Latest news with #Pythagorean
New Statesman
6 hours ago
- Entertainment
- New Statesman
From Stephen King to Noah Eaton: new books reviewed in short
'I Humbly Beg Your Speedy Answer' edited by Mary Beth Norton The world's first personal advice column came about by accident. In early 1691, the Athenian Mercury was a new broadsheet that sought to provide talking points for coffeehouse patrons by answering assorted questions of the day. However, the three-man editorial team quickly started to receive queries of a more intimate nature from their subscribers and found that matters of marriage, lust and courtship interested their readers more than those on medicine, law and the military. This book, nimbly edited and introduced by the historian Mary Beth Norton, contains a broad selection of questions and answers, and plus ça change. 'It is my misfortune to be red-haired,' laments a correspondent with his eye on a woman with the 'greatest aversion' to the shade and asking for a method to turn his locks brown; 'I've a dreadful scold of a wife,' writes another, asking 'how to tame her'; if a man finds his fiancée in bed with another man, is he still duty-bound to marry her? We may now have Mumsnet and Reddit but, nevertheless, many of these three-centuries-old quandaries still come with a there-but-for-the-grace-of-God warning. By Michael Prodger Princeton University Press, 203pp, £20. Buy the book Never Flinch by Stephen King When it comes to reading books by the 'King of Horror' it's best to go in with an open mind and without assuming what will happen next – unless you want to be let down by your deducing skills. This rule clearly applies to King's latest book, Never Flinch. Though a standalone novel, it features a much-loved private investigator, Holly Gibney, and those associated with her investigation firm Finders Keepers. Although the reader is introduced to the murderer from the get-go, this by no means spoils the fun. You may think you know all there is to know, but King's mastery of withholding those final important pieces of information will have you working alongside Holly, perhaps not on unveiling the identity of the criminal, but on their motives. And let's not discard King's signature parallel plotlines which in the end collide to bring everything to light. With a killer on a revenge mission and a religious zealot targeting a celebrity feminist speaker, Never Flinch is not as graphic or as scary as King's previous novels. What makes the book unnerving and impossible to put down is how real and plausible everything described can be. By Zuzanna Lachendro Hodder & Stoughton, 429pp, £25. Buy the book A Perfect Harmony: Music, Mathematics and Science by David Darling 'Math and music are intimately related,' says composer and lyricist Stephen Sondeim. While to many music might seem remote from maths and science, their shared intricacies have been studied for centuries. We all recall Pythagoras' theorem (some more fondly than others), but what about Pythagorean tuning to create the interval of a perfect fifth? Though its mathematical precision fell out of favour by the end of the 15th century, Pythagorean tuning and its 'circle of fifths' remains at the heart of harmonic theory today. It comes as no surprise that many scientists were also musicians. A Perfect Harmony serves to solidify just how interlinked the fields are. From the Neanderthal bone instrument that mimics the musical scales we commonly use today, through musica universalis of the Middle Ages combining arithmetic, geography, music and astronomy, to the two Voyager spacecrafts' cosmic LPs, the disciplines co-exist in perfect harmony. Darling's observant musical odyssey across time reinforces that 'music and maths are endlessly entwined… nourishing one another' and have done so for millennia. After all, at its simplest music is melody and rhythm, and rhythm cannot exist without maths. By Zuzanna Lachendro Oneworld, 288pp, £10.99. Buy the book The Harrow by Noah Eaton The Harrow is a local newspaper – for Tottenham. Not, as its hardened editor John Salmon is sick of explaining, for Harrow: 'As in 'to harrow', to rake the land and drag out weeds, to distress the powerful. As in Christ harrowing Hell, saving the innocent and righteous. Not Harrow as in that miserable bloody town Harrow!' The paper, each issue announces, is 'the guardian of your democracy'. Subscribe to The New Statesman today from only £8.99 per month Subscribe The reality is not quite so grand. The coverage focuses on villains, not victims, because no one cares about the latter. Salmon keeps a shabby office and three staff above a betting shop and spends much of his time harassing off-licence proprietors who have tried to lower their order. But when the prospect of a last-gasp 'big story' heaves into view, Salmon and his team feel their hopes renewed. At well over 400 pages, The Harrow is on the weightier side for a thriller – and for a debut. But author Noah Eaton keeps the story ticking along at a pleasingly alacritous clip. Sometimes the world Eaton has built is told a little indulgently, but all told the story is complex, amusing and readable. By George Monaghan Atlantic Books, 389pp, £18.99. Buy the book Related
India.com
5 days ago
- General
- India.com
Weekly Numerology Horoscope For June 30 - July 6: Destiny Number 2- How This Week Will Turn In Terms Of Love, Finance, Health & More
In the mystical world of numerology, every number carries a unique vibration and symbolic meaning. Your Destiny Number, derived from the full name on your birth certificate, reveals your life's purpose, the opportunities and challenges you're destined to face, and the traits that will guide your path. Shweta Bhardwaj, numerologist and astrologer, Gaura AstroPredictions, brings her insightful weekly numerology predictions for June 30 - July 6, 2025. How To Calculate Your Destiny Number To find your Destiny Number, assign a numerical value to each letter of your full birth name using the Pythagorean system (A = 1, B = 2, ..., I = 9, J = 1 again, etc.), add all the numbers together, and reduce them to a single digit unless it's a Master Number (11, 22, or 33). Your final result is your Destiny Number. For example: Full name: John Smith J(1) + O(6) + H(8) + N(5) = 20 S(1) + M(4) + I(9) + T(2) + H(8) = 24 20 + 24 = 44 → 4 + 4 = 8 → Destiny Number = 8 Destiny Number 2 This week invites Numerology Number 2 individuals to embrace their natural diplomacy and intuition. You may find yourself playing the role of mediator or emotional anchor in personal and professional circles. It's a period of deep emotional sensitivity, but also one where your empathy becomes your superpower. Avoid overthinking and trust your inner calm to lead the way. Career & Finances Workplace dynamics could be slightly tense, but your tactful nature will be key in smoothing things over. Instead of pushing forward aggressively, adopt a cooperative and collaborative approach. Opportunities will arise through partnerships or teamwork. Financially, avoid big investments or loans this week — things are better handled with caution and consultation. Relationships & Love This is a significant week for emotional bonding. For those in relationships, deeper conversations will bring you closer — but be cautious not to internalize others' emotions too much. You're a great listener, but you also need to be heard. Singles may feel nostalgic or drawn to someone who mirrors their emotional depth. Health & Wellness Your emotional sensitivity may manifest physically if left unchecked. Prioritize your mental well-being — journaling, light yoga, or gentle walks can help. Try not to let the moods of others weigh you down. Pay attention to digestion and hydration, as stress may subtly affect your system this week. Lucky Days: Monday & Friday
India.com
5 days ago
- Business
- India.com
Weekly Numerology Horoscope For June 30 - July 6: Destiny Number 1- How This Week Will Turn In Terms Of Love, Finance, Health & More
In the mystical world of numerology, every number carries a unique vibration and symbolic meaning. Your Destiny Number, derived from the full name on your birth certificate, reveals your life's purpose, the opportunities and challenges you're destined to face, and the traits that will guide your path. Shweta Bhardwaj, numerologist and astrologer, Gaura AstroPredictions, brings her insightful weekly numerology predictions for June 30 - July 6, 2025. How To Calculate Your Destiny Number To find your Destiny Number, assign a numerical value to each letter of your full birth name using the Pythagorean system (A = 1, B = 2, ..., I = 9, J = 1 again, etc.), add all the numbers together, and reduce them to a single digit unless it's a Master Number (11, 22, or 33). Your final result is your Destiny Number. For example: Full name: John Smith J(1) + O(6) + H(8) + N(5) = 20 S(1) + M(4) + I(9) + T(2) + H(8) = 24 20 + 24 = 44 → 4 + 4 = 8 → Destiny Number = 8 Destiny Number 1 This week brings a dynamic mix of leadership challenges and personal growth for those governed by numerology number 1. As the natural trailblazer of the numerology chart, you may find yourself in situations that test your independence and demand decisive action. Stay grounded, as impulsive decisions could backfire. Balance confidence with patience. Career & Finances You're likely to be in the spotlight at work. This is an excellent time to take initiative or propose new ideas, especially early in the week. Your charisma will attract attention, but you'll need to back your confidence with preparation. If you're in business, consider reevaluating your strategy or delegating tasks you've been hoarding. Midweek brings financial clarity — a good time to plan budgets or address overdue payments. Relationships & Love In relationships, your assertive energy can either strengthen bonds or create tension, depending on how you channel it. Singles may find themselves attracting equally strong-willed personalities — sparks can fly, but compatibility will require mutual respect. If you're in a committed relationship, focus on listening more and leading less. A thoughtful gesture midweek can bring warmth and reconnection. Health & Wellness Your energy levels may fluctuate, especially if you push too hard without rest. While your natural drive can be a great motivator, don't ignore signs of mental fatigue. Schedule short breaks, meditate, or spend time outdoors. Physical activity will be beneficial, but avoid overexertion. Lucky Days: Tuesday & Saturday
Time of India
7 days ago
- Science
- Time of India
Trigonometry made easy: Solve complex math problems faster and score higher
Trigonometric identities might seem like abstract mathematical concepts, but they're actually powerful problem-solving tools that can transform seemingly impossible equations into manageable solutions. Whether you're tackling calculus problems or preparing for standardized tests, understanding these fundamental relationships will give you a significant advantage. Think of trigonometric identities as mathematical shortcuts – they reveal hidden connections between different trigonometric functions and provide smart ways to simplify complex expressions. Once you master these relationships, you'll wonder how you ever solved trigonometric problems without them. Three essential identity groups Before diving into strategies, it's crucial to understand the three foundational groups of trigonometric identities. These are the core relationships that connect different trig functions and enable powerful simplifications across a wide range of problems. Reciprocal identities Every trigonometric function has a reciprocal partner, and understanding these relationships is crucial for advanced problem-solving. The reciprocal identities show us that: sin θ = 1/csc θ (sine and cosecant are reciprocals) cos θ = 1/sec θ (cosine and secant are reciprocals) tan θ = 1/cot θ (tangent and cotangent are reciprocals) These relationships work both ways – if sine equals one over cosecant, then cosecant equals one over sine. by Taboola by Taboola Sponsored Links Sponsored Links Promoted Links Promoted Links You May Like Ein Arzt warnt: "Der Hauptgrund für einen dicken Bauch hat nichts mit Kalorien zu tun …" Mehr erfahren Undo This reciprocal nature becomes invaluable when you need to convert between different trigonometric functions or eliminate complex expressions from equations. Quotient identities Quotient identities reveal how tangent and cotangent relate to the fundamental sine and cosine functions: tan θ = sin θ/cos θ cot θ = cos θ/sin θ These identities are particularly useful because they allow you to express any trigonometric function in terms of sine and cosine – often the key to solving complex problems. Notice that cotangent is simply the reciprocal of tangent, which perfectly aligns with our reciprocal identities. Pythagorean identities Derived from the famous Pythagorean theorem, these identities represent some of the most powerful relationships in mathematics: sin² θ + cos² θ = 1 1 + tan² θ = sec² θ 1 + cot² θ = csc² θ The first identity is the foundation of trigonometry, representing the relationship between sine and cosine on the unit circle. The other two identities are derived by cleverly manipulating this fundamental relationship. 4 proven strategies for simplification success Understanding identities is only half the battle. To truly succeed in solving trigonometric problems, you need effective techniques to simplify expressions and equations. The following four strategies are widely used by top students and educators for quick, accurate results. Strategy 1: Convert everything to Sine and Cosine When faced with a complex trigonometric expression, your first move should be converting all functions to sine and cosine. This approach works because sine and cosine are the building blocks of all other trigonometric functions. For example, to simplify tan θ · csc θ, convert both functions: (sin θ/cos θ) · (1/sin θ) = 1/cos θ = sec θ. The sine terms cancel out, leaving a clean, simplified result. Strategy 2: Hunt for Pythagorean patterns Whenever you spot expressions like sin² θ + cos² θ or 1 + tan² θ, immediately think of Pythagorean identities. These patterns often hide in complex expressions, waiting to be discovered and simplified. The key is recognizing that these relationships can substitute entire expressions with single terms, dramatically simplifying your work. Strategy 3: Factor like a pro Trigonometric expressions follow the same algebraic rules as regular polynomials. Look for opportunities to factor out common terms, apply differences of squares, or identify perfect square patterns. For instance, sin θ cos θ + sin θ can be factored as sin θ(cos θ + 1), making further simplification possible. Strategy 4: Use the conjugate technique When dealing with expressions containing terms like (1 - sin θ), multiplying by the conjugate (1 + sin θ) often reveals simplification opportunities. This technique frequently converts complex fractions into recognizable Pythagorean patterns. Why these identities matter beyond the classroom Trigonometric identities aren't just academic exercises – they're essential tools in engineering, physics, and computer science. Engineers use them to analyze wave patterns and electrical circuits. Physicists apply them to understand oscillations and rotational motion. Computer graphics programmers rely on them to create realistic animations and 3D models. Understanding these identities develops critical thinking skills and pattern recognition abilities that extend far beyond mathematics. They teach you to see hidden relationships and find elegant solutions to complex problems. Success with trigonometric identities comes from understanding rather than memorization. Start with the fundamental relationships, then practice recognizing patterns in various expressions. Focus on understanding why these identities work, not just how to use them. Is your child ready for the careers of tomorrow? Enroll now and take advantage of our early bird offer! Spaces are limited.
Chicago Tribune
23-06-2025
- Science
- Chicago Tribune
Oak Lawn students' numbers line up for new football stadium ticket booth
Students at Oak Lawn Community High School got hooked on construction, incorporating what they learned in geometry classes to create new structures and other items around campus. Their latest undertaking is a ticket booth for the school's football field. They did all the work with a little help from teachers Sara Strelow, who teaches geometry, and Kyle Kowalski, a career technology educator. The students previously had created a shed, so for the ticket booth, teachers modified the plans to add windows, and graphic design students will be recruited to design the door. 'Students were up on the roof doing electrical, painting. It's all basic fundamentals, Kowalski said. But it's definitely a case of learning by doing. 'You've got to be okay screwing up.' Part of what's made the class work, according to the two teachers, is the students' motivation. 'They always do their stuff,' said Strelow. 'In other classes, it's like pulling teeth.' 'They outperformed my regular geometry class on every assessment,' said Strelow. The two-period class starts each session in Strelow's classroom, where students work on the math needed to construct the projects. Then they move into Kowalski's workshop or even outside.' Math lessons sometimes include the Pythagorean theorem with its A squared plus B squared equals C squared to help calculate angles for roofing, as well as volume and surface areas. Kowalski said they also incorporated artificial intelligence into the process to calculate the costs of building materials. Some of the actual construction took place at the football field. 'The school allowed us to purchase battery powered tools so they can be moveable,' Kowalski said. The class had its beginnings three years ago when math chair Chris Newton and the two teachers traveled to a conference in St. Paul, Minnesota where the idea was presented. Then they adapted it to OLCHS, after spending a year on the planning. Math isn't Kowalski's thing, nor is construction Strelow's, and the two have completely different personalities. Kowalski is spontaneous and Strelow says she's very 'Type A and plans everything.' But the two make it work. Kowalski said he brings ideas to Strelow and she may put it into a document to try. 'We're both willing to give up what we're used to and try something different,' said Strelow. Kowalski said he's even taught a few of the math lessons and has taken tests with the students as a way of showing he's part of the team. 'They kind of enjoy watching that,' he said. 'They sometimes beat me.' They also learned to collaborate as a way to bring out the best in students and help them succeed. Students get a small electrical unit in his class and also learn about drywall and plumbing. They've made saw horses and a miniature golf course. The teachers are hoping to get industry professionals to speak to the students, host events and offer financial support. There were 22 students in the class, including eight females. But the class is a popular one and enrollment has increased each year. Once the new field house is complete, the two said they'll be able to move their space to one of the gyms. The class appears to be bringing out the best in many students, even the ones who aren't pros at math or construction, according to their teachers. 'They're all different, from AP honors, regular and even remedial,' said Strelow. 'It's interesting to see the kids you thought were going to struggle, flourish.'
