Some are straighteners, others add shine and remove most of the frizz, etc. Having struggled with my thick, wavy hair all my life, i was certainly intrigued.
Updates will be posted as they become available. This material will be included in a forthcoming summer book with the tentative title Experiencing Geometry in Two- and Three-Dimensional Spaces.
This new book will be an expanded and updated version of Experiencing Geometry on Plane and Sphere. This material is in draft form and may not be duplicated or quoted without the author's written permission, except for purposes of review or trying out the material with students.
As always comments are welcome and will affect the final draft. Send comments to dwh2 cornell. Chapter 2 Straightness on Sphere, Cylinder, and Cone It is important for you to see that, if you are not building a notion of straightness for yourself for example, if you are taking ideas from books without thinking deeply about themthen you will have difficulty building a concept of straightness on other surfaces.
Only by developing a personal meaning of straightness for oneself does it become part of one's active intuition. We say active intuition to emphasize that intuition is in a process of constant change and enrichment, that it is not static. What Is Straight on a Sphere? Imagine yourself to be a bug crawling around on a sphere.
This bug can neither fly nor burrow into the sphere. The bug's universe is just the surface; it never leaves it. What is "straight" for this bug? What will the bug see or experience as straight? How can you convince yourself of this?
Use the properties of straightness such as symmetries which you talked about in Problem 1. Suggestions Great circles are those circles which are the intersection of the sphere with a plane through the center of the sphere. See examples illustrated in Figure 2. The first step to understanding this problem is to convince yourself that great circles are straight lines on a sphere.
Think what it is about the great circles that would make the bug experience them as straight. To better visualize what is happening on a sphere or any other surface, for that matteryou must use models. This is a point we cannot stress enough.
The use of models will become increasingly important in later problems, especially those involving more than one line. You must make lines on a sphere to fully understand what is straight and why. An orange or an old, worn tennis ball work well as spheres, and rubber bands make good lines.
Also, you can use ribbon or strips of paper. Try placing these items on the sphere along different curves to see what happens. Also look at the symmetries from Problem 1. The important thing to remember here is to think in terms of the surface of the sphere, not in 3-space.pfmlures.com offers 67 pipe straightness tolerances products.
About 44% of these are cleaning brushes, 28% are steel pipes, and 5% are stainless steel pipes.
A wide variety of pipe straightness tolerances options are available to you, such as 16mn, q, and 10#. Cal. Cal. Chamber Reamers at Pacific Tool and Gauge. scale (HRC) for testing steel uses a spheroconical diamond indenter having a ° cone angle and a µm radius spherical tip.
In the uncertainty budget of HRC tests, cone flank straightness fitting at ± ( to ) µm of the left and right.
trace, located from – µm to – µm on the left and the cone flank straightness. Donald Lynch Boulevard, Marlborough, MA , USA Tel: demonstrates maximum straightness and does not adopt a Delivering Innovative Medical Technologies HANDLES, HUBS & DEPLOYMENT SYSTEMS Luers, hubs & handles – molding & insert molding.
the straightness of the cone flank is measured “adjacent to the blend”  which leaves some flexibility in the choice of the size and position of the windows on the flanks.
pfmlures.com offers 65 pipe straightness tolerances products. About 46% of these are cleaning brushes, 27% are steel pipes, and 6% are stainless steel pipes. A wide variety of pipe straightness tolerances options are available to you, such as 16mn, q, and 10#.