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ðŸ’ĄThe first happiness equation. 😍

Happiness happens more easily. If...

✅ expect less things.

✅ more accepting of the reality.

Many times, we do the opposite.

❌ expect things to go the way we want.

❌ don't accept the reality that it happened.

When those things don't go as expected,

Suffering is common.

If friends are looking for simple happiness,

Try to apply this simple happiness equation.

Thank you for the good idea of HOME RUN.

Author: Mr. Jothna Thien, Genius

Publisher: KOOB

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# Books # Psychology # Develop yourself # Read books # Book review

2025/10/31 Edited to

... Read moreāļ„āļ§āļēāļĄāļŠāļļāļ‚āđ€āļ›āđ‡āļ™āđ€āļĢāļ·āđˆāļ­āļ‡āļ—āļĩāđˆāļ—āļļāļāļ„āļ™āđ‚āļŦāļĒāļŦāļēāđāļĨāļ°āđƒāļāđˆāļāļąāļ™āļ—āļĩāđˆāļˆāļ°āļĄāļĩāđƒāļ™āļŠāļĩāļ§āļīāļ•āļ›āļĢāļ°āļˆāļģāļ§āļąāļ™ āđāļ•āđˆāļŦāļĨāļēāļĒāļ„āļĢāļąāđ‰āļ‡āļ„āļ§āļēāļĄāļŠāļļāļ‚āļāļĨāļąāļšāđ„āļĄāđˆāđ„āļ”āđ‰āļĄāļēāļ‡āđˆāļēāļĒāļ­āļĒāđˆāļēāļ‡āļ—āļĩāđˆāļ„āļīāļ” āđ€āļžāļĢāļēāļ°āđ€āļĢāļēāļĄāļąāļāļˆāļ°āļ•āļąāđ‰āļ‡āļ„āļ§āļēāļĄāļ„āļēāļ”āļŦāļ§āļąāļ‡āļŠāļđāļ‡āđ€āļāļīāļ™āđ„āļ› āļŦāļĢāļ·āļ­āđ„āļĄāđˆāļĒāļ­āļĄāļĢāļąāļšāļ„āļ§āļēāļĄāđ€āļ›āđ‡āļ™āļˆāļĢāļīāļ‡āļ—āļĩāđˆāđ€āļāļīāļ”āļ‚āļķāđ‰āļ™āļ‹āļķāđˆāļ‡āļ­āļēāļˆāđāļ•āļāļ•āđˆāļēāļ‡āļˆāļēāļāļ—āļĩāđˆāļ•āđ‰āļ­āļ‡āļāļēāļĢ āļāļēāļĢāļĨāļ”āļ„āļ§āļēāļĄāļ„āļēāļ”āļŦāļ§āļąāļ‡āļāļąāļšāļŠāļīāđˆāļ‡āļ•āđˆāļēāļ‡āđ† āļ—āļĩāđˆāđ€āļāļīāļ”āļ‚āļķāđ‰āļ™āđƒāļ™āļŠāļĩāļ§āļīāļ•āļˆāļķāļ‡āđ€āļ›āđ‡āļ™āļ§āļīāļ˜āļĩāļŦāļ™āļķāđˆāļ‡āļ—āļĩāđˆāļˆāļ°āļŠāđˆāļ§āļĒāđƒāļŦāđ‰āđ€āļāļīāļ”āļ„āļ§āļēāļĄāļŠāļļāļ‚āđ„āļ”āđ‰āļ‡āđˆāļēāļĒāļ‚āļķāđ‰āļ™ āļāļēāļĢāļ•āļąāđ‰āļ‡āļ„āļ§āļēāļĄāļ„āļēāļ”āļŦāļ§āļąāļ‡āļ—āļĩāđˆāļ™āđ‰āļ­āļĒāļĨāļ‡āđ„āļĄāđˆāđ„āļ”āđ‰āļŦāļĄāļēāļĒāļ„āļ§āļēāļĄāļ§āđˆāļēāđ€āļĢāļēāļ•āđ‰āļ­āļ‡āļŦāļĒāļļāļ”āļ„āļ§āļēāļĄāļŦāļ§āļąāļ‡āļŦāļĢāļ·āļ­āļ„āļ§āļēāļĄāļāļąāļ™ āđāļ•āđˆāđ€āļ›āđ‡āļ™āļāļēāļĢāļ›āļĢāļąāļšāđƒāļˆāđƒāļŦāđ‰āļŠāļēāļĄāļēāļĢāļ–āļĒāļ­āļĄāļĢāļąāļšāļŠāļ–āļēāļ™āļāļēāļĢāļ“āđŒāđƒāļ™āļ›āļąāļˆāļˆāļļāļšāļąāļ™āđ„āļ”āđ‰āļĄāļēāļāļ‚āļķāđ‰āļ™ āđ€āļŠāđˆāļ™ āļ–āđ‰āļēāđ€āļĢāļēāđ€āļˆāļ­āđ€āļŦāļ•āļļāļāļēāļĢāļ“āđŒāļ—āļĩāđˆāđ„āļĄāđˆāđ€āļ›āđ‡āļ™āđ„āļ›āļ•āļēāļĄāļ—āļĩāđˆāļŦāļ§āļąāļ‡ āđ€āļĢāļēāļˆāļ°āđ„āļĄāđˆāļĢāļđāđ‰āļŠāļķāļāļœāļīāļ”āļŦāļ§āļąāļ‡āļŦāļĢāļ·āļ­āļ—āļļāļāļ‚āđŒāđƒāļˆāļĄāļēāļāđ€āļāļīāļ™āđ„āļ› āđ€āļžāļĢāļēāļ°āđ€āļĢāļēāļ•āļąāđ‰āļ‡āđƒāļˆāđ„āļ§āđ‰āđāļĨāđ‰āļ§āļ§āđˆāļēāļŠāļīāđˆāļ‡āđ€āļŦāļĨāđˆāļēāļ™āļĩāđ‰āļ­āļēāļˆāđ€āļāļīāļ”āļ‚āļķāđ‰āļ™āđ„āļ”āđ‰ āļ™āļ­āļāļˆāļēāļāļ™āļĩāđ‰āļāļēāļĢāļĒāļ­āļĄāļĢāļąāļšāļ„āļ§āļēāļĄāļˆāļĢāļīāļ‡āđƒāļ™āļŠāļīāđˆāļ‡āļ—āļĩāđˆāđ€āļāļīāļ”āļ‚āļķāđ‰āļ™āļ­āļĒāđˆāļēāļ‡āđ€āļ•āđ‡āļĄāđƒāļˆ āđ€āļ›āđ‡āļ™āļ­āļĩāļāļāļļāļāđāļˆāļŠāļģāļ„āļąāļāļ—āļĩāđˆāļŠāđˆāļ§āļĒāļĨāļ”āļ„āļ§āļēāļĄāļ—āļļāļāļ‚āđŒāđāļĨāļ°āđ€āļ›āļīāļ”āđ‚āļ­āļāļēāļŠāđƒāļŦāđ‰āđ€āļĢāļēāđ€āļŦāđ‡āļ™āļ—āļēāļ‡āđ€āļĨāļ·āļ­āļāđƒāļŦāļĄāđˆāđ† āļŦāļĢāļ·āļ­āļĄāļļāļĄāļĄāļ­āļ‡āđƒāļŦāļĄāđˆāđ† āļ—āļĩāđˆāļ­āļēāļˆāļŠāđˆāļ§āļĒāđƒāļŦāđ‰āļŠāļĩāļ§āļīāļ•āļ”āļĩāļ‚āļķāđ‰āļ™ āđ‚āļ”āļĒāđ„āļĄāđˆāļĒāļķāļ”āļ•āļīāļ”āļāļąāļšāļŠāļīāđˆāļ‡āļ—āļĩāđˆāđ„āļĄāđˆāļŠāļēāļĄāļēāļĢāļ–āđ€āļ›āļĨāļĩāđˆāļĒāļ™āđāļ›āļĨāļ‡āđ„āļ”āđ‰ āļŦāļ™āļąāļ‡āļŠāļ·āļ­ HOME RUN āđ‚āļ”āļĒāļ„āļļāļ“āđ‚āļˆāđ‰ āļ˜āļ™āļē āđ€āļ˜āļĩāļĒāļĢāļ­āļąāļˆāļ‰āļĢāļīāļĒāļ° āđ„āļ”āđ‰āļĢāļ§āļšāļĢāļ§āļĄāļ„āļ§āļēāļĄāļ„āļīāļ”āđāļĨāļ°āđāļ™āļ§āļ—āļēāļ‡āļ—āļĩāđˆāļŠāđˆāļ§āļĒāđƒāļŦāđ‰āļ„āļ™āđ€āļĢāļēāđ€āļ‚āđ‰āļēāđƒāļˆāļ•āļ™āđ€āļ­āļ‡āđāļĨāļ°āļžāļąāļ’āļ™āļēāļ„āļ§āļēāļĄāļŠāļļāļ‚āđ„āļ”āđ‰āļ‡āđˆāļēāļĒāļ‚āļķāđ‰āļ™ āļœāđˆāļēāļ™āļāļēāļĢāļ›āļĢāļąāļšāđ€āļ›āļĨāļĩāđˆāļĒāļ™āļ—āļąāļĻāļ™āļ„āļ•āļīāđāļĨāļ°āļ§āļīāļ˜āļĩāļ„āļīāļ”āļ—āļĩāđˆāđ€āļŦāļĄāļēāļ°āļŠāļĄāļāļąāļšāđ‚āļĨāļāļ›āļąāļˆāļˆāļļāļšāļąāļ™ āļāļēāļĢāļ™āļģāļŠāļĄāļāļēāļĢāļ„āļ§āļēāļĄāļŠāļļāļ‚āļ‚āđ‰āļ­āļ—āļĩāđˆāļŦāļ™āļķāđˆāļ‡āļ™āļĩāđ‰āđ„āļ›āđƒāļŠāđ‰āđƒāļ™āļŠāļĩāļ§āļīāļ•āļˆāļĢāļīāļ‡ āļ­āļēāļˆāđ€āļĢāļīāđˆāļĄāļˆāļēāļāļāļēāļĢāļŠāļąāļ‡āđ€āļāļ•āđāļĨāļ°āļĢāļąāļšāļĢāļđāđ‰āļ„āļ§āļēāļĄāļ„āļēāļ”āļŦāļ§āļąāļ‡āļ—āļĩāđˆāđ€āļĢāļēāļĄāļĩāđƒāļ™āđāļ•āđˆāļĨāļ°āļ§āļąāļ™ āđāļĨāļ°āļĨāļ­āļ‡āļ›āļĢāļąāļšāļĨāļ”āļĨāļ‡āļ—āļĩāļĨāļ°āļ™āđ‰āļ­āļĒ āļžāļĢāđ‰āļ­āļĄāļāļąāļšāļāļķāļāļĒāļ­āļĄāļĢāļąāļšāļŠāļīāđˆāļ‡āļ—āļĩāđˆāđ€āļāļīāļ”āļ‚āļķāđ‰āļ™āđ‚āļ”āļĒāđ„āļĄāđˆāļ•āļąāļ”āļŠāļīāļ™āļŦāļĢāļ·āļ­āļ›āļāļīāđ€āļŠāļ˜ āļ‹āļķāđˆāļ‡āļāļēāļĢāļāļķāļāļāļ™āđāļšāļšāļ™āļĩāđ‰āļŠāđˆāļ§āļĒāļ—āļģāđƒāļŦāđ‰āđ€āļĢāļēāļĄāļĩāļ„āļ§āļēāļĄāļŠāļļāļ‚āđ„āļ”āđ‰āļ­āļĒāđˆāļēāļ‡āļĒāļąāđˆāļ‡āļĒāļ·āļ™āđāļĨāļ°āļŠāļĄāļ”āļļāļĨ āļŠāļļāļ”āļ—āđ‰āļēāļĒāļ™āļĩāđ‰ āļāļēāļĢāđ€āļ›āļīāļ”āđƒāļˆāđ€āļĢāļĩāļĒāļ™āļĢāļđāđ‰āđāļĨāļ°āļ—āļ”āļĨāļ­āļ‡āđƒāļŠāđ‰āļŠāļĄāļāļēāļĢāļ„āļ§āļēāļĄāļŠāļļāļ‚āļ™āļĩāđ‰āļˆāļ°āļ—āļģāđƒāļŦāđ‰āđ€āļĢāļēāļĢāļąāļšāļĄāļ·āļ­āļāļąāļšāļŠāļ–āļēāļ™āļāļēāļĢāļ“āđŒāļ•āđˆāļēāļ‡āđ† āđ„āļ”āđ‰āļ”āļĩāļ‚āļķāđ‰āļ™ āđāļĨāļ°āļžāļēāđ€āļĢāļēāđ„āļ›āļŠāļđāđˆāļŠāļĩāļ§āļīāļ•āļ—āļĩāđˆāļĄāļĩāļ„āļ§āļēāļĄāļŠāļļāļ‚āļ‡āđˆāļēāļĒāļāļ§āđˆāļēāđ€āļ”āļīāļĄāļ­āļĒāđˆāļēāļ‡āđāļ—āđ‰āļˆāļĢāļīāļ‡

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Feel & Look ðŸ”ĨHOTðŸ”Ĩ By Summer: (It’s 4 Weeks Away)👙☀ïļ
Example 4-Week âœĻWeight lifting/ GymâœĻ Plan Weekly Structure: Day 1: Glutes + Cardio Day 2: Upper Body + Cardio Day 3: Legs + Cardio Day 4: Upper Body + Cardio Day 5: Glutes + Cardio Day 6: Cardio/Running/HIIT Day 7: Active Recovery Repeat every week, repeated every month âĪïļ â€”â€”â€”â€”â€”â€”â€”
Chalie_Baker

Chalie_Baker

1344 likes

Handwritten math notes show a geometric proof involving a triangle, its incircle, and incenter. The derivation uses formulas for IA, IB, and inradius 'r' to establish the relationship IA · IB = IC · AB, as stated in the article.
AB × CI = AI × BI, part 3
This proof starts with the relations of IA and IB, where I is the incenter of the right triangle, and uses algebraic manipulation to get AB × IC. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

15 likes

A hand holds the book "The Psychology of Money" by Morgan Housel, a Barnes & Noble exclusive edition with a bonus chapter. The cover features a brain made of dollar bills, with a bookshelf and a blurred person in the background.
The Psychology of Money 💰
1 Month of Reading 📖 Summarized in a 5 Minute Summary Title & Author: The Psychology of Money — Morgan Housel * Core Theme: Financial success is driven more by behavior, emotions, patience, and psychology than intelligence or technical knowledge. * Problem It Solves: Why smart people
Steven Bou

Steven Bou

68 likes

A study desk with a laptop, open books, and notes, featuring the text overlay "You're studying Too much," suggesting a need for balanced study habits.
A handwritten outlining guide showing main topics, sub-topics, and details, with the text overlay "organizes information in a logical and structured way."
A digital Pomodoro timer set to 25:00 with a start button and task list, featuring the text overlay "take breaks" to encourage time management.
🛑 studying!
Kiddingâ€Ķdon’t stop studying. Just maybe stop the 12 hour, excessive highlighting cram sessions. These are my tips on how I actually started learning the information I was reading, saw my grades improved, and noticed I was overall less stressed about school! This semester is my first time “in
s h e l b y ˙áĩ•Ë™

s h e l b y ˙áĩ•Ë™

205 likes

6 Rich things people won’t tell you
Let’s pull back the curtain, sis. Wealthy people know some things they don’t like to share, but I’ve got you. Here’s what they won’t tell you: 1ïļâƒĢ Time is more valuable than money. They don’t waste it on distractions. Every hour is intentional. 2ïļâƒĢ Networking > everything. Who you know
CEO of Rich Girl Energy âœĻ

CEO of Rich Girl Energy âœĻ

348 likes

The Gates I am careful about in 2024
As believers, we are called to be vigilant and intentional about what we allow into our lives. In today's digital age, where information and influences surround us, it is crucial to be mindful of the three gates that can shape our thoughts, words, and actions: the Eye gate, the Mouth gate, and
🎀Solange🎀

🎀Solange🎀

548 likes

What I wish someone showed me before my first Hesi exam.
I cant say these exact questions will be on your exam, but I also cant say they wont What you do with that information is up to you. Message me for details on my HESI study materials and support services. #hesientranceexam hesientranceexam #hesia2 #hesitest #examtips #studyguide
Nurse Terry

Nurse Terry

2 likes

How I keep Myself TONED 🍑160+ Protein 🍑 Fasting
🍋The ideal calorie deficit for effective weight loss: A tried-and-true guideline from experts suggests aiming for a deficit of approximately 500 calories per day. 🍋This balanced approach typically results in shedding around 1-2 pound per week, setting you on the path to your desired goals. 🍋
Chalie_Baker

Chalie_Baker

318 likes

How to ðŸ”ĨToneðŸ”Ĩ Your Way to a âœĻSleeker Silhouette!âœĻ🍋
Achieving a slim and toned upper body while also developing strong, defined abs is a common goal for many women. The key to reaching this goal lies in a balanced approach that combines cardiovascular exercise, strength training, proper nutrition, and lifestyle adjustments. Here’s my guide to he
Chalie_Baker

Chalie_Baker

346 likes

A plate with a chicken croissant sandwich, watermelon slices, baby carrots, hummus, tortilla chips, and almonds, alongside a glass of water. Overlay text reads "LOSE WEIGHT WHILE EATING Get control over your diet" with "Lemon8" and "@chalie_baker" at the bottom.
A white page with text titled "1. Understanding Macronutrients: The Foundation of Your Diet," detailing the role of carbohydrates as the primary energy source, with tips and examples for healthy swaps. The Lemon8 logo is faintly visible at the bottom.
A white page with text describing proteins as building blocks for muscle repair and satiety, with tips and examples. It also covers fats as essential for hormones and absorption, providing tips and healthy swap examples. The Lemon8 logo is faintly visible at the bottom.
Eat Better, Not Less: The 🔑 to Lasting Weight Loss
Weight loss doesn’t mean deprivation or constant hunger—it’s about understanding how to nourish your body while maintaining a calorie deficit. This guide will provide an in-depth look at the roles of macronutrients, portion control, meal timing, calorie management, healthy food swaps, and the s
Chalie_Baker

Chalie_Baker

225 likes

Right triangle relations based on similarity
In any right triangle, dropping the lone altitude (the only one that crosses the interior of the triangle) produces many relations including the Pythagorean Theorem and the Reciprocal Pythagorean Theorem. One of my favorite formulae from geometry that the distance of the lone altitude can be found
cubicequation

cubicequation

36 likes

The image illustrates solving quadratic equations by factoring. It shows the general form XÂē+bx+C=0, its factored form (X-r)(X-s)=0, and an example XÂē-5x+6=0. The example shows (X+3)(X+2)=0 leading to X=-3 or X=-2, alongside an X-factor diagram and verification calculations.
solving quadratic equation using factor ðŸŦķ
#math #mathnotes #lemon8edu
candy

candy

44 likes

The image displays the mathematical derivation of the Quarter Squares Rule, showing how the difference of two quarter squares, ((a+b)/2)^2 - ((a-b)/2)^2, simplifies to the product ab for real numbers a and b. The final formula is highlighted.
Quarter Squares Rule
Given two real numbers a, b such that a > b, then then the difference of squares will equal the product of the two numbers. This formula was used for centuries to calculate large products. #math #maths #mathematics #algebra #arithmetic
cubicequation

cubicequation

12 likes

A hand-drawn diagram of a triangle with an inscribed circle, illustrating the inradius 'r' and deriving the formula for the area of a triangle (Δ = rs) using the semi-perimeter 's' and side lengths a, b, c.
The incircle, inradius and equating area formulae
The area of a triangle can be found using the inradius. Using Heron’s formula, one can find the length of the circumradius and the inradius using just the side lengths of the triangle. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

10 likes

BOOKS I WISH I COULD READ FOR THE FIRST TIME AGAIN
Do you ever just think about books you’ve read before and wish you could read them for the first time again? I think about these books ALL the time and wish I could get the feeling of when I first read them ðŸĨē 𝙏𝙝𝙚 𝙇𝙞ð™Ļð™Đ: 💌 Love & Other Words by Christina Lauren ðŸ—Ąïļ Throne of Glass by Sarah J.
cam !!

cam !!

17 likes

A handwritten page showing mathematical formulas for triangle area and sine ratios. It includes Heron's formula, area formulas using sine, and derivations for sin A, sin B, sin C, and csc A, csc B, csc C in terms of the triangle's sides and semi-perimeter.
Sine ratios in terms of the triangle’s sides
In any oblique triangle, the sine ratios can be found in terms of the sides using the given formulae. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

3 likes

A handwritten page details trigonometric relations for a regular pentagon, using side 'a', diagonal 'b', and circumradius 'R'. It presents derivations and results for various sums and products of trigonometric functions (tan, sec, csc, cot) involving angles π/5 and 2π/5, such as 10 = tanÂē(π/5) + tanÂē(2π/5).
Trigonometric relations in the regular pentagon
In the regular pentagon, a = side length, b = length of the diagonal & R = length of the circumradius. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

49 likes

A handwritten mathematical derivation on lined paper showing the distance between the orthocenter (O) and circumcenter (P) of a triangle. It uses the property aÂē+bÂē+cÂē=7RÂē to simplify Euler's theorem, concluding that OP = R√2 for a heptagonal triangle.
Simplifying the distance between two points in the heptagonal triangle
In a prior post, I derived the distance formula between the orthocenter and the circumcenter using a complicated argument involving similar triangles. In this post, I used a simple formula to get the required answer. #math #maths #maths #geometry #trigonometry
cubicequation

cubicequation

11 likes

A woman in pink athletic wear and headphones poses in a gym, showcasing her hamstrings. Text overlay reads "3 EXERCISES FOR HAMSTRING GROWTH" and "Peach Gym". An arrow points to her hamstring.
A woman in pink athletic wear performs sumo squats with a barbell in a gym. Text overlay reads "1. sumo squats". The gym features pink walls and black equipment.
A woman in pink athletic wear performs hip thrusts with a barbell, using a bench in a gym. Text overlay reads "2. hip thrusts" and "Big Peach Gym".
the hamstring equation i swear byðŸ’ŠðŸ―
i LOVE a good hamstring pump! i’ve been working hard the past few years to grow them and i finally see it paying off! a few of my current favorites include: - sumo squats (landmine, smith machine, dumbell) - hip thrusts (landmine, smith machine, barbell, hip thrust machine) - single leg h
healthlifemorgan

healthlifemorgan

47 likes

The Let Them Theory
this book, a must read !! #letthem #book
Daniela Morando

Daniela Morando

14 likes

A handwritten mathematical proof on lined paper, showing a right triangle with an inscribed circle and its incenter. The derivation leads to the formula IC â€Ē IB = (AB - AC) â€Ē IA, demonstrating a relationship between segments connected to the incenter.
IC × IB = (AB - AC) × IA, part 1
In a right triangle, there is an interesting relationship between the segments that connect from the vertices to the incenter (labeled I). The product of the distances of the two shorter segments is equal two the distance of the longest segment multiplied by a factor that itself is the difference b
cubicequation

cubicequation

11 likes

A handwritten mathematical derivation of the sine double angle identity, sin B = 2 sin(B/2) cos(B/2), on grid paper. It features a right-angled triangle with labeled sides and angles, using geometric principles and algebraic steps to reach the final boxed identity.
Sine double angle identity derivation
Using established facts like the angle bisector theorem and the Pythagorean theorem, one can derive the sine double angle identity. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

19 likes

Proof of the First Mollweide Formula
#math #maths #mathematics #trig #trigonometry
cubicequation

cubicequation

9 likes

A handwritten math proof on lined paper shows a triangle with its altitudes intersecting at the orthocenter. Ceva's Theorem is applied using trigonometric expressions for segment lengths, demonstrating that the product equals one, thus proving the concurrency of altitudes.
Proving orthocenter concurrency
The orthocenter is where the altitudes of a triangle are concurrent. This fact is proven with Ceva’s theorem. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

9 likes

A handwritten page illustrates Garfield's Proof of the Pythagorean Theorem. It features a geometric diagram of a trapezoid formed by three right triangles, alongside algebraic steps that equate the trapezoid's area to the sum of the triangles' areas, leading to the derivation of aÂē + bÂē = cÂē.
Proof of the Pythagorean Theorem, part 2
This is an augmented version of the first proof discovered by US President James Garfield. By slicing the original diagram in half, a trapezoid is created with three right triangles overlaying it so an equating of areas can occur. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

6 likes

A handwritten page displays a triangle diagram with an inscribed circle and its incenter. It illustrates the derivation of the inradius (IA) using the triangle's area formula and side lengths (a, b, c, and semi-perimeter s), concluding with the formula IA = sqrt(bc(s-a)/s).
Six half-angle trig identities in terms of sides
In an oblique triangle, the six trigonometric ratios of the half-angles can be written in terms of the sides. The half-angles appear because the angle bisectors meet at the incenter of the triangle. These specific identities are solved for angle A, which is typically the angle of smallest measure.
cubicequation

cubicequation

11 likes

A motivational text graphic titled 'YOU CAN'T POUR FROM AN EMPTY CUP' on a light gray background. The text, by @dia.seltenreich, emphasizes the importance of self-love and acceptance as a prerequisite for giving to others, highlighting that you must fill your own cup first.
Fill Your Cup First 🔑â„đïļðŸ‘‡
You can’t pour from an empty cup. You can give your time, your energy, your love—but only if you’ve filled yourself first. The world will take as much as you’re willing to give, but when you’re running on empty, you give less than what you’re capable of. You’ve got to refill to overflow. Don’t m
RoadToRiches

RoadToRiches

6 likes

A handwritten planner with daily tasks, overlaid with text asking "why everyone quits their NEW YEARS RESOLUTIONS & how to avoid quitting yours!".
A laptop on a couch with text listing reasons people quit New Year's resolutions: Lack of Clear Goals, Unrealistic Expectations, All or Nothing Mindset, Lack of Strong "Why", Poor Planning, No Support System, and Misunderstand Habit Formation.
A shelf with books and plants, featuring text advising to "SET SPECIFIC GOALS" by making resolutions measurable and time-bound, with examples like saving money or waking up early.
these 7 things will kill your resolutions ☠ïļ
did you know that 80% of people abandon their new years goals by the first week of february? setting goals is a science - and a lot of us just haven’t found the equation yet! these are the top 7 resolution killers ☠ïļâĪĩïļ 1ïļâƒĢ LACK OF CLEAR GOALS vague resolutions like "get healthy" or
carley â—ĄĖˆ

carley â—ĄĖˆ

142 likes

A handwritten mathematical proof on lined paper, showing a right-angled triangle ABC with its incircle and inradius 'r'. The proof uses the semiperimeter 's' and algebraic steps to derive the identity IB * IC = (AB - AC) * IA, relating segments from the incenter to the vertices.
IC × IB = (AB - AC) × IA, part 2
This proof starts with an identity about the inradius of the right triangle and an identity about a segment connecting the incenter to the medium-sized angle. This proof seems more natural given that the semiperimeter is used more with oblique triangles than right triangles. #math #maths #m
cubicequation

cubicequation

9 likes

A light gray image features the phrase 'Soft Girl' in pink, with the message 'You have to add prayers into that grind. Your hustle means nothing without God.' in black. 'Spiritual Awareness' is in yellow, with 'Lemon8' and '@mochamonroe' at the bottom, surrounded by decorative hearts and flowers.
Spiritual Awareness
Hustle is just hustle if you’re not adding GOD to the equation! #godfirst #hustle #Lemon8 #lemon8lifecoach #hellolemon8 #blackgirllemon8 #foryou #foryoupage #explore #faith
Mocha Monroe

Mocha Monroe

11 likes

How I gain weight (and maintain it)
First thing I’d like to point out, is that there are a bunch of way to ‘gain’ weight, but not all of them are healthy and I don’t recommend hitting the local McDonald’s and stuffing your face with as many calories as possible. You want to up your calories, yes, but you also want to make sure the ca
Jazmine Lopez

Jazmine Lopez

20 likes

(r+s)/(a+b) + h/c = 1
Another relation valid in any right triangle. It’s proven using the concept of similar triangles. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

5 likes

A handwritten math solution on lined paper, featuring a triangle diagram with orthocenter (O) and circumcenter (P) labeled. It derives the formula for the squared distance between them, dÂē = 9RÂē - (aÂē+bÂē+cÂē), using trigonometric identities and cosine rules.
The distance between the orthocenter and the circumcenter of a triangle
In any acute triangle, the distance between the orthocenter and the circumcenter is found with quite a nice formula that relate the sides and the circumradius. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

8 likes

A handwritten mathematical proof on lined paper demonstrates that any number of the form 4n+3 cannot be expressed as the sum of two squares. It uses modular arithmetic to analyze the possible remainders of squares (even, odd, or mixed) when divided by 4.
Any number of the form 4n+3 cannot be expressed as the sum of two squares.
This is a fact that comes from elementary number theory. If you have a number that has a remainder of 3 when divided by 4, it can’t be written as a sum of two square numbers. Numbers like 7, 11, 15 etc. can’t be written in that form.
cubicequation

cubicequation

3 likes

A handwritten page showing a geometric proof of Ceva's Theorem. It features a triangle ABC with cevians AX, BY, CZ intersecting at point P, along with auxiliary lines. Below the diagram are mathematical steps using similar triangles to derive the theorem's formula.
Proving Ceva’s theorem
Ceva’s theorem is used to prove the concurrency of segments (aka cevians) that come off the vertices and intersect with the opposite side. This proof uses similar triangles to prove the validity of the theorem. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

14 likes

A handwritten page showing the initial steps of deriving Heron's formula. It includes a triangle with its circumcircle, the formula for the circumradius R, cosine rules, and the derivation of partial areas (Δa, Δb, Δc) using R and trigonometric identities.
Deriving Heron’s formula using the circumradius of the triangle
Heron’s formula is a useful formula to find the area of a triangle using only the triangle’s side lengths. This is a lesser-known derivation of the formula, but quite a cool one nonetheless. #math #maths #mathemati cs #geometry #trigonometry
cubicequation

cubicequation

8 likes

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