Ellipse - Revision history

DT Online: Added Template

2016-06-02T19:02:29Z

Added Template

← Older revision		Revision as of 19:02, 2 June 2016
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			__TOC__


			=====Description=====

	An [https://en.wikipedia.org/wiki/Ellipse '''Ellipse'''] is a '''[[Conic Sections\|Conic Section]]''' and has the appearance of a circle which has been squashed slightly. Unlike a circle, which has a single '''Diameter''', the ellipse has a '''Major Axis''' and a '''Minor Axis'''. The shape of an ellipse is sometimes mistakenly referred to as an '''''oval''''', but an oval is the shape of a rectangle with two semi-circular ends - like a running track for example.		An [https://en.wikipedia.org/wiki/Ellipse '''Ellipse'''] is a '''[[Conic Sections\|Conic Section]]''' and has the appearance of a circle which has been squashed slightly. Unlike a circle, which has a single '''Diameter''', the ellipse has a '''Major Axis''' and a '''Minor Axis'''. The shape of an ellipse is sometimes mistakenly referred to as an '''''oval''''', but an oval is the shape of a rectangle with two semi-circular ends - like a running track for example.

	The ellipse has two points of ''focus'', or '''''foci'''''. These can be found on the Major Axis by using half its length as a radius, and striking an arc centred on one end of the Minor Axis as shown.		The ellipse has two points of ''focus'', or '''''foci'''''. These can be found on the Major Axis by using half its length as a radius, and striking an arc centred on one end of the Minor Axis as shown.


			=====Constructions=====

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			{{Drawing Instruments Buyers Guide}}

DT Online: Added links

2015-04-05T12:28:40Z

Added links

← Older revision		Revision as of 12:28, 5 April 2015
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	<span style="color: green">'''Note:'''		<span style="color: green">'''Note:'''
	Ellipses may also be drawn by more precise methods and with '''Tangents''' and '''Normals''' drawn if needed - see '''[[Conics]]''' for more details.		Ellipses may also be drawn by more precise methods and with '''[[Tangents and Normals\|Tangents]]''' and '''[[Tangents and Normals\|Normals]]''' drawn if needed - see '''[[Conics]]''' for more details.
	</span>		</span>
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DT Online: Corrected link

2015-04-05T10:25:09Z

Corrected link

← Older revision		Revision as of 10:25, 5 April 2015
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	<span style="color: green">'''Note:'''		<span style="color: green">'''Note:'''
	Ellipses may also be drawn by more precise methods and with '''Tangents''' and '''Normals''' drawn if needed - see '''[[~~Conic Sections~~]]''' for more details.		Ellipses may also be drawn by more precise methods and with '''Tangents''' and '''Normals''' drawn if needed - see '''[[Conics]]''' for more details.
	</span>		</span>
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DT Online: Changed Images

2015-02-21T17:20:40Z

Changed Images

← Older revision		Revision as of 17:20, 21 February 2015
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	* Points on the ellipse can be found where each pair of projection lines meet as shown.		* Points on the ellipse can be found where each pair of projection lines meet as shown.
	* Sketch a fair curve through the points ''(or use [https://en.wikipedia.org/wiki/French_curve '''French Curves'''] or a [https://en.wikipedia.org/wiki/Flat_spline '''flexible strip'''] for example)''		* Sketch a fair curve through the points ''(or use [https://en.wikipedia.org/wiki/French_curve '''French Curves'''] or a [https://en.wikipedia.org/wiki/Flat_spline '''flexible strip'''] for example)''
	\| [[File:~~Ellipse1~~.~~jpg~~\|350px\|right]]		\| [[File:CirclesEllipse.png\|350px\|right]]
	\|-		\|-
	\| '''Drawing an Ellipse using a loop of string'''		\| '''Drawing an Ellipse using a loop of string'''
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	* Place the drawing on a board and insert pins at each Foci then make a loop of string to go around them and reach the end of the Minor Axis when pulled tight.		* Place the drawing on a board and insert pins at each Foci then make a loop of string to go around them and reach the end of the Minor Axis when pulled tight.
	* Hold a pencil inside the loop and keep the string tight as the pencil is pulled around to draw the complete ellipse as shown.</span>		* Hold a pencil inside the loop and keep the string tight as the pencil is pulled around to draw the complete ellipse as shown.</span>
	\| [[File:~~Ellipse2~~.~~jpg~~\|350px\|right]]		\| [[File:StringEllipse.png\|350px\|right]]
	\|}		\|}
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DT Online at 12:40, 19 February 2015

2015-02-19T12:40:34Z

← Older revision		Revision as of 12:40, 19 February 2015
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	An [https://en.wikipedia.org/wiki/Ellipse '''Ellipse'''] is a '''[[Conic Sections\|Conic Section]]''' and has the appearance of a circle which has been squashed slightly. Unlike a circle, which has a single '''Diameter''', the ellipse has a '''Major Axis''' and a '''Minor Axis'''. The shape of an ellipse is sometimes mistakenly referred to as an '''''oval''''', but an oval is the shape of a rectangle with two semi-circular ends - like a running track for example.		An [https://en.wikipedia.org/wiki/Ellipse '''Ellipse'''] is a '''[[Conic Sections\|Conic Section]]''' and has the appearance of a circle which has been squashed slightly. Unlike a circle, which has a single '''Diameter''', the ellipse has a '''Major Axis''' and a '''Minor Axis'''. The shape of an ellipse is sometimes mistakenly referred to as an '''''oval''''', but an oval is the shape of a rectangle with two semi-circular ends - like a running track for example.

	The ellipse has two points of ''focus'', or '''''~~focii~~'''''. These can be found on the Major Axis by using half its length as a radius, and striking an arc centred on one end of the Minor Axis as shown.		The ellipse has two points of ''focus'', or '''''foci'''''. These can be found on the Major Axis by using half its length as a radius, and striking an arc centred on one end of the Minor Axis as shown.

	{\| cellpadding="5"		{\| cellpadding="5"
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	\| '''Drawing an Ellipse using a loop of string'''		\| '''Drawing an Ellipse using a loop of string'''
	\| <span style="color:#B00000">		\| <span style="color:#B00000">
	* A property of the ellipse is that the sum of the distances from any point on the curve to each of its two ~~Focii~~ is constant.		* A property of the ellipse is that the sum of the distances from any point on the curve to each of its two Foci is constant.
	* Start by setting compasses, or similar, to half the Major Axis and strike arcs on it from one end of the Minor Axis as shown.		* Start by setting compasses, or similar, to half the Major Axis and strike arcs on it from one end of the Minor Axis as shown.
	* The intersections found by the two arcs are the Focii of the ellipse.		* The intersections found by the two arcs are the Focii of the ellipse.
	* Place the drawing on a board and insert pins at each ~~Focii~~ then make a loop of string to go around them and reach the end of the Minor Axis when pulled tight.		* Place the drawing on a board and insert pins at each Foci then make a loop of string to go around them and reach the end of the Minor Axis when pulled tight.
	* Hold a pencil inside the loop and keep the string tight as the pencil is pulled around to draw the complete ellipse as shown.</span>		* Hold a pencil inside the loop and keep the string tight as the pencil is pulled around to draw the complete ellipse as shown.</span>
	\| [[File:Ellipse2.jpg\|350px\|right]]		\| [[File:Ellipse2.jpg\|350px\|right]]

DT Online at 18:55, 18 February 2015

2015-02-18T18:55:11Z

← Older revision		Revision as of 18:55, 18 February 2015
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	----		----
	<span style="color: green">'''Note:'''		<span style="color: green">'''Note:'''
	Ellipses may also be drawn by more precise methods with '''Tangents''' and '''Normals''' drawn if needed - see '''[[Conic Sections]]''' for more details.		Ellipses may also be drawn by more precise methods and with '''Tangents''' and '''Normals''' drawn if needed - see '''[[Conic Sections]]''' for more details.
	</span>		</span>
	----		----

DT Online at 18:54, 18 February 2015

2015-02-18T18:54:07Z

← Older revision		Revision as of 18:54, 18 February 2015
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	\| <span style="color:#B00000">		\| <span style="color:#B00000">
	* Draw two circles from the same centre: one with its diameter equal to the Major Axis, and one equal to the Minor Axis.		* Draw two circles from the same centre: one with its diameter equal to the Major Axis, and one equal to the Minor Axis.
	* Divide the circles into a number of segments - say, 12 as shown.		* Divide the circles into a number of segments ''(say, 12 as shown)''.
	* Project vertically from where the radial lines intersect the outer circle and .horizontally from where they meet the inner circle ''(or vice versa)''		* Project vertically from where the radial lines intersect the outer circle and .horizontally from where they meet the inner circle ''(or vice versa)''
	* Points on the ellipse can be found where each pair of projection lines meet as shown.		* Points on the ellipse can be found where each pair of projection lines meet as shown.

DT Online: Created Ellipse

2015-02-18T18:52:11Z

Created Ellipse

New page

An [https://en.wikipedia.org/wiki/Ellipse '''Ellipse'''] is a '''[[Conic Sections|Conic Section]]''' and has the appearance of a circle which has been squashed slightly. Unlike a circle, which has a single '''Diameter''', the ellipse has a '''Major Axis''' and a '''Minor Axis'''. The shape of an ellipse is sometimes mistakenly referred to as an '''''oval''''', but an oval is the shape of a rectangle with two semi-circular ends - like a running track for example.

The ellipse has two points of ''focus'', or '''''focii'''''. These can be found on the Major Axis by using half its length as a radius, and striking an arc centred on one end of the Minor Axis as shown.

{| cellpadding="5"
|-
| '''Drawing an Ellipse using Concentric Circles'''
| 
* Draw two circles from the same centre: one with its diameter equal to the Major Axis, and one equal to the Minor Axis.
* Divide the circles into a number of segments - say, 12 as shown.
* Project vertically from where the radial lines intersect the outer circle and .horizontally from where they meet the inner circle ''(or vice versa)''
* Points on the ellipse can be found where each pair of projection lines meet as shown.
* Sketch a fair curve through the points ''(or use [https://en.wikipedia.org/wiki/French_curve '''French Curves'''] or a [https://en.wikipedia.org/wiki/Flat_spline '''flexible strip'''] for example)''
| [[File:Ellipse1.jpg|350px|right]]
|-
| '''Drawing an Ellipse using a loop of string'''
| 
* A property of the ellipse is that the sum of the distances from any point on the curve to each of its two Focii is constant.
* Start by setting compasses, or similar, to half the Major Axis and strike arcs on it from one end of the Minor Axis as shown.
* The intersections found by the two arcs are the Focii of the ellipse.
* Place the drawing on a board and insert pins at each Focii then make a loop of string to go around them and reach the end of the Minor Axis when pulled tight.
* Hold a pencil inside the loop and keep the string tight as the pencil is pulled around to draw the complete ellipse as shown.
| [[File:Ellipse2.jpg|350px|right]]
|}
----
'''Note:'''
Ellipses may also be drawn by more precise methods with '''Tangents''' and '''Normals''' drawn if needed - see '''[[Conic Sections]]''' for more details.

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[[Category:Primary]]
[[Category:Secondary]]
[[Category:Geometry]]