can also use this game board to work on alphabet recognition with toddlers and preschoolers!
Check out the STEM Saturday co-hosts top posts in Science, Technology, Engineering & Math!
Party Cloud Dough | Glittery Fizz from The Science Kiddo
Valentine’s Day Polygon Building from Lemon Lime Adventures
© 2015 – 2017, Stir The Wonder. All rights reserved.


- We charge R449 per square meter to fit and supply standard paving bricks.We charge R99 per square meter to install paving supplied and this applies to 50 squares or more if its lets say 10 squares we charge labour per hour
- Standard concrete slabs are generally lower in cost per square foot than the alternative. Typically, you will pay 10%-15% more if you choose paving stones over standard concrete slabs. If you decide to upgrade to stamped concrete, paving stones will most likely cost you the same or even less in most cases.
How much does it cost to lay paving per square meter?
- There are 50 bricks (standard size 230x110x76mm) per square metre. When you lay each side by side there are 9 bricks per lineal metre. If you lay them end to end there are 4.5 per lineal metre.
- Paving bricks are going for R3500 per 1000 bricks.
How many paving bricks are in a pallet?
- Paving Brick Interlock 80mm Per Pallet (480) 9.6m2.


There are two dominant No Free Lunch theorem’s that relate to computing. One is focused towards search and optimisation, while the other is for supervised machine learning.
The Key Point
Eric Cai eloquently describes the No Free Lunch theorem in relation to Machine Learning. He describes the theorem as a series of simplifications and assumptions that apply to a problem and it’s solution. In turn, he also points out that the simplifications and assumptions that work for one problem and it’s solution will not nescessarily work on another problem, thus making the solution ineffective.
The “No Free Lunch” theorem states that there is no one model that works best for every problem
The idea that a solution cannot be picked up and applied to another problem without any work at all is most likely the origin of the name.
The original No Free Lunch Theorems for Optimization paper can be found here, if you’re into that kind of thing.


Animation (not currently working on Macs with Safari, will just be a pause).
stats_applet_10_prob - digitalfirst.bfwpub.comAn even simpler example of probability in action is a coin toss. My favorite kind of gambling math relates to.
Chapter 5: Probability - UCLA Statistics
Tutorpace provides students help with Coin toss probability calculator for any grades in any subjects including math, algebra, trigonometry and geometry.
How to create an unfair coin and prove it with mathThe probability of an event is the chance that the event will occur in a given situation.
When a coin is tossed, there lie two possible outcomes i.e head or tail.
1 Probability, Conditional Probability and Bayes FormulaRecord the number of heads AND tails that result from the 10 tosses in Chart 1 under OBSERVED (keep tally marks on separate sheet of paper and place only the total in Chart 1). 3. Toss the coin 50.
Probability Calculator - getcalc.comThe Coin Toss Probability Calculator will calculate the Probability for it.Consider, you toss a coin once, the chance of occurring a head is 1.
Calculating probability - lynda.com
How to Combine the Probability of Two Events | Sciencing
Runs in coin tosses; patterns in random seating - The DO Loop
In fact, this coin-tossing RTM has everything to do with probability distributions.
Probability distributions - University of Notre DameA simple analysis essentially following that of Diaconis and company enabled us to calculate the probability of heads as a function of.
When we toss a coin, there could be two possible outcomes either heads or tail.The total number of possible outcomes is therefore 4 and the number of outcomes where the result is two heads is 1.This equality was implicitely built into the calculation of the probability.
The calculation of the sum of probability-weighted log probabilities measures and captures this effect.
Probability and Coin Tossing - Programming | DaniWeb
Learning from One Coin Toss, Part 1 - Information Measures
Probability, geometry, and dynamics in the toss of a thick
What is Probability - Ken Ward's Mathematics Pages
Applying Algebra to Statistics and Probability. how to calculate the probability that three tosses. probability that a particular coin toss will.Coin Toss Program. 0. My goal is to make a program that outputs the probability of n amount of coin tosses,. you can calculate one if you know the other.
1. Probability - cosmologist.infoThe two events are (1) first toss is a head and (2) second toss is a head.An idealized coin consists of a circular disk of zero. with equal probability.
Probability and Coin Tossing. 0. 2. the coin is fair i.e. the probability of tails is the same as heads, P(T).In this module, you will learn how to calculate and apply the vitally useful.
Coin toss Probability Calculator calculates the probability of getting head and tail for the given number of coin tosses.


Check Out the Main Types of Homomorphic Encryption
The main purpose of homomorphic encryption technology development is to create a far more advanced form of protection for the encrypted data. In simple words, Homomorphic encryption allows an algorithm to perform an infinite number of multiplications and additions to encrypted data. In the end, you will get a cipher text that will let you carry out the same operations again on the encrypted data but only to reveal it.
The main challenge with homomorphic encryption is that producing the required encryption algorithm is extremely difficult. But there are several types of homomorphic encryption to help organizations and expert individuals.
·Fully Homomorphic Encryption
Some experts argue that the fully homomorphic encryption is the pot of gold in the list of homomorphic encryption types. Understanding this type of homomorphic encryption is quite easy. It involves an infinite number of calculations taking place over the cipher text such as addition and multiplications. Still, the end result of the same operations will always be valid.
This type of homomorphic encryption was introduced by Craig Gentry in 2009. Following the initial development in 2009, there have been various improvements to the original algorithm over time. It still remains one of the most popular homomorphic encryption algorithms to date.
·Partially Homomorphic Encryption
In partially homomorphic encryption, the algorithms will support infinite instances of a particular operation taking place. It will lead to an algorithm that’s additively homomorphic. That means, encrypting two plaintexts’ addition and adding two separate cipher texts will produce the same result.
It’s worth mentioning that partially homomorphic encryption algorithms aren’t difficult or as complicated as fully homomorphic encryption type. Some of the most common homomorphic encryption algorithms fall under this category.
It will still require you to have extensive knowledge about the calculations and processing criteria of homomorphic encryption to produce the required algorithms. Plus, the applicability of every encryption type can vary depending on the operations taking place.
·Somewhat Homomorphic Encryption
You will find the names of homomorphic encryption’s types rather amusing. Right after “partially homomorphic encryption” is “somewhat homomorphic encryption”. It’s a real type! But, it’s considerably different compared to fully homomorphic encryption.
In this type, the number of calculations that the encryption algorithm can perform on the data will remain limited. In simple words, a particular operation will involve a finite number of calculations. For instance, any combination that involves five multiplications or additions will produce a valid result through somewhat homomorphic encryption.
However, if the same somewhat homomorphic encryption supports a combination of six operations, the end result may become invalid. It’s even more challenging since it involves the creation a finite number of operations.
Homomorphic encryption is the potential solution to various data privacy and company utility issues. Using homomorphic encryption, companies can perform data analytics on users’/customers’ information without actually viewing it. Otherwise, it would be data privacy invasion, i.e. if companies have to view their users’ personal information.
In a similar sense, if the users/customers control the encryption keys/cipher text to their information, companies will have no option other than to comply with targeted advertising. But homomorphic encryption will have high storage requirements and can involve slow processes.