#Concavity

One of the most surprising optical illusions is the “dinosaur that follows you with its eyes,” which is based on the manipulation of angles and perspective. This illusion is created using a paper or cardboard dinosaur figure designed with the head in reverse concavity (curving inward instead of outward). When you observe the figure from a certain angle, the brain—accustomed to interpreting faces and figures as convex—is fooled and perceives that the dinosaur is turning its head to follow you with its gaze. This effect is especially convincing because it challenges perceptual logic and plays with how our brain processes depth and perspective.

The Smile vs. The Frown! (Concavity & Inflection Points) 😊☹️ ​ ​In Calculus, we don’t just care if a graph is going Up or Down. We care about how it is bending. This is called Concavity. ​1. Concave Up (The Smile) 😊 A curve is Concave Up when it bends toward the sky. ​The Rule: "Concave up, like a cup." ​The Math: The second derivative is positive (f''(x) > 0). It means the slope is increasing—even if the graph is going down, it’s slowing its fall and preparing to rise. ​2. Concave Down (The Frown) ☹️ A curve is Concave Down when it bends toward the ground. ​The Rule: "Concave down, like a frown." ​The Math: The second derivative is negative (f''(x) < 0). The "momentum" is fading. ​3. The Inflection Point (The Switch) 🔄 The Inflection Point is the most important dot on the graph. It is the exact millisecond where the "Smile" turns into a "Frown." ​The Math: This happens where the second derivative equals zero (f''(x) = 0). ​Why does this matter? In the real world, an Inflection Point is a "Turning Point." ​In Economics: It’s when a booming market starts to slow down before it actually crashes. ​In a Pandemic: It’s when the "Curve" starts to flatten. ​If you can find the Inflection Point, you can predict the future before it actually happens! 🔮 ​Follow @plotlab01 for more Calculus Visuals & Smart Math! 🚀 ​ ​Concavity Explained, Inflection Point Calculus, Second Derivative Test, Concave Up vs Down, Curve Sketching, Mathematical Modeling, Turning Points, Calculus Basics, Derivatives, Rate of Change, Plotlab01. ​ ​#Calculus #MathVisuals #Mathematics #Engineering #StudyTips

Turning points and inflection points often look almost identical on a graph — but mathematically they behave very differently. At a turning point, the slope becomes zero and the function changes direction. At an inflection point, the curve changes its shape (concavity), but the function may keep increasing. Watch the tangents carefully in the animation and see what really changes. Can you spot the difference? Save this if it helped you understand calculus more clearly.

That rib hump isn't just bone—it's your spine rotating under pressure. Stop "stretching" it. You need to breathe into the concavity and de-rotate the convexity. Fix the root cause before it's too late. 🧬 Apply for the anti-surgery protocol at the top of my profile! #scoliosis #scoliosissurgery #scoliosisawareness #scoliosisexercises #ribhump #spinex . . . SEO: Scoliosis rib hump fix | Concave side breathing | Stop curve progression | Idiopathic scoliosis protocol | Unilateral spinal correction.

Precalculus question: concavity #math #tutor #precalculus #STEM

What is the name of this concavity on a Chest X-Ray? ANSWER AP (AORTOPULMONARY WINDOW) 👨🏽‍💻This is a really important review area! Usually there should be a concavity between the contour of the aorta and the pulmonary trunk. Sometimes this can be tricky to see especially when the descending aorta is ectatic but it is an important review area on every frontal chest X-Ray you look at 👨🏽‍💻When there is a lymph node or primary lung cancer the AP window is ‘obliterated’ in that you can’t make out the margins of the aorta and pulmonary trunk 👨🏽‍💻This can be the only abnormality on the film so if you don’t look for it, you could miss it

One of the most surprising optical illusions is the “dinosaur that follows you with its eyes,” which is based on the manipulation of angles and perspective. This illusion is created using a paper or cardboard dinosaur figure designed with the head in reverse concavity (curving inward instead of outward). When you observe the figure from a certain angle, the brain—accustomed to interpreting faces and figures as convex—is fooled and perceives that the dinosaur is turning its head to follow you with its gaze. This effect is especially convincing because it challenges perceptual logic and plays with how our brain processes depth and perspective.

🕺회전근개 강화, 누워서 핸드폰만 있으면 충분합니다. 회전근개의 본 역할은 단순히 힘을 내는 것이 아니라, 어깨가 움직이는 모든 각도에서 관절을 안정화하는 것입니다. ✅견관절은 관절와가 얕아 구조적으로 불안정하고, 관절 내 압력(흡입력, concavity compression)에 크게 의존합니다. 이 때문에 회전근개는 어깨가 움직이는 순간마다 빠르고 정교하게 반응해야 합니다. ✅하지만 벌리기만 하는 고정된 패턴의 운동은
자극은 느껴질 수 있어도, 실제 어깨 움직임처럼
각도가 계속 변하는 환경까지는 만들기 어렵습니다. 💡이번 영상은
회전근개가 본래 역할을 하도록 만드는 간단하고 효과적인 운동입니다. ✔️옆으로 누운 자세에서 동작을 진행하면 서서 할 때보다 상부 승모근의 보상 개입은 줄어들고, 견갑이 비교적 안정된 상태에서 어깨 관절을 조절하는 환경을 만들 수 있습니다. ✔️손등 위에 올린 핸드폰을 떨어뜨리지 않기 위해 팔의 각도를 미세하게 조절하는 과정 자체가 회전근개가 관절 중심을 유지하는 연습이 됩니다. 📚Neumann(2017) Kinesiology of the Musculoskeletal System 👨🏻‍🏫관절의 구조적 불안정성과 회전근개의 동적 안정화 역할(concavity–compression)을 설명 📚Burkhart et al.(2003) The disabled throwing shoulder. Arthroscopy 👨🏻‍🏫회전근개–견갑 복합체의 협응 실패가 기능적 어깨 장애로 이어질 수 있음을 제시 📚Ludewig & Cook(2000) Alterations in shoulder kinematics and associated muscle activity. JOSPT 👨🏻‍🏫견갑 운동 이상 시 상부 승모근의 근활성 변화가 나타남을 보고

Morning Glory Sign: Midbrain Atrophy in Progressive Supranuclear Palsy 🌸🧠 Spot the “Morning Glory Sign” on axial FLAIR MRI! 🌸 Concavity of the lateral midbrain tegmentum is a hallmark of Progressive Supranuclear Palsy (PSP). Learn how midbrain atrophy shapes this classic neuroimaging clue. #NeuroImaging #PSP #BrainMRI #Neurology #NeuroRadiology ProgressiveSupranuclearPalsy MorningGlorySign

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Concavity of the Curve | G. Tewani | JEE Mathematics 🛒 Available now at Cengage Amazon Store: https://amzn.to/40XDhtW Understand the concept of Concavity of a Curve with a clear and analytical explanation by G. Tewani. This topic is an important part of Differential Calculus and is frequently used in JEE Main & Advanced problems. 📘 Book Reference: Cengage Mathematics for JEE Main & Advanced – Calculus by G. Tewani This session covers: ✅ Concept of concavity and curvature ✅ Second derivative test for concavity ✅ Points of inflection ✅ Graphical interpretation of functions ✅ JEE-level conceptual and numerical illustrations 💡 Mastering concavity helps in analyzing the behavior of functions and solving advanced calculus problems effectively. 👉 Subscribe for more concept videos, solved illustrations, and exam-focused strategies by Cengage. #JEEMathematics #Calculus #Concavity #GTewani #Cengage #JEEMain #JEEAdvanced #CrackJEE2026

1) Concave side🌜 Spinous process rotates towards this side → vertebral body rotates opposite, so spinous deviates into concavity Compressed and tight side → shortened tissues + reduced segmental space cause compression Rib cage collapsed → ribs approximate due to side-flexion + rotation coupling Requires stretching → shortened muscles/fascia need length restoration Side bending away from this side → opens concavity and decompresses collapsed segments Treatment requires vertebral body rotation towards this side → counter-rotation to derotate spine and reduce asymmetry Fascia is tight – needs release → chronic shortening increases fascial density and stiffness 2) Convex side🌛 Vertebral body rotates towards this side → vertebral rotation drives rib prominence on convexity Weak and overstretched → prolonged lengthening reduces force-generating capacity Rib cage prominent (hump) → rib posterior displacement due to vertebral rotation Requires strengthening → elongated muscles need active tension and control Side bending towards this side → encourages activation and load acceptance on convex side Treatment requires spinous process rotation towards this side → indirect vertebral derotation via posterior element guidance Fascia is elongated and overstretched – needs tension control → lacks elastic recoil, needs controlled loading not release Important Note from Myofit ⬇️ Pelvic hike/rotation and scapular level correction will vary in C-shaped vs S-shaped scoliosis — this must be carefully assessed and corrected accordingly. #ScoliosisRehab #3DPostureCorrection #SpinalBiomechanics #PhysioAssessment #PosturalCorrection scoliosis concave convex biomechanics spinal rotation rib hump correction physiotherapy posture analysis kinetic chain scoliosis rehab 3D correction pelvic rotation scapular imbalance