Steiner line and isogonal lines

by flower417477, Jul 18, 2025, 5:56 AM

$\odot O$ is the circumcircle of $\triangle ABC$,$H$ is the orthocenter of $\triangle ABC$
$D$ is an arbitrary point on $\odot O$
$E$ is the reflection point of $D$ wrt $BC$,$EH$ meet $OD$ at $F$.
$K$ is the reflection point of $A$ wrt $OH$.
$P$ is a point on $\odot O$ such that $PK$ is parallel to $BC$,$Q$ is a point on $OH$ such that $PQ$ is parallel to $EH$.
$N$ is the circumcenter of $\triangle PQK$
Prove that $AF,AN$ is a pair of isogonal lines wrt $\angle BAC$
Attachments:
geometry
isogonal lines
circumcircle
steiner line
geometric transformation
reflection
Euler Line
L

too much tangencies these days...

by kamatadu, Jan 20, 2023, 7:18 PM

Let $\Omega$ be a circle and $\gamma_1,\gamma_2$ be circles internally tangent to $\Omega$ at $P$ and $Q$. Assume that $\gamma_1$ and $\gamma_2$ are also externally tangent at point $T$. Prove that the line through $P$ perpendicular to $PT$ meets line $QT$ on $\Omega$.
geometry
geometric transformation
homothety
Inversion
L

Rectangle EFGH in incircle, prove that QIM = 90

by v_Enhance, Jul 18, 2014, 7:48 PM

Let $ABC$ be a triangle with incenter $I$, and suppose the incircle is tangent to $CA$ and $AB$ at $E$ and $F$. Denote by $G$ and $H$ the reflections of $E$ and $F$ over $I$. Let $Q$ be the intersection of $BC$ with $GH$, and let $M$ be the midpoint of $BC$. Prove that $IQ$ and $IM$ are perpendicular.
geometry
rectangle
incenter
geometric transformation
reflection
geometry proposed
L

IMO Shortlist 2011, G1

by WakeUp, Jul 13, 2012, 11:30 AM

Let $ABC$ be an acute triangle. Let $\omega$ be a circle whose centre $L$ lies on the side $BC$. Suppose that $\omega$ is tangent to $AB$ at $B'$ and $AC$ at $C'$. Suppose also that the circumcentre $O$ of triangle $ABC$ lies on the shorter arc $B'C'$ of $\omega$. Prove that the circumcircle of $ABC$ and $\omega$ meet at two points.

Proposed by Härmel Nestra, Estonia
geometry
circumcircle
trigonometry
geometric transformation
IMO Shortlist
L

Chords and tangent circles

by math154, Jul 2, 2012, 3:13 AM

Circles $\Omega$ and $\omega$ are internally tangent at point $C$. Chord $AB$ of $\Omega$ is tangent to $\omega$ at $E$, where $E$ is the midpoint of $AB$. Another circle, $\omega_1$ is tangent to $\Omega, \omega,$ and $AB$ at $D,Z,$ and $F$ respectively. Rays $CD$ and $AB$ meet at $P$. If $M$ is the midpoint of major arc $AB$, show that $\tan \angle ZEP = \tfrac{PE}{CM}$.

Ray Li.
geometric transformation
geometry proposed
geometry
homothety
L

Show that AB/AC=BF/FC

by syk0526, Apr 2, 2012, 3:06 PM

Let $ ABC $ be an acute triangle. Denote by $ D $ the foot of the perpendicular line drawn from the point $ A $ to the side $ BC $, by $M$ the midpoint of $ BC $, and by $ H $ the orthocenter of $ ABC $. Let $ E $ be the point of intersection of the circumcircle $ \Gamma $ of the triangle $ ABC $ and the half line $ MH $, and $ F $ be the point of intersection (other than $E$) of the line $ ED $ and the circle $ \Gamma $. Prove that $ \tfrac{BF}{CF} = \tfrac{AB}{AC} $ must hold.

(Here we denote $XY$ the length of the line segment $XY$.)
This post has been edited 5 times. Last edited by syk0526, Apr 4, 2012, 6:48 AM
geometry
circumcircle
trigonometry
parallelogram
geometric transformation
reflection
Asymptote
L

Lots of perpendiculars; compute HQ/HR

by MellowMelon, Jul 26, 2011, 9:14 PM

In an acute scalene triangle $ABC$, points $D,E,F$ lie on sides $BC, CA, AB$, respectively, such that $AD \perp BC, BE \perp CA, CF \perp AB$. Altitudes $AD, BE, CF$ meet at orthocenter $H$. Points $P$ and $Q$ lie on segment $EF$ such that $AP \perp EF$ and $HQ \perp EF$. Lines $DP$ and $QH$ intersect at point $R$. Compute $HQ/HR$.

Proposed by Zuming Feng
geometry
incenter
geometric transformation
homothety
AMC
USA(J)MO
USAMO
L

Perpendicularity

by April, Dec 28, 2008, 4:09 AM

Point $D$ lies inside triangle $ABC$ such that $\angle DAC = \angle DCA = 30^{\circ}$ and $\angle DBA = 60^{\circ}$. Point $E$ is the midpoint of segment $BC$. Point $F$ lies on segment $AC$ with $AF = 2FC$. Prove that $DE \perp EF$.
This post has been edited 1 time. Last edited by v_Enhance, Jan 25, 2016, 3:51 PM
Reason: \equal -> =
geometry
circumcircle
geometric transformation
reflection
homothety
parallelogram
Hi
L

incircle with center I of triangle ABC touches the side BC

by orl, Jun 26, 2005, 12:16 PM

Given a triangle $ABC$. Let $O$ be the circumcenter of this triangle $ABC$. Let $H$, $K$, $L$ be the feet of the altitudes of triangle $ABC$ from the vertices $A$, $B$, $C$, respectively. Denote by $A_{0}$, $B_{0}$, $C_{0}$ the midpoints of these altitudes $AH$, $BK$, $CL$, respectively. The incircle of triangle $ABC$ has center $I$ and touches the sides $BC$, $CA$, $AB$ at the points $D$, $E$, $F$, respectively. Prove that the four lines $A_{0}D$, $B_{0}E$, $C_{0}F$ and $OI$ are concurrent. (When the point $O$ concides with $I$, we consider the line $OI$ as an arbitrary line passing through $O$.)
geometry
circumcircle
ratio
geometric transformation
reflection
analytic geometry
homothety
L

Midpoints of altitudes and concurrent cevians

by darij grinberg, Jul 5, 2004, 1:18 PM

Let $ ABC$ be a triangle. Let $ A_1$, $ B_1$, $ C_1$ be the midpoints of its sides $ BC$, $ CA$, $ AB$, and $ A_2$, $ B_2$, $ C_2$ the midpoints of the altitudes from $ A$, $ B$, $ C$. Show that the lines $ A_1A_2$, $ B_1B_2$, and $ C_1C_2$ meet at one point.
projective geometry
geometry
geometric transformation
reflection
LaTeX
geometry proposed
L
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The Bisectorpoint of olympiad.asy and of geometry.asy in Asymptote
Labeling the Intersecectionpoints of Circle and Line
Can you help me please?
crop3D.asy
The Cube in asy
Draw me a circle!
The perpendicularmark of the Extension of asy.exe "geometry.asy"
But what about the Readability of the Picture?
So nice to see you!
Draw a function with two variables. Here the Circle.
Draw me a grid! - grid.asy
What color is the background here?
The Intersection Aerea of two Circles with and without the Incircle
Marking Angles and Line Segments
The Art of Diplomacy and the Didactics of Mathematics
+ January 2020
Draw me a burning Candle with Circles
The drawn Egg on texample.net
Signs for: lightning, male, female, and angle
StickIntervalMarker in asy
asy-keywords
About bary.asy
Bezulated Varepsilon
A nice Cube
Display the Height, Depth, and Width of a box in LaTeX
Path Ticks in an Arrow
asy.exe and convert of ImageMagick on Windows
The hungarian heartsuite
More on subfigures in asy
The different Cosins in the Triangle
Indicating that two lines are parallel
+ December 2019
Plot me an Integral in Asy
Draw me a 3D-Ring
Die Stelle einer Funktion mit maximaler Krümmung
Extrude texpath with Label Text in Asymptote
+ November 2019
Meine Funktion g_3(x)
Hints and Tips on AoPS - demonstrating Example
Teilfunktionen der Kardioide und ihre konstitutiven funktionalen Elemente
+ October 2019
myshipout in asy
Drawing Hyperbolas with the Modul geometry in Asymptote
The Statement fontcommand in asy
Draw the array of texpath in asy and shift it.
Drawing a cylinder
+ September 2019
Insquare of Circumcircle of Cardioid
+ June 2019
The Regular Intriangle in the Circumncircle of the Cardioid
+ May 2019
Latest News from May 2019 about the Inner Secrets of the Cardioid
+ March 2019
cases in LaTeX
size() in asy without unitsize()
Make me a complex picture in asy!
+ February 2019
Ask asy to display the first n Fibonacci Numbers
Sectoring the Cicle into five congruent Regions in Asymptote
Label a line with a caligraphic letter "l".
We are not at all at the End with the Power of a Point with Respect to a Circle.
Playing around with texpath(Label"...")
+ January 2019
Inversion and Symmetric Arbelos with Pappus Chain
The Tangents of a curved Path when Crossings a Line
Background Colors
marker[] MarkFillDraw in asy
Fibonacci-Numbers and Lucas-Numbers
Function Gaussian Normal Distribution
Extracting the Bezier control points
The Sector of an Ellipse
Nice Typography of the Golden Ratio
The Super-Ellipse
The Arbelos (following Baptiste GORIN)
Arbelos and Limaçon
The Pentagon
Complications with "buildcycle" in asy
What is the Ratio from Blue to Green?
Je vais essayer de jeter un œil sur le code...
The Bisectorline of a Line in the Triangle (with geometry.asy)
The Incircle of the Arbelos
The Golden Arbelos with Hat
Law of sines
Golden Partition of One
Shoddow me!
Learn from the Golden Arbelos
A regular or a half-regular Octogon?
+ December 2018
Encore des cercles-wiki
A small Macro to fetch and display Coordinates in asy
The upright varphi in asy on AoPS
The Golden Right Triangle
Squaring a Rectangle only with Compass and Ruler
RMS-AM-GM-HM on AoPS-wiki
Right Triangle: Calculate the Legs - One Leg relatively known, Hypothenuse known
From the symmetrical to the asymmertical Arbelos
Meine beste Freundin
One Construction of the Circumcirle with it's Midpoint
Labeling "dot"-Coordinates - The Meaning and the Changement of "defaultformat"
Draw me a Circle using the two Functions cos and sin!
Find tangentlines on certain Points of an arbitrairy Path
We must continue with the Arbelos!
draw-border-of-a-line (from stackexchange)
In the Context: Testing asy for FF game
Asy at the Home of EPFL (École polytechnique fédérale de Lausanne)
+ November 2018
Circle-Intersections - Tangent-Lines - Tangent-Points
Readable Formatting and Cocatenating: Asy-Output of Reals with LaTeX- siunitx
The Problem of Beginning and Ending of Counting
Overdrawing of a label: Use layer()
The Ellipse
The Greek Letters phi and Phi
Enscirbe a Half Circle with Radius of the Golden Ratio into the Normal Parabola
Tangent Circles - The Golden Window
Inner Con-Text and Outer Con-Text
Circum-Rectangle of three Tangent Circles, two of them of Same Size
Show me the Knife of asy!
Occasionally the 111. Birthday of Astrid Lindgren
Circle Inversion
asy: Fetch and format and display the value of several reals in one label
Show me the Stars!
Asy. - Figure directly together with the Listing
In asy: picture - frame - picture.fit() - add
From the Silver Rectangle (DIN) to the Equilateral Triangle
Asymptote 3D: Replace extension with closestmidpoint. - Just show how it works.
Hide me! - Show me!
+ October 2018
Equilateral and 30-60-90-Triangle
We recall our Silver Trapezoid.
Fonction donnant la factorielle de n de façon itérative / récursive
Extension of a Line using the relpoint of geometry in asy
Do you understand?
label(format()) in asy
"Fixed-size objects" in asy
+ September 2018
1overx.asy - how to handle this case of the division by zero in asymptote
The Cosine Theorem
Icosahedron
Label me in asy!
+ August 2018
TeX or LaTeX - The Name of the Game
The Appearance of the Right Angle in the Helix-Spiral
GoldTriangle tikz2asy
Moebius Strip 3D in asy
Lines in the Polygon
+ July 2018
The bisectorpoint D of a triangle ABC
The slanted letter N and the Question of the Pre-Existance of the undrawn Line
Earth-Tectonic
Afterimage of looking into the Sun
+ June 2018
Circle and Half-Circle and Circle
Complex Plane in asy
+ May 2018
How do you make me a defined angle - like 43 degrees?
Thales's theorem
+ April 2018
About the Condtion that there is an Incircle in the Isosceles Trapezoid
Pythagorean addition of Metafont. - What says asy?
Two lines intersect inside a circle
Power of a point with respect to a circle theorem, theorem of Ptolemy
Understanding Code Sample No. 24 of Asymptote trial
What radius is here around F: sqrt(2)/2, and what y-height has F: .25?
Five little circles and one big circle
Cool or uncool? - This is here the question.
+ March 2018
Five Points and Conics
On the right Way towards the Solution of the Cross-Section for the Frustum
3-4-5-Triangle and Golden Ratio
Ptolemy's theorem
Ask and Task and the Letter T. - The Isosceles Trapezoid.
Isosceles Trapezoids bulit on other regular Polygons
The Graphs of sin(x) and cos(x)
The Trapezoid in the Pentagon
Circumcenter and Circumradius of the Isosceles Trapezoid
Trial on the letter A of Luca Pacioli
Another Golden Trapezoid
Graphing on Millimeterpaper
The Circle Power of a Point and the Golden Ratio
True or false. - True or not true. - This here is the question.
Learning the use of subpath
A Circle with a Radius equals Zero ...
Usage of Fonts
Power of a Point in asy
one-two-three
+ February 2018
I asked a Painting Woman to draw me a Tulip.
Randomness by AoPS user NeoMathematicalKid in the Testforum
Regenbogen-Blume
The posed Problem Geometry 14 of AoPS user leequack
Path, path, path. - Path, path.
pen makepen(path);
Can someone make a 7, 15, 17 triangle for me?
The White's illusion
Negativ slant of the italic greek varphi to get the upright form in asy
Linecaps and Linejoins
triads.asy
The Greek key mp2asy
The "double period" asy-connector ".."
The Acrobat easily drawn
mydotted
Give me a Smile
One beside of the other. - Side by Side.
+ January 2018
Boolean Ratio Bingo
The flash governs everything. - Even squares.
Laterst News from 2018 about the Golden 60 Degree Trapezoid
Laterst News from early 2018 about the Golden 60° Trapezoid
circles.asy from the official asy-Gallery
Die Moendchen des Hippokrates
Center of Mass in the Golden 60 Degree Trapezoid
Why does (2*sqrt(12.5))/sqrt(2) = 5?
Elegant Asymptote Programming - One-Liners / One-Pagers
Laterst News about the Golden Trapezoid from the year 2017
The so called Flower of Life
+ December 2017
Circumcircle in the Golden Trapezoid
Heaviside step function in asy-code from wiki
Extension of a Line-Segment
Quadrilateral with unknown Angles
Further on to the Cardioid
+ November 2017
Tangents to two touching Circles
subpicture and superpath
Grid of Dots and Grid of Lines in Asymptote
Split an ordinary Prime down into a Complex Prime
The How-to of a Sinusoidal Wave Graph
+ October 2017
dirtime/reltime/mintime (and a transfer-trial)
+ September 2017
asy: "no matching function 'intersectionpoint(line, path)"
exactly what a lattice point is
The Icon-Arrow and Confusion
+ August 2017
Das passt dazu, dass ...
Draw me a Circle in Asymptote
\def\dds{\texttt{doc / docstrip}}
testme-testme
Logique of the Use of the Equilateral Triangle as Logo
Gaussian Standard Normal Distribution
dot-dot-dot. - dotsize & the behind of it
Orthocenter and (pi^2/6)^-1 Sected Equilateral Triangle
Orthocenter and Golden Sected Side of Equilateral Triangle
+ July 2017
You see to program Asymptote to find...
Und ich darf auch (...)!
+ June 2017
Ellipse and Tangent-Line on the Ellipse
Incircle and Altitudes of Triangle and Trapezoid
Inscribe a half Golden Ellipse into the Equilateral Triangle
Ï€^2/6=1.644...
+ May 2017
Three tangent Circles
a plusminus intersectionDir
Tangents on a Circle
dot-dot-dot dotsize
The Root-Spiral
dot-dot-dot Open-Dot in 3D-asy
Multyplication by Intersectionpoints - Red x Blue = Green
Draw me a bulb
Phyllotaxis and Golden Ratio
+ April 2017
Millimeterpaper
markers1.asy and markers2.asy
Arc - Arc - Arc. - Draw Arc and Markangle.
+ March 2017
Good Morning, Sweet Cherry Blossom.
Marry me!
Golden Ratio in the Golden Trapezoid
Why do the nares of humans point downwards?
Study arcsubtended
ON THE EMPLOYMENT OF CURVES IN THE SOLUTION OF PROBLEMS.
(Why?) Is this not a 3-4-5-Triangle?
Some Trigonometric Values of the Golden Ratio
Arrangement of the Location of the Right Triangle
Graphing a Circle in two special Steps
The Problem of Align in Asymptote with TeXeR
The Labeling in Pythagoras.asy
Push me a Triangle
Unitcircle and Ellipse
+ February 2017
Use of Color in the Graphics-Language Asymptote
Half-Circle-Tangent in Square, 3-4-5-Triangle, Knauthian Fig
Einander aehnliche Drachen-Vierecke und Kreis-Tangenten
In-Kreis und Ankreise des Dreiecks, speziell 3-4-5-Dreieck
Beeing on Out-Look for more News about the 3-4-5-Triangel
draw cloud shape in Asymptote
Penmargin
Two Squares and a Circle and the Golden Ratio
Pascal Triangle
dotfactor * = 5;
QED - myqed in LaTeX
Draw an Angle in Asymptote with a Tick Mark in it.
Tangent-Line on a Hyperbola from an arbitrairy Point A
Hexa-Gon and 12-Gon
Draw me the Cube in 3D
Handeling with Strings in Asymptote
Why is the Sum of the Angles in the Triangle 180 Degree?
3-4-5-Triangle and Square
asy-3d outline --- The Little Gauss
+ March 2016
Dirty Trick to circumvent Division-by-Zero-Problem?
+ April 2015
Compass-Directions, DotMargin(s), and PenMargin(s)
Draw me a Grid
The Regular Octagon
+ March 2015
Simple Inequalities
Art for Understanding. Art and Problem-Solving
The most simple figure containing √2, √3, and √5
New Retry of my last Picture about the GR in the Cardioid
+ February 2015
Circumcircle of the Cardioid, Trigonal Grid, and Golden Ratio
+ September 2014
Bananas or not Bananas?
+ August 2014
wL - writeLaTeX
+ July 2014
The trigonal Hexagon-Pack
+ June 2014
Labeling with the distance-feature of geometry.asy
Triangles
+ May 2014
The Sentences-Group of Pythagoras
Ride with your bicycle
The Circle inscribed in the Semi-Circle
Squared Gold
This is a Concret to explain the Sense of the Root-Spiral
Trials of Arrow-Design in Asymptote
The Art of Coming Down
New Ways finding Cardioids
The Idea of a Meta-Font
More Changes of the Control-Points c1 and c2
The Unit-Cube and the Golden Ratio
+ April 2014
Circle and Square - Logo-like & colored
The distance EC
Remember sqrt(5) through 5 with this Figure
AoPS with Bounding-Boxes
The 6-Point-Method
Smoothness in Asymptote
Depression and Fibonacci-Numbers – a Connection?
+ March 2014
Label or label?
Explain "shift(pair)*" / "rotate(angle, pair)*" with labelpath
The Bisectorpoint (in Asymptote) and Complex-Number-Calculation
Transform a Domino-Triangle into a 3-4-5-Triangle
In Itself Buckled or out of it Stretched and so Rotated Polygon
Pentagrammatical Logic in the Circle
Asymptote: Labels with \lbrace and \rbrace
+ February 2014
The 3-4-5-Triangle in the 7x7-Square and the Knauth-Figure
+ May 2013
- Woman! -
+ March 2013
Inner Secrets of the Cardioid
+ February 2013
Apply the Pythagorean Theorem to x^2+x-1=0
+ January 2013
The Knauth-Triangle
The half-regular Octagon in the Knauth-Figure
How far does the Horse jump in the Chess-Game?
+ November 2012
The Cathetes-three-and-four-Triangle in the Six-times-six-Square
+ March 2011
The Domino-Triangle - Part 1
+ January 2011
The broken Eye of Horus, Part 1
+ December 2010
The Heartsuite-Point in the Pentagram to Chrismas
Shouts
Submit

  • The aura

    by centslordm, May 12, 2025, 8:05 PM

  • same, luckyleaf

    by MightySpider, Mar 31, 2025, 4:06 AM

  • woah this blog is older than me lol
    nice blog! :coolspeak:

    by luckyleaf77, Jan 11, 2025, 3:20 PM

  • admits
    ed

    by sixoneeight, Aug 10, 2024, 12:13 AM

  • https://artofproblemsolving.com/community/c3841395

    by Rename, Jul 21, 2024, 3:12 PM

  • wow cool blog! :D

    by BakedPotato66, Jan 10, 2024, 2:27 AM

  • Awesome!

    by Neurotricity, Oct 20, 2022, 9:38 AM

  • Can I be contrib? Thanks!

    by MC413551, Oct 8, 2022, 2:14 PM

  • Very nice blog :)

    by programmeruser, Sep 19, 2022, 12:23 PM

  • Wow! this is EPIC!

    by mathkid369, Jul 11, 2022, 2:43 PM

  • This blog is amazing! I've found so much useful information on here. Thank you!

    by je100, Mar 25, 2022, 5:04 PM

  • Unarguably one of the best blogs on AoPS created by one of the most amazing people on AoPS :)

    by player01, Mar 24, 2022, 6:38 PM

  • Thank you for this wonderful resource, K-A! It's helped me a lot. Not many sites have asymptotic tutorials that make sense, or Google just understands "asymptote" wrong.

    by fuzimiao2013, Dec 12, 2021, 6:43 PM

  • wow you are a pro at asymptote great job klaus-anton!!!

    by HWenslawski, Oct 20, 2021, 5:24 PM

  • Amazing blog. You are so good at asymptote!

    by player01, Aug 27, 2021, 12:48 PM

  • ngl, Klaus-Anton is pr0 at LaTeX and asymptote

    by mathlearner2357, Mar 19, 2021, 9:44 AM

  • Thanks! This blog had a lot of asymptote functions that I needed for olympiad geometry diagrams.

    by eduD_looC, Mar 16, 2021, 12:28 AM

  • @player01 now 30k visits

    by ObjectZ, Feb 2, 2021, 2:14 PM

  • @pog now 29k visits :P

    by player01, Nov 11, 2020, 5:14 PM

  • 18 shouts and 26k visits?

    by pog, Sep 9, 2020, 3:48 PM

  • yeet
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    by ARay10, Sep 4, 2020, 4:21 PM

  • What software do you use to make asymptote diagrams?

    -πφ

    by piphi, Jun 18, 2020, 3:09 AM

  • dang this is an old blog

    by CoolCarsOnTheRun, Jun 7, 2020, 10:07 PM

  • Is it possible to export an asymptote drawing as an SVG?

    -piphi

    by piphi, May 12, 2020, 6:56 PM

  • Yah, I remember that...

    by sonone, May 1, 2020, 2:39 PM

  • Actually, the making pies thing is from AoPS challenge problems in PA2.

    by RedSox2, Apr 23, 2020, 4:53 PM

  • I like your blog. How did you learn so much?

    by sonone, Apr 3, 2020, 2:36 PM

  • nice blog!

    by matharcher, Mar 21, 2020, 2:10 AM

  • wow, this is awesome! Im subscribing

    by piphi, Feb 12, 2020, 8:28 PM

  • Yes sure it is!

    by mathboy282, Dec 21, 2019, 9:38 PM

  • I like this blog. It is very helpful.

    by Chishimotoji, Jan 23, 2019, 3:12 AM

  • Great blog!

    by WizardMath, Mar 9, 2018, 10:59 AM

  • Asymptote = good = probably better that I ever will be

    by coolmath34, Nov 23, 2017, 1:03 AM

  • Wow you are good at asy!

    by fuegocaliente, May 24, 2017, 9:20 PM

  • first shout of 2017!!

    by Mathisfun04, Mar 6, 2017, 3:00 PM

  • Nice asymptote!

    by Boomer, Apr 2, 2014, 4:22 PM

  • :blush: I wonder, I wonder.

    by Klaus-Anton, Jan 8, 2011, 6:19 PM

  • First shout!

    by El_Ectric, Jan 4, 2011, 9:14 PM

38 shouts
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ford
Ford Circle
Ford circles
Ford Kreis
Ford Kreise
form
Formatting
Formel
formula
Fraktur
Freundschaft
function invert
Gaetan Marris
Geodesy
Geogebra
geometric mean
Geometric Mean Theorem
geometric progression
Gergonne Point
german
Geschichte
gingerbread
Giovanni Salvemini
global
Gm
Goethe
Golden 60 Degree Trapezoid
Golden Arbelos
Golden Banner
Golden Circle
Golden Circles
Golden Ellipse
Golden Frustum
Golden Gnomon
Golden Traoezoid
Golden Window
Goldenes 60 Grad Trapez
good
Gothic
graph.asy
greetings
Grid of Lines
grpoint
Guide
Halb Silberne Ellipse
handy
Hans Georg Gadamer
Haus vom Nikolaus
Healing Art
heart
heartsuite
Hermeneutik
hexagon
HGG
history
Hm
hyperbola
ifeven
ifodd
illusion
Imagin re Eihheit
Imagin re Zahlen
imaginary numbers
Imaginary Unit
Immanuel Kant
Incircle Isosceles Trapezoid
Individualization
inequalities
Inkreis
inner tangents
inscribed square
Integral
intelligent
Intersection
intersectionpoint
intersections
intouch
invers
Inverse Value
ipen
Iteration
Jean Castillion
Jim Herfferon
jpen
jump.asy
Karl Kraus
Kegelschnitte
Kehrwert
keywords
kiss
KISS Principle
Klassische Kardioide
Knauth Figure
knife
KonTiki
Kosinus
Kritik
Kunst
Kunst des Verstehens
Labeling
labelscalefactor
LaTeX Array
latex package
LaTeX Symbol
Law of Cosines
LeftSide
Lemnicate of Bernoulli
Lemniscate of Bernoulli
lie
Liebe
linecaps
linejoins
LineMargin
LineMargins
listing
Local
Local Maximum
Locus
long division
Love Feelings
lowercase
lshort
Lucas
mandala
MAP
markangle
Marris
mathasttext
mathematik
matrix
max
Max Planck
mean
means
measure
Meine beste Freundin
Meinmond
Memory
metapost
mf2asy
Michelle Delapenha
min
Miquel
Miquel-Circle
Mnemotic Art
modification
Monotone Spline
morality
mpost
Multiple Arrows
multiplication
music
Mymoon
Natural Spline
Nested Loop
node
Notation of Constants
Notizen
Number of the beast
numbers
Object
oblique
obtuse
Olaf Scholz
Olympic Rings
operator..
optimization
Osculating Circle
outer tangents
package
Painting
pairs uvw
Pappus Chain
parallel
parallel marks
Parallel Tangents
parallelogram
parallels
parametric equation
Parametric Function
pascal triangle
paterns.asy
pathticks
Patterns
pedal curve of a circle
Pentagramm
percent sign
perpendicular
perpendicular bisector
perpfactor
Personalization
Peter Gallin
Ph. Ivaldi
Phi
Photosythesis
Phu Nguyen
pie
plot
plunge
pm
Poesie
point(path p real r)
points
Polar Circle
polar equation
polar graph
polarcircle
portrait
post pics
powers
Pre-Existance
Primfaktorzerlegung
Problem of Apollonius
ProfCollege
ps2asy
pstricks
pstricks-add
pstricks2asy
Pythagorean Fibonacci Tree
Pythagorean Triple
Pythagoreisches Tripel
Quadrat
quadratic function
quality
quartercircle
rad2deg
radius
rag
Rainbow
random
Real
really smart
reals uvw
Rearrangement
rectangle
recursion
Reduced Latitude
reduzierte Breite
Reflexionen
regular polygon
regular triangle
Reiteration
relative
relpoint of a segment
rename
Render
rfrac
Riemann Surface
right angle
right angle mark
RightSide
Rms
rose
rotate
rotation
roundcap
roundedpath
roundjoin
SAS Triangle
sayings
Scaling
Schwabacher
Second Fermat Point
second leg
Segment
Selfie Quote
Semi latus rectum
Semiincircle
Sentence of Thales
seperate picture
Sepulchral Stone
set
Sharp Golden Triangle
SharpArrow
shipout
showthe
Sides
Silver Trapezoid
similarity
sine
Sine Theorem
sinus
Skepticism
smakelijk
Smart
SmoothShading
Solit Complementary
space
Special Points
Spline
sport
Sportwissenschaft
Spracherwerb
Sprachphilosophie
spring
sqrt
squarecap
squareroot 2
squareroot 8
squareroot3
Squares on Triangle
StackExchange
stackrel
Star
StealthHead
Steiner Chain
string array
String Cocatenation
Substitution
subtended
Summer Time
Superellipse
svg
Symmetric Arbelos
synchron
Tailing Patterns
Tan
Tangens
tangent circles in circle
Tangente
tangents to parabola
tasty
tbinom
Technik
Tetradic
TeXBook
text
textgreek
tfrac
Thales Circle
the golden ratio
The letter N
The texbook
theater
theorem of Thales
ThreeFourFiveTriangle
tick
tick mark
Tiling
times(path p pair z)
times(path p real xa)
Torus
trailing zeros
trajectory
Tran Quan
Tran-Quan-Square
transparency
Trapezoid with Incircle
Triadic
triangle aerea
Triangle with Incircle
triangleabc
Trigonal
trigonomety
trilinear coordinates
Trisection of Angle
truesize
Trueth
TUG
Twin Circles
twincircle
twincircles
Two Circles
Typograohy
underset
unfill
unit
unitsquare
unitvector
Unterbewusstsein
upgreek
Uppercase
Uppercase Letters
upright greek
Urteilskraft
uvw
vector
Verbindung
Verkleinerungsform
Vesiva Piscis
Viviani
Void
war
Waynet
Weisheit
width
wise
Wissen
Wurzel 15
Wurzel 2
Wurzel 3
Wurzel 5
xaxis
xpen
yaxis
ypen
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