https://surroundedbymath.com/changes/Calculus and everyday math explained with the arithmetic shown: limits, derivatives and integrals; loans, compound interest, taxes and retirement; calories and heart rate; coffee, pi, seasons and power lines. Every figure links to a textbook, course notes or government source.en-ushttps://surroundedbymath.com/money/apr-vs-apy/https://surroundedbymath.com/money/apr-vs-apy/Wed, 21 Oct 2026 00:00:00 GMTAPR is the yearly rate before compounding; APY is the rate after it. See the formula, 5% and 24% examples, a calculator and how loan fees change APR.https://surroundedbymath.com/daily-life/calculus-in-everyday-life/https://surroundedbymath.com/daily-life/calculus-in-everyday-life/Wed, 21 Oct 2026 00:00:00 GMTFollow one ordinary day and watch calculus run under a cooling coffee, a speedometer, a fenced garden, a bacteria count and a filling tub, with the math shown.https://surroundedbymath.com/core-ideas/chain-rule-explained/https://surroundedbymath.com/core-ideas/chain-rule-explained/Wed, 21 Oct 2026 00:00:00 GMTThe chain rule in plain words: inside and outside functions, rates that multiply, step-by-step examples, real-life uses and the mistakes to avoid.https://surroundedbymath.com/money/compound-interest-formula/https://surroundedbymath.com/money/compound-interest-formula/Wed, 21 Oct 2026 00:00:00 GMTThe compound interest formula A = P(1 + r/n)^(nt) with a calculator, worked examples, solving for rate and time, APY and the Rule of 72.https://surroundedbymath.com/core-ideas/derivative-rules-cheat-sheet/https://surroundedbymath.com/core-ideas/derivative-rules-cheat-sheet/Wed, 21 Oct 2026 00:00:00 GMTDerivative rules of a first calculus course on one page: all six trig functions, a^x, logs, inverse trig, with examples.https://surroundedbymath.com/daily-life/derivatives-in-real-life/https://surroundedbymath.com/daily-life/derivatives-in-real-life/Wed, 21 Oct 2026 00:00:00 GMTWhere derivatives show up in real life: speed, population, money, best sizes and linked rates. Each example comes with its numbers worked out.https://surroundedbymath.com/core-ideas/fundamental-theorem-of-calculus/https://surroundedbymath.com/core-ideas/fundamental-theorem-of-calculus/Wed, 21 Oct 2026 00:00:00 GMTThe Fundamental Theorem of Calculus links derivatives and integrals. Part 1, Part 2, worked examples, when to use each, and when it fails.https://surroundedbymath.com/world/gold-in-an-oscar-statuette/https://surroundedbymath.com/world/gold-in-an-oscar-statuette/Wed, 21 Oct 2026 00:00:00 GMTAn Oscar is cast bronze with a thin 24-karat gold plating. See the plating math: about 0.5 to 6.5 grams of gold, and why solid gold would cost about $414,000.https://surroundedbymath.com/daily-life/hidden-math-in-a-normal-day/https://surroundedbymath.com/daily-life/hidden-math-in-a-normal-day/Wed, 21 Oct 2026 00:00:00 GMTFollow one ordinary day through sleep, GPS, groceries, a forecast, a recipe and savings, and see the arithmetic hiding in each, with the numbers sourced.https://surroundedbymath.com/world/how-fast-does-coffee-cool/https://surroundedbymath.com/world/how-fast-does-coffee-cool/Wed, 21 Oct 2026 00:00:00 GMTCoffee cools fast at first and slower later. The law behind it, how to find your cup's cooling constant, measured data, and what milk and lids change.https://surroundedbymath.com/money/how-long-to-pay-off-a-loan/https://surroundedbymath.com/money/how-long-to-pay-off-a-loan/Wed, 21 Oct 2026 00:00:00 GMTWork out how many months a loan takes to pay off with the loan-term formula, a calculator, worked examples and what extra payments change.https://surroundedbymath.com/money/how-us-income-tax-brackets-work/https://surroundedbymath.com/money/how-us-income-tax-brackets-work/Wed, 21 Oct 2026 00:00:00 GMTEach bracket taxes only the slice of income inside it. IRS 2026 and 2025 tables for every filing status, a $100,000 example and a calculator.https://surroundedbymath.com/daily-life/integrals-in-real-life/https://surroundedbymath.com/daily-life/integrals-in-real-life/Wed, 21 Oct 2026 00:00:00 GMTWhere integrals show up in real life: fuel burned, distance from speed, a race decided by area, net versus total travel. Each one worked out.https://surroundedbymath.com/money/loan-payment-formula/https://surroundedbymath.com/money/loan-payment-formula/Wed, 21 Oct 2026 00:00:00 GMTThe fixed monthly loan payment formula, a calculator, where it comes from, worked examples and common mistakes.https://surroundedbymath.com/health/maximum-heart-rate-formulas/https://surroundedbymath.com/health/maximum-heart-rate-formulas/Wed, 21 Oct 2026 00:00:00 GMTThe maximum heart rate formulas compared: 220 minus age, Tanaka, Gellish, Nes and Gulati, with population, error, an age table and worked example.https://surroundedbymath.com/core-ideas/optimization-with-derivatives/https://surroundedbymath.com/core-ideas/optimization-with-derivatives/Wed, 21 Oct 2026 00:00:00 GMTHow to solve optimization problems with derivatives: the steps, 4 worked examples with answers (fence, box, revenue, can), checks and common mistakes.https://surroundedbymath.com/money/rent-vs-buy-math/https://surroundedbymath.com/money/rent-vs-buy-math/Wed, 21 Oct 2026 00:00:00 GMTCompare renting and buying with one budget: payment formula, unrecoverable costs, break-even year, the 5%, 2% and 30% rules and a calculator.https://surroundedbymath.com/health/resting-metabolic-rate-formulas/https://surroundedbymath.com/health/resting-metabolic-rate-formulas/Wed, 21 Oct 2026 00:00:00 GMTThe resting metabolic rate formulas side by side: coefficients, who each was built on, worked example and how far they disagree and miss.https://surroundedbymath.com/money/retirement-savings-math/https://surroundedbymath.com/money/retirement-savings-math/Wed, 21 Oct 2026 00:00:00 GMTA retirement number is one division: yearly spending minus Social Security, over a withdrawal rate. Worked examples, 2026 limits and a calculator.https://surroundedbymath.com/money/rule-of-72/https://surroundedbymath.com/money/rule-of-72/Wed, 21 Oct 2026 00:00:00 GMTDivide 72 by the yearly rate to estimate how long money takes to double. The formula, worked examples, a calculator, an accuracy table and why 72.https://surroundedbymath.com/health/sleep-cycle-math/https://surroundedbymath.com/health/sleep-cycle-math/Wed, 21 Oct 2026 00:00:00 GMTSleep cycles average 90 minutes, so bedtime math is subtraction. See the formula, bedtime tables, a cosine model, and why cycles vary from 60 to 110 minutes.https://surroundedbymath.com/health/total-daily-energy-expenditure/https://surroundedbymath.com/health/total-daily-energy-expenditure/Wed, 21 Oct 2026 00:00:00 GMTTDEE is resting energy times an activity factor. The Mifflin-St Jeor step, five multipliers, a worked example, a calculator and how big the error is.https://surroundedbymath.com/core-ideas/what-is-a-derivative/https://surroundedbymath.com/core-ideas/what-is-a-derivative/Wed, 21 Oct 2026 00:00:00 GMTA derivative is the instantaneous rate of change of a function: the slope of its tangent line. Plain meaning, worked examples, notation and when it fails.https://surroundedbymath.com/core-ideas/what-is-a-limit/https://surroundedbymath.com/core-ideas/what-is-a-limit/Wed, 21 Oct 2026 00:00:00 GMTA limit is the value a function approaches as its input nears a point. Plain meaning, worked examples, when limits fail to exist, and the formal definition.https://surroundedbymath.com/core-ideas/what-is-an-integral/https://surroundedbymath.com/core-ideas/what-is-an-integral/Wed, 21 Oct 2026 00:00:00 GMTAn integral adds up a changing quantity: for a positive function it is the area under the curve. Plain meaning, worked examples, the Fundamental Theorem.https://surroundedbymath.com/daily-life/what-is-calculus-used-for/https://surroundedbymath.com/daily-life/what-is-calculus-used-for/Wed, 21 Oct 2026 00:00:00 GMTWhat calculus is used for in real life: speed, growth, profit, medicine and engineering, with worked examples, careers and where the ideas came from.https://surroundedbymath.com/world/what-is-pi/https://surroundedbymath.com/world/what-is-pi/Wed, 21 Oct 2026 00:00:00 GMTPi is a circle's circumference divided by its diameter, about 3.14. See the formulas, how many digits you need, what pi is used for, and its history.https://surroundedbymath.com/learning/why-math-education-struggles/https://surroundedbymath.com/learning/why-math-education-struggles/Wed, 21 Oct 2026 00:00:00 GMTU.S. math scores plateaued in 2013 and fell after 2019. See the NAEP, PISA and adult-skills numbers, what builds the gaps, and how math anxiety fits in.https://surroundedbymath.com/world/why-power-lines-use-high-voltage/https://surroundedbymath.com/world/why-power-lines-use-high-voltage/Wed, 21 Oct 2026 00:00:00 GMTHigh voltage means low current, and heat loss grows with the square of the current. Worked example, transformers, HVDC and underground cables explained.https://surroundedbymath.com/world/why-seasons-happen/https://surroundedbymath.com/world/why-seasons-happen/Wed, 21 Oct 2026 00:00:00 GMTEarth's 23.44 degree tilt causes the seasons, not distance from the Sun. See the sun-height math, daylight by latitude, and why the tilt slowly changes.