The STEM of Golf

Part 1

By Wayne Carley

In the continuing revelation of what STEM really means in our lives, let’s continue to explore the STEM skills necessary in participate and excel at a sport so many enjoy. In previous issues of STEM Magazine we’ve looked at the STEM of football, basketball, soccer, hockey and other sports. In the midst of our summer and in honor of the recent U.S. Open, let’s dig into the STEM of Golf.

Golf is intensely mathematical, with strong engineering applications. The math and engineering are personal in application, with the technology being primarily in the equipment. The science of Golf (the systematic accumulation of knowledge) permeates all aspects. What is really interesting is that we don’t actually learn these math applications to be effective at golf. For successful golfers (low scoring), we seem to be born with many of these practical applications and experiential knowledge of the following mathematics.

Math is of course defined as  “The science of numbers and their operations, interrelations, combinations, generalizations, and abstractions”. Golf is certainly all of this and includes the math domains of geometry, analysis, topology, combinatorics, number theory, algebra, math physics and more.

If you enjoy any sport, but say you hate or don’t understand math, this is a real contradiction. What I hope you will consider and better understand is that you already know so much math, you just don’t realize it or see it in your daily life. That being said, let’s consider the geometry of golf.

Geometry noun

ge·​om·​e·​try | \ jē-ˈä-mə-trē /  

Definition of geometry

1a : a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids

Golf is 3 dimensional and requires 3 dimensional thinking to solve golfs primary problem: Get the ball in the hold with as few swings (strokes) as possible.

Geometric considerations are:

– the flight of the golf ball ( apex or height reached, distance desired, possible obstacles to be avoided, velocity of ball flight to get from point A to point B). This geometric problem can only be solved by the golfer by using the engineering method that we will cover later, in conjunction with the technology in the golf bag, the golfers ability to use it well, and a dozen questions that need to be ask for each and every golf shot.

The golfer must visually determine where they want the golf ball to land for the first shot. Once decided, the distance needs to be estimated, usually in yards. A golf club must be chosen with the correct angle of attack for the desired ball flight. Proper physical alignment toward target must be decided, usually in degrees. The speed of the golf swing must be estimated to drive the ball along the chosen flight path. Just when you thought we were done, other consideration must be considered for success. If there is wind, the direction and speed of the wind need to be evaluated. Will a head wind slow the forward movement? If so, how much? Will a tail wind speed the flight progression? If so, how much? Will a cross wind cause a deviation in the alignment of the shot? If so, how much?

Air temperature or density directly impacts ball flight, thus distance and accuracy. This is measured in degrees. The hotter the air, the thinner the air, thus less resistance to flight requiring another recalculation of club use and strike force required. The humidity of the air is important and often in direct contradiction to air temperature. Relative humidity is the most common consideration and is the ratio of the current absolute humidity to the highest possible absolute humidity (which depends on the current air temperature). A reading of 100 percent relative humidity means that the air is totally saturated with water vapor and cannot hold any more, creating the possibility of rain. This doesn’t mean that the relative humidity must be 100 percent in order for it to rain — it must be 100 percent where the clouds are forming, but the relative humidity near the ground could be much less. Hot temperatures with low moisture content or low humidity result in thin air, less resistance to ball flight and longer distances. Hot temperatures with high moisture content or high humidity result in thick air, more physical air resistance to flight and shorter distances.

Let’s not forget altitude measured in feet above sea level for golfing purposes. Air density or thickness at sea level is greater than air density at higher altitudes. Therefore, the distance a golf ball travels at the beach is less than the distance it travels in Denver Colorado at 5,280 feet above sea level. Under similar atmospheric conditions using the same club, same ball, and same striking force, the ball in Denver will travel significantly further.

The math and geometry of golf is so very complicated and we’ve only scratched the surface. When all of the aforementioned aspects are decided, the human golfer must physically execute a golf swing the allows for the calculations to be accurately realized. This is where the challenge really exists. The brain has done its work, and now the body is called upon to execute the mental formula.

This was the first shot of our round of golf. Everything we’ve just calculated must be done again, an average of 100 times for the typical golfer. Your results may vary.

Silicon Valley To Women Who’ve Left Tech: Please Come Back

Published in STEM Magazine


When Kim Poletti exited the tech industry in 2005 to take some time to raise her 10-month-old daughter, she left as a successful project manager leading technical teams for IBM. But when she tried to get back into the workforce 10 years later, she had a hard time getting anyone to even interview her.

“Most people just aren’t interested in looking at somebody who has a 10-year break on their résumé. Trying to convince them that I still had these skills and probably actually had more skills as a result of being a stay-at-home mom was difficult,” Poletti said. “I feel like that role isn’t really valued that much in our culture.”

Across many industries, women who pause their careers find it difficult to return to work as they are often met with recruiters turned off by big résumé gaps and perhaps questioning their reasons for leaving in the first place. In Silicon Valley, this is a major reason why women hold just 18 percent of tech positions and just 33 percent of all jobs in the tech industry, according to an analysis of company reports provided by 500 Miles, a startup that helps candidates make informed decisions about where to work and helps companies find talent.

But as Silicon Valley struggles to bring more women into its ranks, a handful of tech giants, including PayPal, Intel and IBM, are tapping into this group of workers who have long been ignored with programs that are designed to make it easy for them to transition back into the industry. These programs employ numerous tactics to close the deal, including flexible and reasonable work hours that can accommodate women with families, unlike the grueling schedules that dominate some tech companies such as Amazon and many startups.


Companies launching “returnship” programs also train their managers so they know how to work with individuals who are coming back to tech. Rather than avoiding résumés with gaps, they’re trained to look for them: Is this a qualified woman who took a break and may want to come back?

Returnees are given multiple points of contacts throughout their companies by assigned multiple mentors in addition to their direct supervisors. To ensure their careers will be able to advance, companies launching returnship programs offer their interns training across a broad range of topics, including how to write a résumé, conduct a job interview and promote themselves. Additionally, these programs provide women with multiple networking opportunities both inside and outside their companies so they can start rebuilding their connections throughout the tech industry.

“These are talented women who have the skills but they just happened to take some time off,” said Claudia Galvan, the former senior director of the Anita Borg Institute for Women and Technology and an industry veteran. These women find it “almost impossible to go back to work, or if they do go back to work, they have to take totally different jobs from what their career was, a demotion, of course pay cuts — and that’s if they get the opportunity to get back into the workforce.”

“It’s almost considered career suicide to leave,” Galvan said.

At PayPal, for example, the payments-processing company is set to launch its “Recharge” program in February. Through Recharge, PayPal will bring on eight women who will be paid interns with the company for 20 weeks, giving the women an on-ramp back into tech. PayPal is hoping to hire the women at the end of their internships but also wants to give them the freedom to explore other options.

“If the pilot program is successful, we want to expand that,” said M.J. Austin, a senior technologist at PayPal. Austin experienced the difficulty of leaving and coming back herself after leaving the industry in 2001 to raise her newborn children. She was able to return to work three years later by way of eBay and PayPal thanks to a mentor who championed her abilities. “That support coming in the door to say, ‘Hey, we’re behind you,’ will give you an opportunity to really shine.”

Incorporating Children’s Literature into Mathematics Instruction

By Madeline Bailey / Texas A&M University

In the world of present day education, incorporating reading and writing into classrooms of every grade level and discipline has become the norm, often to the chagrin of upper level STEM (Science, Technology, Engineering and Math) teachers who do not see these concepts as particularly relevant to their subject. However, despite the initial mixed sentiments, it has become clear that not only does the integration of reading and writing, specifically in the form of children’s literature, positively impact students’ comprehension, but also their retention and overall attitudes towards the subject.

Benefits of Incorporation

Over the course of several years of study, the incorporation of children’s literature into the math classroom has been found to markedly improve student performance in several areas, the most important of which being comprehension and retention (Mink &Fraser, 2005). By offering mathematical vocabulary and ideas in an understandable and developmentally appropriate format, children’s books allow students the opportunity to better understand and retain abstract mathematical concepts without being overwhelmed (Padula, 2004).

Comprehension of Mathematical Content

For generations, “traditional” mathematics instruction was the norm in classrooms across the United States (Mattone, 2007). Students were shown a series of steps that they were to use to solve a given problem, and they were expected to repeat these steps until the problem could be solved almost mechanically. This method in no way presented mathematical ideas as particularly relevant or understandable to students. However, in modern mathematics classrooms, the integration of children’s literature is revitalizing math education.

In order to use children’s books to their fullest mathematical potential, teachers must make their content relevant and meaningful to their students. For example, using a math fiction book as an introduction to a specific concept, paired with a classroom discussion to explain the concept and a follow-up activity emphasizing the mathematical content, students are exposed to the same idea several times in a variety of ways.

Retention of Mathematical Content

Not only are children’s books familiar to students, they are also much more appealing than say, a math textbook. Using children’s literature in math classrooms has been found to not only improve student performance, but attitudes towards math as well (Mink & Fraser, 2005). This integration encourages the students to be interested and excited about learning math, which makes them far more likely to understand, apply, and retain the information (Mink & Fraser, 2005)


The most damaging mindset when teaching mathematics revolves around students asking when they will ever use math in their daily lives. The only way to overcome this increasingly prevalent idea is to consistently demonstrate how math is a relevant and important part of life for everyone everywhere.

Encouraging students to read self-selected texts and find embedded math ideas is another way to enhance math instruction. When students see the use of math in situations that they can relate to, they are better able to understand not only the usefulness, but necessity of math in everyday life.

Recommendations for Teachers
  1. Choose books that are appropriate and relevant to students.
  2. Encourage math-based conversations and the use of mathematics as a means of communication.
  3. Encourage discussion of mathematical concepts and allow students to find the explanations that make the most sense to them.
  4. Integrate self-selected literature to show that math is universal as well as useful.
  5. Design appropriate extension activities that compliment both the included texts and core math concepts.

Overall, the effective incorporation of children’s literature into the mathematics classroom has been proven to aid in students’ comprehension and retention of math concepts, regardless of whether or not the text is mathematically focused. Children’s books provide a familiar, unintimidating format for students to be exposed to both concrete and abstract ideas, thinking, and patterns. The context of a story also encourages connections between the underlying mathematical ideas and the real world, emphasizing the fact that math is a fundamental component of everyday life. Finally, no literature-based math lesson is complete without an appropriate extension or follow-up activity. These activities serve to further explain and repeat the concepts introduced in the text, while giving students the opportunity to apply them and demonstrate mastery.

Re-fusion of Music to STEM Education

By Azam Shaghahgi for STEM Magazine


Music the aesthetic of rhythms, is a blend of expression of feelings, art, skill and math. Pythagoras explains the relations between the math and music: “There geometry in the humming of the strings, there is music in the spacing of the spheres.”

Redefining music in the “M” in S.T.E.M (Science, Technology, Engineering, Math) is easier to understand the medium of the intervals between notes and derived musical tones from geometrical patterns, mathematicians have linked music to numbers.”

The young Canadian female model-turned DJ player Eva Shaw explains the distinctive

correlations between music, math and science as “ineluctable”.


Azam Shaghaghi: Would you describe the vibe of music writing?

Eva Shaw:

When writing music, you find a specific pattern of notes that when they’re put together, create a sound you like.  You might be influenced by trends in music in chord structure and sound in general.  I think I use math without being conscious of it. Depending on the feeling you’re trying to achieve with a song, you can adjust the tempo, pitch, structure, and chord progressions to achieve the vibe you want. There’s a correlation in measurement of time and frequency. There’s always a certain beat count, rhythm and structure. I actually think structure is one of the most important features in a song that you may not necessarily consider as a listener. Proper order and repetition is part of most pop music.


Eva found her art and music talent at her early 17th. The urge to create the music, mixing the rhythms and feelings, she explains. “The musical scale is related to math, of course.  The distance between notes (pitch) is the way of dividing up the scale. Rythym is a way of dividing up time. Each scale repeats musical intervals , normally after each octave. Betweens octaves, there is a frequency range (this varies depending on the note).”

Making music for a living, she obtained a residency at the Hakkasan nightclub in Las Vegas after it opened in 2013 and has preferred at many music festivals and slew of other venues all over the world; but she believes she would be a scientist if she was not a DJ player.


How do you relate music to science?

Eva Shaw:

I think music is related to our biology as well. Certain rhythms, beats and sounds make us feel specific ways. I can relate a heart beat to a music beat and I think your body has a natural rhythm.  When you hear a beat, you feel it too. You can also physically feel certain frequencies but not necessarily hear them. We use this knowledge for mixing songs; cutting and boosting specific frequencies.

You can actually see music visually in wave forms and graph out sounds and music. A lot of musicians can tell by looking at a wave form what it sounds like. When producing music, I also create sounds using synthesizers. You can change the way something sounds by adjusting the wave forms within the synthesizer.


How do you see technology has impacted the music industry?

Eva Shaw:

Technology has made music more accessible to people who either want to create it, buy it and/or listen to it. You can upload your own compositions to websites such as Soundcloud, and you can just as easily find and stream music from artists. I think there are lots of benefits to technology and music. But, I also wonder if perhaps it takes away some of the value of people’s relationship to music. There was a certain excitement about going to a CD store (or record store) and finding that physical disc. Record labels used to really “break” (introduce an artist to the public) whereas now an artist has the ability to “break” themselves. I think with the growth of technology, artist’s music can get lost in the shuffle. Record labels need to find new and creative ways to identify new artists and work with the new and changing technology.


Many from science and also music field such as “The Boards of Canada” have called “Music is Math” what do you think of that?

Eva Shaw:

The relationship between music and math and science has definitely existed for a long time . Even Beethoven, who famously went deaf , continued to make music.  We can guess it was probably a combination of hearing the notes in his mind, musical structure he’d learned and maybe feeling the pulses. It’s funny because I was never interested in math in school and I think it’s because I was never taught to connect it with human things like music and art. I think if it’s taught with examples that one can use in real life such as examples in music, kids in school will be more open and interested to learn. If someone had told me, “maybe you will become a musician or a music producer, and this information will help you in your future”, I would have been  more interested. I was always interested in science,  specifically biology and the human body. I am the type of person who goes by feeling, a lot of the time. If I think something sounds , looks or feels right, I go with it. You can’t always find a formula for that.

Home Visits With a STEM Twist

By Brenda Iasevoli


Research shows that home visits reduce absences and improve test scores and school climate, but what if they could also spark an interest in the science, technology, engineering, and math, or STEM, fields? That’s the question the college of education at Sacramento State University set out to answer when it began training in home visits for math and science teacher candidates.

These teachers are the key to opening up STEM fields to lower-income students and students of color, said Deidre B. Sessoms, a professor in the college of education at Sacramento State, where all candidates get their training in high-needs districts, including Sacramento City Unified, San Juan, and Elk Grove. “We don’t have enough students of color going into the STEM field and we have a hard time keeping girls and girls of color interested in math and science,” said Sessoms. “So while we want all of our students to have this training, it is especially important for our math and science teachers.”


Eyes on the Goal

It’s unusual for a school of education to provide home-visit training for its candidates, but science teacher Jennifer Clemens and physical education instructor LuTisha Stockdale bet the investment will pay off. “The earlier teachers try this in their careers, the better,” said Clemens. “It helps to just jump in, shadow teachers, and see how the whole conversation works. You’ve got to take away the mystery and fear early on.”

“Parents tend to be a bit hesitant or unsure about how to act around a teacher, but home visits help to break down that barrier,” she said. “The visits help to show that you are not such a scary person. It’s more about, ‘I’ve got the kids at school and you’ve got them at home and we should be working together.'”


STEM for All

As a student teacher, Endean builds relationships with her students and families by going to high school sporting events, and the personal knowledge she has gained has come in handy in the classroom. She once explained arcs to her soccer-playing students by reminding them about what they do when they make a penalty kick. “You have to think about where you kick the ball from with your foot to make sure you get it over or around the goalie,” she explained. “How hard do you have to kick the ball?” When they answered “pretty hard,” she told them that’s the “initial velocity.”

Endean’s students, the majority of whom are black and Hispanic, will dismiss certain jobs, she said, mainly because they don’t see other people like them in the field. So she has decided she will use her own story as an example when she visits her students’ homes next year. “I’m a woman in a STEM field,” she said. “I have a degree in astronomy and math, with a focus in physics. It’s not common for a woman to be in these fields, but here I am.”


Dreams for the Future

Training STEM teachers in home visits will help to broaden their impact, according to Steve Sheldon, an associate professor in the school of education at Johns Hopkins University. He has done research on home visits in Washington, D.C., and is now doing a national study of the impact of home visits nationwide for Parent Teacher Home Visits.

But math and science teachers should be careful not to take STEM promotion too far, warned Clemens, the science teacher at Arthur A. Benjamin Health Professions High School. She thinks the benefits of careers in science and other fields should come out naturally through a conversation about the hopes and dreams students and parents have for the future.