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Will I ever need math? A mathematician explains how math is everywhere – from soap bubbles to Pixar movies

Curious Kids is a series for children of all ages. If you have a question you’d like an expert to answer, send it to [email protected] .

Will I ever need math besides for school or work? – Hadassah G., age 9, New Jersey

It can be easy to think that you need math only to do your algebra or geometry homework or if you have a job as an engineer. But, in fact, math pops up everywhere – even in the soap bubbles in your kitchen sink.

While washing dishes when I was 13, I noticed that the soap bubbles formed tiny 3D polygons, packed together like a honeycomb, but not all of these shapes were perfectly round. Why did some of the bubbles look like hexagons? Why were others shaped like squares full of air? Why didn’t I see any star-shaped bubbles, or bubbles with spikes?

When I learned that math could help answer these questions, I thought that was so cool! Now, as a professor of mathematics who studies how people learn math through play , I understand why bubbles are naturally lazy . I even studied the math behind the reason I saw only some shapes in soapy dishwater.

Besides helping explain the behavior of bubbles and other curiosities of nature, math is likely part of many of your everyday activities, along with the technology you enjoy and even the inner workings of your brain. Doing math isn’t just about computing, memorizing, solving an equation or doing word problems by yourself. It’s really about creative problem-solving and logical thinking with other people.

Math in everyday life

Many topics you learn in elementary school – like fractions, percentages and measurements – are useful in everyday life.

For example, if you want to build a fence around your house, paint your walls a new color or with a design , or sew yourself a new outfit or quilt , all of those activities require knowledge about measurement and scaling. More complicated construction projects, such as building a treehouse , require lots of mathematical problem-solving skills.

Once you’ve laid out the plans for one of these projects, you need to buy all the materials. Percentages – which are special kinds of fractions – are especially important to understand when managing money. Understanding percentages can help you budget your money and increase your net worth .

Beyond budgeting, you might find yourself using percentages when cooking a double batch of brownies, determining how much medicine to take when you’re sick or understanding the weather forecast .

Your favorite technology needs math

Math is an essential tool that animators use to make movies.

Studios like Pixar rely on ideas from geometry to bring characters like Ember from “Elemental” to life. With an understanding of geometric transformations like reflections, rotations and translations, you can use your computer to make your own animations.

Coordinate systems, which are fundamental to geometry, show up in video games like Minecraft. The 2D Minecraft world uses a 2D coordinate system – with an x-axis and a y-axis – where you can move north, south, east or west. In the 3D Minecraft world, there’s also a z-axis, allowing you to move up and down. Middle and high school teachers can even use Minecraft to help students learn math concepts.

Many high-paying jobs use math , especially probability – again, fractions. Understanding probability helps doctors identify how effective medical treatments are, informs coaches about ways their teams can improve and aids cryptographers in keeping private information – like your email password or ATM PIN – secret. Cryptography combines probability with number theory to create secret codes that are difficult to crack.

Math helps your brain

Math can have a big impact on your internal life, too. You can use math activities to train your brain the same way you would train your body for a sport. Doing math helps your brain become flexible so you can better handle new tasks and ideas of all kinds.

Even doing things that don’t look like your math homework, such as crossword puzzles, word searches and board games like Set and Blokus , are deeply mathematical activities that help your brain get stronger . This kind of mental training helps the brain pay attention and solve problems and improves memory. A strong working memory supports brain functions that lower the risk of Alzheimer’s disease and dementia .

Having a stronger, more flexible brain also aids quantitative literacy , which can help you make sense of graphs that appear in the media, reflect critically about news and understand health and financial information.

Math can even help you outsmart artificial intelligence . With the rise of AI, it’s important to be able to think creatively, reason logically and make connections between concepts – whether mathematical or not. Puzzling through a difficult math problem nurtures these skills, even if you don’t get the right answer right away.

It’s important to remember that doing math doesn’t require you to be fast or to get the correct answer right away. In fact, you can learn a lot by getting the wrong answer . Working with other people can also help you to make sure you really understand the problem and builds communication and teamwork skills .

Math is so much more than memorizing times tables and filling out homework problem sets. So next time you kick back to watch your favorite animated movie, or start saving up for a fancy new tech gadget, hopefully you’ll appreciate how math is woven into so many parts of life.

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Discussion and hints

The above shows the results of simulations on this problem for two frequencies of excitation, ω. The upper plot where ω is less than the natural frequency, ω n , and the lower plot where ω is greater than ω n . In each plot, the RED curve is the forcing F(t) and the BLUE curve is the particular solution of the EOM, x P (t). As can be seen from these simulation results:

• The response for ω < ω n has the steady-state response of x P (t) moving in phase with the forcing F(t). That is, during the time that the block is displaced to the right, the force is acting to the right. Conversely, during the time that the block is displaced to the left, the force is acting to the left.
• The response for ω > ω n has the steady-state response of x P (t) moving 180° out of phase with the forcing F(t). That is, during the time that the block is displaced to the right, the force is acting to the left, and during the time that the block is displaced to the left, the force is acting to the right.

In your analysis for this problem, you will be determining the natural frequency ω n  of the system, along with the steady-state response. Be sure to check your answer in the end: does it demonstrate the phase relations seen in the above simulation results?

Any questions?? Please ask/answer questions regarding this homework problem through the "Leave a Comment" link above.

17 thoughts on “Homework H6.I - Sp24”

Once you have the EOM, you can use the equation for x_p(t) to find the second derivative. Then you can sub these two equations into the EOM and solve for the constants.

Is this the method of undetermined coefficients essentially?

Yes. You just have to find all the forces that act on the direction of acceleration times mass and then substitute your x=Asin(wt)+Bcos(wt) (with derivatives) into the corresponding x's to find your constants. These constants can then be substituted back into your original x equation.

If the natural frequency and the forcing frequency are the same is that when it can be considered in phase?

When this happens, I believe they are in phase and when they are equal the affect it has is that the two are in resonance - which increases the amplitude of the oscillator

When omega = omega_n, the system is in resonance. At resonance, the forcing and response are 90° out of phase.

When subbing x_p(t) and the second derivative of x_p(t) into your standard EOM, the coefficient before x will be w_n^2 making it the method to solve for A and B. You can separate the coefficients into coswt and sinwt as well. Plugging those values back into x_p(t) will give your answer for c.

When deciding for the direction of the force of the springs, is there an instance when all three would be pointing in the same direction?

When determining the direction of the spring forces, envision the block in a position corresponding to positive x (here, to the right). With the block displaced to the right, the spring on the left side is stretched - that spring then will pull on the block to the left. Also, the springs on the right would be compressed, and pushing on the block to the left. Therefore, the direction of all three spring forces will be to the left.

For this problem, I set up my FBD and used F_x to find my EOM. This was pretty straightforward. To find the particular solution, we can look in the textbook for the x_p equation.

When solving for A, solve for natural frequency using sqrt(k/m) and sub it into the equation.

For this problem, an easy way to find the EOM is to sum the forces in X. If you're unsure of how to find a particular solution, I highly recommend watching an example video on this. EX 6.C.1 is very straightforward in this process.

In this problem, all the spring forces are acting to the left, as you can imagine that the block is moving to the right, and the springs resist that motion.

The problem statement asks for the particular solution. If it were to ask for the entire solution, you would also have to solve the homogeneous EOM (the left side = 0), like we've been doing for the last few homework assignments.

Also, because the forces we are using are sine waves, the particular solution should also just be a sine wave.

A helpful example of a similar problem is problem 6.C.2. Looking over this problem helped me to solve for x_p

The force balance equation is set up the same as previous problems with the springs resisting the motion, and the only thing added is the force in the positive direction.

In part C I found it helpful to use x = Asin(wt) +Bcos(wt) and then using that to solve for the particular solution.

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Ask chatgpt4 and get answers.

• #2 in Education
• 4.7 • 15.9K Ratings
• Offers In-App Purchases

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Description.

Experience the future of communication with Question.AI, the ultimate AI Chatbot app that's revolutionizing the way you gather information, communicate, and stay informed across various facets of life. Whether you're a student, a professional at work, an inquisitive mind, or a business enthusiast, our app is designed to make your life easier, smarter, and more efficient in any context. 【Key Features】 - Simplicity at its Best: Seeking answers has never been easier. Just ask your questions, and our intuitive AI will promptly provide you with accurate responses. No need for complex commands or jargon - it's like having a knowledgeable friend by your side 24/7. - Your Personal Assistant: From quick facts to in-depth research, Question.AI is your personal assistant ready to assist you. Need a definition, explanation, or summary? Count on us to deliver information tailored to your needs. - Global Connectivity: Break language barriers effortlessly. With the ability to translate into 140+ languages, Question.AI ensures you can communicate and connect with individuals from all around the world. Expand your horizons and broaden your perspectives with ease. - Intelligent Writing: Enhance your writing with AI-powered suggestions. Whether you're crafting an email, composing a report, or writing creatively, our app's intelligent writing feature offers insightful recommendations to make your content shine. - Adaptable Across Occasions: Question.AI is your versatile companion across various occasions, whether it's for studying, working, managing your business, or simply enhancing your daily life. We're here to assist you in every scenario. 【Why Choose Question.AI?】 With a commitment to excellence and user satisfaction, Question.AI stands out as the ultimate AI Chatbot app: - User-Friendly: Our user-centric design prioritizes simplicity and accessibility, ensuring a seamless experience for users of all ages. - Instant Insights: Get answers in real-time, allowing you to make informed decisions and impress others with your newfound knowledge. - Trusted Accuracy: Our AI's responses are backed by robust algorithms, ensuring that the information you receive is reliable and up-to-date. - Empowering Communication: Break down language barriers, foster connections, and engage with a global community effortlessly. - Unleash Creativity: Elevate your writing and communication skills with AI-powered suggestions that refine and elevate your content. Ready to embark on a journey of knowledge and connection? Download Question.AI now and experience the future of communication in the palm of your hand. Get started today! 【Contact us】 Email: [email protected] Official Website: www.questionai.com Instagram: @question.ai_app YouTube: @QuestionAI-Official Facebook: bit.ly/QuestionAI_FB TikTok: @question.ai_app Discord: bit.ly/QuestionAI_DC Messenger Group: https://m.me/j/AbaNe6U1Rhv5NAiL/ Privary Policy: https://www.questionai.com/privacy-policy Terms and Conditions: https://www.questionai.com/useTerm

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Ratings and Reviews

15.9K Ratings

I’ve never been so greatful towards an app before, usually there was a deal with other apps that you had only a few tries before you had to pay for the full thing or wait your time…which 90% of the time didn’t even give you an answer or help… I’ve never had something this smooth be so dang helpful 😭❤️ Not only did it help me pass my test (88% omg 😍) but it also gave helpful advice and dumbed it down for me so i didn’t have to read through everything. Quite literally gave me the information i wanted and also the answer which is AMAZING 😨❤️Helped me better understand the questions SO THANK YOU 🙏 will definitely be using this on math 🥶 hoping for the same smoothness on math since it’s what i struggle with but overall just from a first time use i’m deeply thankful for this app!! 😭🙏❤️

Developer Response ,

Thank you for your positive feedback! I'm delighted to hear that you're enjoying the application. Please feel free to share any suggestions you have directly, and I'll do my best to assist or pass them along to the appropriate team for consideration.

I LOVE this app!! 💞💞💖💖

So I use edgecourseware and some of the questions can get VERY hard, and it gets to the point I want someone smart to answer it for me. So the other day I was scrolling on TikTok just to find THIS helpful app, and I think of my edgecourseware. So I’m all like “omg! This app can help me with edgecourseware!” So I don’t hesitate to download it. I get on edgecourseware and show the camera to a hard question and press the button, and it gives me the answer! And this thing has retakes on it so I had to retake the test cause I was always getting wrong answers on it! And the scores would come out bad too! So I see my test scores to compare them, 60% - 100% !! I love this app. If it weren’t for this app, I would have never passed the test! 🩷🩷 xoxo

Pretty good, but…

I really like this app because when I’m having a hard time with my math in school, I go onto this app and check to see if my answers are right. If not, I see what I did wrong which prevents mistakes and helps me to learn. Especially since not too many people I know understand my math, it makes it a lot easier. There’s absolutely no ads, and if you’re confused about something, you can ask it any question. However, it can’t do the work of area correctly. I had an answer of 168, even my dad checked it, and it told me 288, which is far off. I don’t even know how it got that answer. It’s good for basically any math, except for geometry and area, and you know that sort of thing. I also was simplifying expressions and it gave me wrong answers for 2 of them even though I did them in school and checked it with the class. You have to be careful that way.

We genuinely appreciate your openness in sharing your thoughts with us. It is through such insights that we can enhance our services and accuracy in the short future.

App Privacy

The developer, 3HOUSE , indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .

Data Used to Track You

The following data may be used to track you across apps and websites owned by other companies:

Data Not Linked to You

The following data may be collected but it is not linked to your identity:

• Identifiers

Privacy practices may vary, for example, based on the features you use or your age. Learn More

Information

English, Arabic, Dutch, French, German, Indonesian, Italian, Japanese, Korean, Malay, Portuguese, Russian, Simplified Chinese, Spanish, Traditional Chinese, Vietnamese

• Question.AI DPro - Monthly $9.99
• Question.AI Pro-Monthly $8.99
• Question.AI DPro - yearly $99.99
• Question.AI Plus-yearly $34.99
• Question.AI Plus- Monthly Free $9.99
• Question.AI Plus Special Offer $9.99
• Questionai Pro - Monthly $9.99
• Question.AI Pro-yearly $59.99
• Question.AI CPro - Monthly $14.99
• Question.AI DPro - Monthly New $9.99
• Developer Website
• App Support
• Privacy Policy

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