Complete SAT Math Practice Tests (work in progress)
Click the timestamp below to see that question directly in the video
Deriving the Quadratic Formula
Using the "completing the square" method to derive the famous formula.
Thermometer Word Problem
Can a Fahrenheit and a Celsius thermometer are in the same room, what temperature must the room be for the thermometers to read the same value?
- Solving equations
- Graphing equations
- Interpreting graphs
- System of equations
Balancing forces on a pulley
Crate on a freely rolling ramp
Deriving the equations of motion
Conservation of Energy on a roller coaster
Conservation of Energy to determine minimum required velocity
Acceleration of a car on an inclined plane
Compass and Straight Edge Constructions
How to find the center of a circle
If you have a circle, and you don't know where the center is, you can use simply a compass and a straight edge to find the center. Handy for accurately measuring the diameter of circular objects
Another way to find the center of a circle
Regular Pentagon with Compass and Straight edge
This is one of several ways to construct a true regular pentagon using pencil and paper. All that is required is a straight edge and a compass. You don't even need a ruler or protractor.
I'm using Geogebra in this video, so it ends up being exactly perfect. One might say "hey that's cheating!" I understand the urge to think so, however the construction technique in the video is proper. The pentagon I end up with is not automatically generated, it's properly constructed.
The accuracy and quality of a pentagon drawn with an actual compass and straight edge will VASTLY depend on how careful you are. Also, the larger you make the overall shape, the better the final pentagon will be.
How to Draw Inscribed and Circumscribed Circles
Tutorial on how to construct inscribed and circumscribed circles manually using pencil, paper, a straight edge, and a compass.
Also handy for bisecting an angle, and finding perpendicular bisectors.
Visual Proof of Viviani's Theorem
From Wikipedia: Viviani's theorem, named after Vincenzo Viviani, states that the sum of the distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude.
I made this video using the iOS version of Geogebra. It's also available for Android. 100% free! This was an experimental video and there is no audio. I simply played around with the app while recording what I was doing on my screen.
The construction shows that when the equilateral triangle is broken up into 3 smaller triangles, those small triangles can be stacked and their overall height will be the same as the original equilateral triangle.
The Nepalese flag design is prescribed by a specific set of geometric construction steps, written into the country's constitution. It is possible to draw it with only a compass and straight edge. But Geogebra is fun to use too!
Try drawing it yourself! Click the arrow to the right for complete instructions. Try it yourself!
Instructions for drawing the flag of Nepal
(A) Method of Making the shape inside the Border
(1) On the lower portion of a crimson cloth draw a line AB of the required length from left to right.
(2) From A draw a line AC perpendicular to AB making AC equal to AB plus one third AB. From AC mark off D making the line AD equal to line AB. Join BD.
(3) From BD mark off E making BE equal to AB.
(4) Touching E draw a line FG, starting from the point F on line AC, parallel to AB to the right hand-side. Mark off FG equal to AB.
(5) Join CG.
(B) Method of making the Moon
(6) From AB mark off AH making AH equal to one-fourth of line AB and starting from H draw a line HI parallel to line AC touching line CG at point I.
(7) Bisect CF at J and draw a line JK parallel to AB touching CG at point K.
(8) Let L be the point where lines JK and HI cut one another.
(9) Join JG.
(10) Let M be the point where line JG and HI cut one another.
(11) With center M and with a distance shortest from M to BD mark off N on the lower portion of line HI.
(12) Touching M and starting from O, a point on AC, draw a line from left to right parallel to AB.
(13) With center L and radius LN draw a semi-circle on the lower portion and let P and Q be the points where it touches the line OM respectively.
(14) With the center M and radius MQ draw a semi-circle on the lower portion touching P and Q.
(15) With center N and radius NM draw an arc touching PNQ at R and S. Join RS. Let T be the point where RS and HI cut one another.
(16) With center T and radius TS draw a semi-circle on the upper portion of PNQ touching at two points.
(17) With center T and radius TM draw an arc on the upper portion of PNQ touching at two points.
(18) Eight equal and similar triangles of the moon are to be made in the space lying inside the semi-circle of No (16) and outside the arc of No (17) of his Schedule.
(C) Method of Making the Sun
(19) Bisect line AF at U, and draw a line UV parallel to AB line touching line BE at V.
(20) With center W, the point where HI and UN cut one another and radius MN draw a circle.
(21) With center W and radius LN draw a circle.
(22) Twelve equal and similar triangles of the sun are to be made in the space enclosed by the circle of No (20) and No (21) with the two apexes of two triangles touching line HI.
(D) Method of Making the Border
(23) The width of the border will be equal to the width of TN. This will be of deep blue color and will be provided on all the sides of the flag. However, on the given angles of the flag the external angles will be equal to the internal angles.
(24) The above mentioned border will be provided if the flag is to be used with a rope. On the other hand, if it is to be hoisted on a pole, the hole on the border on the side AC can be extended according to requirements.
Explanation:- The lines HI, RS, FE, ED, JG, OQ, JK and UV are imaginary. Similarly, the external and internal circles of the sun and the other arcs except the crescent moon are imaginary. These are not shown on the flag.