# Tag Archives: chord

## GEOSTRUCT, a program for investigative geometry

I have been developing this computer software / program / application for some years now, and it is now accessible as a web page, to run in your browser.

It provides basic geometric construction facilities, with lines, points and circles, from which endless possibilities follow.

Just try it out, it’s free.

Click on this or copy and paste for later : www.mathcomesalive.com/geostruct/geostructforbrowser1.html

.Here are some of the basic features, and examples of more advanced constructions, almost all based on straightedge and compass, from “make line pass through a point” to “intersection of two circles”, and dynamic constructions with rolling and rotating circles.

Two lines, with points placed on them

Three random lines with two points of intersection generated

Five free points, three generated circles and a center point

Three free points, connected as point pairs, medians generated

Two free circles and three free points, point pairs and centers generated

GIF showing points of intersection of a line with a circle

Construction for locus of hypocycloid

GIF showing a dilation (stretch) in the horizontal direction

Piston and flywheel

Construction for circle touching two circles

Construction for the locus of a parabola, focus-directrix definition.

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Filed under education, geometry, math, operations, teaching

## Calculus without limits 3

So you tried, or you didn’t, now here is the derivative of 1/sqr(x)

Filed under algebra, calculus, education, teaching

## Calculus without limits 2

As h approaches zero
I quietly despair.
It really is the limit.

The funny thing about the calculus is that it was brought into existence by Isaac Newton in 1666 or earlier, and was developed and used without the idea of limits for over 150 years. The first attempt to get rid of the troublesome infinitesimals was by Cauchy in 1821, where he introduced the chord slope (f(x + h) – f(x))/h. The whole business of finding a satisfactory definition of the derivative was finally achieved by Weierstrass in the mid 19th century.

So here we go with cubics, and the same approach can be used for any whole number power of x, even negative ones. You should try it.

Next time  sin(x) and cos(x), so no more  sin(h)/h stuff.

Filed under algebra, calculus, education, teaching, verse

## Calculus without tears (that is, without limits)

“As h approached zero I reached the limit of my understanding.”

So it seemed to me that calculus without limits would be a good idea.

Not just for powers of x, but also for trig, exp and log functions.

This is the first of several posts on this subject.