Corona virus update 5/25 - @home instruction going well; looking forward to resuming in-center - see note on this page
News from Mathnasium of Fairfield
The Baffling and Beautiful Wormhole Between Branches of Math
Jul 9, 2018
EULER’S IDENTITY: Math geeks extol its beauty, even finding in it hints of a mysterious connectedness in the universe. It’s on tank tops and coffee mugs. Aliens, apparently, carve it into crop circles (in 8-bit binary code). It’s appeared on The Simpsons. Twice.
What’s the deal with Euler’s identity? Basically, it’s an equation about numbers—specifically, those elusive constants π and e. Both are “transcendental” quantities; in decimal form, their digits unspool into infinity. And both are ubiquitous in scientific laws. But they seem to come from different realms: π (3.14159 …) governs the perfect symmetry and closure of the circle; it’s in planetary orbits, the endless up and down of light waves. e (2.71828 …) is the foundation of exponential growth, that accelerating trajectory of escape inherent to compound interest, nuclear fission, Moore’s law. It’s used to model everything that grows.
Enter Leonhard Euler, the one-eyed Swiss genius whom Frederick the Great lovingly called “our Cyclops.” What Euler showed, in his 1748 book Introduction to Analysis of the Infinite, is that π and e are deeply related, but in a very weird way. They’re connected in a dimension perpendicular to the world of real things—a place measured in units of i, the square root of –1, which of course doesn’t … exist. Mathematicians call it an imaginary number.
Courage, pilgrim! Here’s a visual metaphor. Imagine a graph with real numbers on the horizontal axis and, well, imaginary ones on the vertical. Now, remember the exponential function, f(x) = ex, from high school math? Ordinarily it graphs as an upward swooping curve—the very paradigm of progress. But put i in there, Euler showed, and eix instead traces a circle around the origin—an endless wheel of samsara intercepting reality at –1 and +1. Add another axis for time and it’s a helix winding into the future; viewed from the side, that helix is an oscillating sine wave.
The rest is easy: Take that function f(x) = eix, set x = π, and you get eiπ = –1. Rearrange terms and you have the famous identity: eiπ + 1 = 0.
That’s the essence of Euler’s alchemy: By venturing off the real number line into this empyrean dimension, he showed that disruptive, exponential change (the land of e) reduces to infinite repetition (π). You might think you’re getting ahead in the world, but from this astral perch you’re just running laps.
Now, maybe you’ve never thought of math equations as “beautiful,” but look at that result: It combines the five most fundamental numbers in math—0, 1, e, i, and π—in a relation of irreducible simplicity. (Even more astonishing if you slog through the proof, which involves infinite sums, factorials, and fractions nested within fractions within fractions like matryoshka dolls.) And remember, e and π are infinitely long decimals with seemingly nothing in common; they’re the ultimate jigsaw puzzle pieces. Yet they fit together perfectly—not to a few places, or a hundred, or a million, but all the way to forever.
You can take this farther, too. If you write that function above in a more general but still simple form as f(x) = e(zx), where z = (a + bi), what you get is no longer a circle but a logarithmic spiral, combining rotation and growth—now both at the same time! These graceful spirals are also found everywhere in nature, from the whorls in a nautilus shell to the sweeping arms of galaxies. And they’re related, in turn, to the golden ratio (yet another infinite decimal, 1.61803 …) and the Fibonacci sequence of numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …), which neatly describes the arrangement of leaves and petals in plants.
But the weirdest thing about Euler’s formula—given that it relies on imaginary numbers—is that it’s so immensely useful in the real world. By translating one type of motion into another, it lets engineers convert messy trig problems (you know, sines, secants, and so on) into more tractable algebra—like a wormhole between separate branches of math. It’s the secret sauce in Fourier transforms used to digitize music, and it tames all manner of wavy things in quantum mechanics, electronics, and signal processing; without it, computers might not exist.
The takeaway? Those crop-circle aliens were trying to tell us something.
The full article can be found: https://www.wired.com/2014/11/eulers-identity/
Corona virus update 5/25 - @home instruction going well; looking forward to resuming in-center - see note on this page
Nothing but great things to say about David and his team!!
In these times of crisis, David worked quickly to accommodate our preferences and we greatly appreciate the gesture. My kids LOVE going to this center, it is like a second home to them. All the instructors are friendly and knowledgeable, and provide constructive feedback to the students.
This is an excellent Math program and the Fairfield location is fantastic. With the help and support of David Lubner and his friendly tutors, my son became increasingly proficient and confident in Math. My son had gaps in his math instruction from Middle School and their assessment confirmed and identified the weak areas. He received a customized plan based on the assessment results. All he has to do is walk into Mathnasium, grab his individual math binder, find a seat, and get to work. A team of tutors are ready to help, teach and review practice math problems. I'm very happy!
David and Staff are AWESOME!!!
REALLY. The few months our son has been attending turned him into a second tier honor roll student. We cried bc we always knew he could do it but mathnasium has given him the cushion that he needed to excel.
The Aparicio-Jerro family
David Lubner and his Fairfield staff did a fantastic job working with our daughter and helping her advance her math skills at various stages of her academic career (elementary, middle school, high school).
My Daughter was upset with her final report card and as a parent I had to make sure that I found away to help her. When I made that first call and spoke to David, I felt a sense of relief, I saw how he made her comfortable and reassured her that they could help her “understand” different ways to look at math problems and build her confidence back up again. She could finish work without being stressed or sad that she would not be smart at math. She is now happy working out math problems and always has a smile on her face. I know I made the right choice! Thank you David and staff!
My younger 2 daughters have attended Mathnasium, Fairfield, for years. It is our go to place whenever either of them need help with math. The staff is excellent at engaging kids of all ages and helping them master mathematical challenges. It is not rote learning, it is gaining a real understanding of numerical concepts and operations.
Very helpful staff and flexible. There is no set schedule. My 15 yr old son can show up anytime and I can pick him up whenever I get there. They did an intense testing session prior to him starting to analyze his levels and were able to zoom in on what he needs to work on. The tutoring help is customized to each child's needs. He can bring his current homework or get help for upcoming quizzes and exams. He enjoys going. He logs his time spent on an ipad and its tracked to earn credit towards items in the case. Brilliant idea.
I will recommend any of my friends at Mathasium in Fairfield because it’s a great program for children to learn math and the stuff are very dedicated and outstanding. Love always The [LAST NAME REMOVED]’s family!
My daughter’s confidence has increased dramatically since she started to go to Mathnasium. This was a girl who would get upset every time she. had Math homework. Math is now her favorite subject! I am very proud of her and look forward to all the progress she will make here!
We have been thrilled. My son has been excited to go as they incentivize the kids which makes them want to come learn. We also love the monthly feedback so we know exactly what he is working on. We are so happy we are having our other son accessed so he can begin going.
The staff and owner are very kind, encouraging and patient with students of all ages. The teaching style is flexible so allows my son to learn in the style he is most comfortable with. I appreciate that face to face contact is used rather than relying on computers to teach. I'd recommend this location to anyone hoping to help their child be comfortable with math!
As someone who has struggled with math for a long time, our son was reluctant to attend Mathnasium. In a short month, he has realized the benefits and is becoming more confident. He even states that it is fun! He routinely comments on the fun instructors. We are looking forward to continued success over the summer.
The best way to explain how great Mathnasium has been for my son, is to say that I only wish we had started earlier. His math grades in school have improved dramatically and he is much more confident in his abilities now. You guys keep it fun, which keeps him wanting to go. We are very happy clients.
my son was having trouble with algebra 1 -- he received a C for his 9th grade year. He went to Mathnasium for one month, utilizing the time there and left feeling both confident in his algebra 1 knowledge as well as being given an introduction to geometry. This fall he has earned an A in his geometry class for the first quarter. He feels his time at Mathnasium was so incredibly instructive. We recommend it most highly.
Tommy really likes going to Mathnasium! He feels comfortable there and now that school has started, I feel relieved that he can do his math homework with guidance from the Mathnasium tutors. Everything has been great so far!
My girls love coming to mathnasium! The staff and environment are amazing. They make math so enjoyable for them. Mathnasium consistently removes any stress my kids would normally have with in-school math. Their confidence is so high they actually love math class! Can't thank you enough.
Our 2 boys have been attending Mathnasium for 3 years for both summer enrichment and studying throughout middle school. It is a very focused environment with a proven track record of promoting a love of Math. Our boys connect well with all the instructors and leave with a feeling of confidence in knowing that they will excel in Math. And their grades show! Honors Geometry it is for them entering High School! Thank you Mathnasium!
BT Weston CT
Going to Mathnasium had never been a problem for my son Alex. All the staff is responsible, helpful and nice with children. my son grades in math did improve since the first week there. Dave is always welcoming and knows how to address any concerns.
I will refer anytime.
*Staff is exceptionally friendly, patient and smart
*My son feels so comfortable there. He is not hesitant about asking questions or having a team member work one on one with him (which is half the battle!)
*My son needs the support to maintain an A average in math and has consistently done so.
*There does not seem to be a high turnover rate of staff--which adds to the comfort level
*Hooray for Elizabeth! She's an awesome tutor!
My daughter was failing her Mathematics course in high school, since enrolling her at Mathnasium Learning Center, she has been passing. Every time her Physics and Math teachers fail to show her how to solve problems, she goes to Mathenasium and they help her. I wish we had known about Mathnasium when she was in Elementary school.
My daughter is a college student and needed additional help beyond what the school could offer. Your instructors did not make her feel uncomfortable about her needs and took the time she needed to understand the material. Thank you for all of your patience and assistance. She passed the class!!!
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