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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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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 mathematical derivation of the trigonometric identity cos(A+B) = cos A cos B - sin A sin B. The derivation uses a triangle diagram, area formulas, and various trigonometric substitutions, progressing step-by-step to the final identity.
cosA × cos B - sin A × sin B = cos(A+B)
This is an obscure derivation of a well-known trigonometric identity. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

5 likes

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

cubicequation

9 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

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

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 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 person in workout attire stands next to text stating "CARBS DON'T MAKE YOU FAT!". Surrounding them are images of Fairlife chocolate milk, pasta with broccoli, bread, white rice, avocado, and ice cream, illustrating various food types.
A graphic titled "What Should I Eat? Foods with High Quality Carbs" displays images of butternut squash, granola, couscous, sweet potatoes, pasta, lentils, oats, cooked rice, and fruit, each with their carbohydrate content per serving.
Text outlines how to calculate carbohydrate needs for weight loss, including formulas for Basal Metabolic Rate (BMR) for men and women. A yellow cartoon character is shown thinking of a croissant.
Carbs are not the enemy!!✋🏞âœĻðŸĐĩ Weight loss With Carb
I wanted to talk about something that's been on my mind lately—carbohydrates. It seems like carbs have gotten a bad reputation, especially when it comes to weight loss. There's this belief out there that if you want to shed pounds, you have to avoid carbs at all costs. But let me tell y
Chalie_Baker

Chalie_Baker

2026 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

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

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

Daniela Morando

14 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

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

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 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

(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 search results page for "ZODEACX equation system, by: Kedar Moye," showing an AI overview, related terms like "The Equivalent (Moye) Equation System," and social media snippets for Kedar Moye, including his co-ownership of ZODEACX Co.
The ZODEACX Equation, by: Kedar Moye
#mathematics #math #school #college
Kedar Isaiah Gibson Moye

Kedar Isaiah Gibson Moye

4 likes

A handwritten page in a lined notebook displays algebraic equations, specifically Brahmagupta's identity. It shows the expansion of (aÂē+bÂē)(cÂē+dÂē) into two different forms: (ac+bd)Âē+(ad-bc)Âē and (ac-bd)Âē+(ad+bc)Âē, illustrating how the product of two sums of squares can be expressed as a sum of two squares.
Two squares times two squares makes two squares
The sum of two squares times the sum of another two squares equals the sum of yet another two squares. These formulae are used to find examples like 5 × 13 = (2Âē+1Âē) × (2Âē+3Âē) = 65 = 8Âē+1Âē = 7Âē+4Âē. #math #maths #mathematics #algebra #arithmetic
cubicequation

cubicequation

19 likes

A diagram of triangle ABC with orthocenter O and orthic triangle DEF. Formulas for circumradius, area, and derivations for lengths OA, OB, OC are shown in terms of side lengths and area.
Mathematical derivations for the lengths OD, OE, and OF, representing segments from the orthocenter O to the vertices of the orthic triangle DEF, expressed in terms of side lengths and area.
Mathematical derivations for the side lengths of the orthic triangle, DE, EF, and FD, expressed in terms of the main triangle's side lengths a, b, and c.
Find lengths in terms of the sides
O is the orthocenter of the triangle ABC. The lengths centered around point O and the lengths of the orthic triangle DEF are solved in terms of the side lengths. The area of the triangle is found with Heron’s formula. #math #maths #mathemati cs #geometry #trigonometry
cubicequation

cubicequation

5 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

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

cot A + cot B + cot C, part 1
In any oblique triangle, the sum of the three angle cotangents create some interesting formulae involving the sides of the triangle and the circumradius. The Δ is the area of the triangle and can be found using the sides and circumradius as well. #math #maths #mathematics #geometry
cubicequation

cubicequation

19 likes

THE CHEER EQUATION!
@insidecheer + @smoedallday + #cslewis = ðŸ”Ĩ
CALI CHEER SHOW

CALI CHEER SHOW

26 likes

cscÂē ω = cscÂē A + cscÂē B + cscÂē C
ω is the Brocard angle of the triangle. A, B, C are the angle measures of the triangle. a, b, c are the side lengths of the triangle. L₁, L₂, L₃ are the lengths between the vertices and the Brocard point (labeled D). #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

8 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

56 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

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 derivation of the cosine double angle identity, `cos^2(B/2) - sin^2(B/2) = cos B`, on grid paper. It features a right-angled triangle with an angle bisector, applying the Pythagorean theorem and algebraic steps to reach the final identity.
Cosine double angle identity derivation
Using the angle bisector theorem and Pythagorean theorem, one can derive the cosine double angle identity. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

9 likes

A handwritten math note demonstrates solving a quadratic equation using the quadratic formula. It shows the general formula, an example equation (xÂē + 6x - 11 = 0), and a step-by-step solution, including the simplification of the square root (√80 = 4√5) to arrive at the final answer.
Solving quadratic equation using formula ðŸŦķ
#math #mathnotes #lemon8edu
candy

candy

14 likes

The image displays two handwritten mathematical proofs on lined paper. The first proof demonstrates that all primes pâ‰Ĩ3 are of the form 4n+1 or 4n+3. The second proof shows that all primes pâ‰Ĩ5 are of the form 6n+1 or 6n+5, by eliminating even numbers and multiples of 3.
Proofs of some prime number properties
These are two proofs for why prime numbers revolve around multiples of 4 and multiples of 6. #math #maths #mathematics #algebra #arithmetic
cubicequation

cubicequation

7 likes

A handwritten note explaining mixture problems in differential equations, defining rate in/out, and solving an example where a 1000L tank with 100kg sugar is diluted with pure water until only 10kg sugar remains, calculating the time as 460 seconds.
Mixture problem in Differentiable equation
#mathematics #lemon8education #notes
candy

candy

3 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

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 hand-drawn diagram illustrates a triangle ABC with its incircle and incenter (I). The Gergonne point (G) is shown as the concurrency of cevians connecting vertices to incircle tangent points on opposite sides. Ceva's Theorem is applied with segment ratios (s-a, s-b, s-c) to prove its existence.
Proving the existence of the Gergonne point of a triangle
The Gergonne point is where three specific segments are concurrent. These segments come off the vertices and intersect where the incircle is tangent to the side opposite of the vertex. While not as well-known as the most well-known triangle centers, its existence is easily proven with Ceva’s theore
cubicequation

cubicequation

7 likes

A handwritten diagram illustrates a proof of the Pythagorean theorem. A large square, side 'c', contains four right triangles (legs 'a', 'b') and a central square (side 'b-a'). Equations below show the area calculation cÂē = 4(1/2 ab) + (b-a)Âē simplifying to cÂē = bÂē + aÂē.
Proof of the Pythagorean Theorem, part 3
Here’s another classic proof of the Pythagorean Theorem where four triangles are placed in such a way that a small square in the middle of them. From there, an equating of areas occurs. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

8 likes

A handwritten geometric proof of the Pythagorean theorem, aÂē+bÂē=cÂē, is shown. It illustrates a large square formed by four right triangles with legs 'a' and 'b', and a smaller inner square with side 'c'. The area calculation (a+b)Âē = 4(Â―ab) + cÂē simplifies to the theorem.
Proof of the Pythagorean Theorem, part 1
This is one of my favorite geometric proofs. It’s basically a square that’s twisted into a larger square so an equating of areas occurs. #math #maths #mathematics #geometry #trigonometry
cubicequation

cubicequation

4 likes

A desk with a laptop, notebook, and phone displaying "How to study for your type of brain." The main title reads "How to Memorize Anything: Tailored Techniques for Every Type of Brain," accompanied by a pink brain icon.
This section details "1. Spaced Repetition," explaining it as reviewing information at increasing intervals. A diagram illustrates the process of receiving, recalling, and retaining content through four steps. It's best for short-term and semantic memory brains.
This section explains "2. Mnemonic Devices," memory aids using associations. Examples at the top show visualization (fish skeleton), storytelling (rabbit), and acronyms (HOMES for Great Lakes). It's best for semantic and episodic memory brains.
How to Memorize âœĻANYTHINGâœĻ: Tips for ALL 🧠 Types!
âœĻFirst Things First: Get to know your brain 🧠!âœĻ 🧠1. ADHD Brain: The ADHD brain struggles with sustained focus but thrives on novelty and excitement. It processes information quickly but often gets distracted or hyper-focused on areas of interest. 🧠2. Sensory Memory Brain: This brain type is h
Chalie_Baker

Chalie_Baker

19.2K likes

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