Objects defined for a triangle

Fuhrmann triangle

The Fuhrmann triangle, named after Wilhelm Fuhrmann (1833–1904), is special triangle based on a given arbitrary triangle. For a given triangle and its circumcircle the midpoints of the arcs over triangle sides are denoted by . Those midpoints get reflected at the associated triangle sides yielding the points , which forms the Fuhrmann triangle. The circumcircle of Fuhrmann triangle is the Fuhrmann circle. Furthermore the Furhmann triangle is similar to the triangle formed by the mid arc points, that is . For the area of the Fuhrmann triangle the following formula holds: Where denotes the circumcenter of the given triangle and its radius as well as denoting the incenter and its radius. Due to Euler's theorem one also has . The following equations hold for the sides of the Fuhrmann triangle: Where denote the sides of the given triangle and the sides of the Fuhrmann triangle (see drawing). (Wikipedia).

Fuhrmann triangle
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Sierpinski from Pascal

This is a recreation of a short clip from a long form video showing six different ways to construct the Sierpinski triangle: https://youtu.be/IZHiBJGcrqI In this short, we shade odd entries of the Halayuda/Pascal triangle to obtain the Sierpinski triangle. Can you explain why this works?

From playlist Fractals

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Quadratic curvature for algebraic curves | Differential Geometry 14 | NJ Wildberger

In this video we extend the discussion of curvature from parabolas to more general conics, and hence to more general algebraic curves. The advantage of basing things on the parabola is that we get nice connections between curvature and the foci, and that once we move to studying surfaces i

From playlist Differential Geometry

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Orthocenters exist! | Universal Hyperbolic Geometry 10 | NJ Wildberger

In classical hyperbolic geometry, orthocenters of triangles do not in general exist. Here in universal hyperbolic geometry, they do. This is a crucial building block for triangle geometry in this subject. The dual of an orthocenter is called an ortholine---also not seen in classical hyperb

From playlist Universal Hyperbolic Geometry

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How Movies Control Your Brain

Check out our friends at FW:Thinking, "Can Computers Predict Oscar Winners?" http://youtu.be/NNBq67UpkMk SUBSCRIBE to BrainCraft! Click here: http://ow.ly/rt5IE Twitter: https://twitter.com/nessyhill Instagram: http://instagram.com/nessyhill ↓ MORE LINKS AND REFERENCES BELOW ↓ Neuros

From playlist Psychology & Pop Culture

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AP Physics 1 Review of Charge and Circuit | Physics | Khan Academy

In this video David quickly explains each charge and circuit concept and does a sample question for each one. Created by David SantoPietro. Watch the next lesson: https://www.khanacademy.org/science/physics/review-for-ap-physics-1-exam/ap-physics-1-free-response-questions-2015/v/2015-ap-p

From playlist Review for AP Physics 1 exam | AP Physics 1 | Khan Academy

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Laurent Théry : Proof and computation in Coq

Abstract : In this talk, we are going to show on some elementary examples how computation can easily be incorporated inside proof in a proof system like Coq. Recording during the thematic meeting: "Effective analysis: foundations, implementations, certification" the January 14, 2016 at th

From playlist Mathematical Aspects of Computer Science

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24C3: C64-DTV Hacking

Speaker: Peter Fuhrmann Revisiting the legendary computer in a joystick The C64-DTV is a remake of the classic homecomputer sold as a joystick-contained videogame. The talk gives an overview about the structure of the DTV, and shows different hardware and software modifications that ca

From playlist 24C3: Full steam ahead

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What is an obtuse triangle

👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl

From playlist Types of Triangles and Their Properties

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Applying reimann sum for the midpoint rule and 3 partitions

👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the

From playlist The Integral

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How to find the position function given the acceleration function

👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the

From playlist Riemann Sum Approximation

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Midpoint riemann sum approximation

👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the

From playlist The Integral

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How to use midpoint rienmann sum with a table

👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the

From playlist The Integral

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Jean-François Quint - 5/6 Mesures stationnaires et fermés invariants des espaces homogènes

Dans ce cours, je présenterai des résultats que j'ai obtenus récemment en collaboration avec Yves Benoist. Nous avons démontré que, pour certaines actions de groupes sur des espaces homogènes, les adhérences d'orbites sont toutes des sous-variétés. Cet énoncé fait suite à de célèbres trava

From playlist Jean-François Quint - Mesures stationnaires et fermés invariants des espaces homogènes

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VISUAL PROOF | Medians Divides a Triangle into Equal Areas | Using ANIMATION Tools | CREATA CLASSES

Understand the Visual proof of medians divides the triangle into six equal triangles, using ANIMATION & Visual Tools. Visit our website: https://creataclasses.com/ Introduction to Median: https://youtu.be/eHewPlLq7ps For a full-length course on SEGMENTS OF TRIANGLE & TRIANGLE CENTERS: h

From playlist MEDIANS

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VISUAL PROOF | Area of Triangle is 4/3 times area of triangle formed by Medians | CREATA CLASSES

Understand the Visual proof of formula Area of Triangle is 4/3 times area of triangle formed by Medians, using ANIMATION & Visual Tools. Visit our website: https://creataclasses.com/ Introduction to Median: https://youtu.be/eHewPlLq7ps For a full-length course on SEGMENTS OF TRIANGLE &

From playlist MEDIANS

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Infinite Sierpinski Zoom

This is an infinite zoom on the famous Sierpinski triangle fractal. If you want to see six different constructions of this fractal, check out this long form video I made : https://youtu.be/IZHiBJGcrqI . #math #manim #fractal #sierpinski #zoom #infinite #shorts #mathshorts

From playlist Fractals

Related pages

Euler's theorem in geometry | Fuhrmann circle