### 36 Stacked Congruent Cubes

Illustration of 36 congruent cubes stacked at various heights with outer edges forming a square. A 3-dimensional…

### 36 Stacked Congruent Cubes

Illustration of 36 congruent cubes stacked to resemble a 1 by 1 by 1 cube on a 2 by 2 by 2 cube on a…

### 39 Stacked Congruent Cubes

Illustration of 39 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

### 4 Stacked Congruent Cubes

Illustration of 4 congruent cubes stacked in ones and twos. A 3-dimensional representation on a 2-dimensional…

### 50 Stacked Congruent Cubes

Illustration of 50 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

### 56 Stacked Congruent Cubes

Illustration of 56 congruent cubes stacked in twos in the shape of a square. A 3-dimensional representation…

### 56 Stacked Congruent Cubes

Illustration of 56 congruent cubes stacked in heights of 1, 4, and 5 cubes that form a zigzag pattern.…

### 57 Stacked Congruent Cubes

Illustration of 57 congruent cubes stacked in heights of 1 and 5 cubes that form a zigzag pattern. A…

### 59 Stacked Congruent Cubes

Illustration of 59 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

### 64 Stacked Congruent Cubes

Illustration of 64 congruent cubes stacked so they form a cube that measures 4 by 4 by 4. A 3-dimensional…

### 65 Stacked Congruent Cubes

Illustration of 65 congruent cubes stacked at heights increasing from 1 to 5 cubes. A 3-dimensional…

### Second Order Curve Tangents

Any four-point on a curve of the second order and the four-side formed by the tangents at these points…

### Tangent Curve

Illustration showing a tangent curve.

### 2 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 2 smaller congruent cylinders. The small cylinders are externally tangent…

### 3 Congruent Tangent Right Circular Cylinders

Illustration of 3 right congruent tangent circular cylinders. The height of all the cylinders is greater…

### 3 Congruent Tangent Right Circular Cylinders

Illustration of 3 right congruent tangent circular cylinders.

### 3 Congruent Tangent Right Circular Cylinders

Illustration of 3 right congruent tangent circular cylinders. The height of all the cylinders is greater…

### 3 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 3 smaller congruent cylinders. The small cylinders are externally tangent…

### 4 Congruent Tangent Right Circular Cylinders

Illustration of 4 congruent tangent right circular cylinders. The height of all the cylinders is greater…

### 4 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 4 smaller congruent cylinders. The small cylinders are externally tangent…

### 4 Tangent Cylinders

Illustration of 4 congruent cylinders with diameters less than the height. The cylinders are externally…

### 7 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 7 smaller congruent cylinders. The small cylinders are externally tangent…

### 7 Tangent Cylinders

Illustration of 7 congruent cylinders with diameters less than the height. 6 of the cylinders are equally…

### 7 Tangent Cylinders

Illustration of 7 congruent cylinders with diameters less than the height. 6 of the cylinders are equally…

### Construction Of A Cyma

An illustration showing how to construct a cyma, or two circle arcs that will tangent themselves, and…

### 12-Point Star Inscribed In A Dodecagon

Illustration of a 12-point star (24-sided polygon) inscribed in a regular dodecagon. This can also be…

### Ellipse Inscribed In A Circle

Illustration of an ellipse, whose major axis is vertical, inscribed in a circle whose diameter is equal…

### 2 Ellipses Inscribed In A Circle

Illustration of 2 concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

### 2 Ellipses With Equal Vertical Axes

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The…

### 2 Ellipses With Equal Vertical Axes

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The…

### 3 Concentric Ellipses

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The…

### 3 Concentric Ellipses

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes, which…

### 3 Concentric Ellipses

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The…

### 4 Concentric Ellipses

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The…

### 4 Concentric Ellipses

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The…

### 4 Concentric Ellipses

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes, which…

### 5 Concentric Ellipses

An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes. The…

### 5 Concentric Ellipses

An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes, which…

### 6 Concentric Ellipses

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes. The…

### 6 Concentric Ellipses

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes, which…

### Ellipses Inscribed In A Circle

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

### Ellipses Inscribed In A Circle

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

### Construction Of An Equilateral Triangle Inscribed In A Circle

An illustration showing how to construct an equilateral triangle inscribed in a circle. "With the radius…

### Centrifugal Force

"If a body be fastened to a string and whirled, so as to give it a circular motion, there will be a…

### Tangent galvanometer

"The galvanometer is an instrument for determining the strength of an electric current by means of the…

### Model Of Geometric Relationships In 2 Circles

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates…

### Model Of Geometric Relationships In 2 Circles

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates…

### Model Of Geometric Relationships In A Circle

An illustration showing a model of a circle with an exterior angle formed between a tangent and a secant…

### Model Of Geometric Relationships In A Circle

An illustration showing a model of a circle with angles formed between tangents and secants that illustrates…

### Construction Of A Hexagon In A Circle

An illustration showing how to construct a hexagon in a given circle. "The radius of the circle is equal…

### Cyclic Hexagon

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle…

### Cyclic Hexagon

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle…

### Auxiliary Circle and Hyperbola

Illustration of a hyperbola and its auxiliary circle. "Any ordinate of a hyperbola is to the tangent…

### Hyperbola Tangent Triangles

All triangles formed by a tangent and the asymptotes of an hyperbola are equal in area.

### Angle Expressed As An Inverse Function

Illustration that can be used to show that when given an angle, expressed as an inverse function of…

### Conic Foci Involution

The lines joining any point on a conic to the two foci are equally inclined to the tangent and normal…

### Lemniscate

A Lemniscate is, in general, a curve generated by a point moving so that the product of its distances…

### Parabola Foci Properties

The segments between the point of intersection of two tangents to a conic and their points of contact…

### Tangent to a Parabola

Illustration of a tangent line drawn from an external point to a parabola.

### Tangents and Chords of a Parabola

Illustration showing that the area of a parabolic segment made by a chord is two thirds the area of…